From 48a5c8dbe49bb64ba54615acc6157a1c68ad7a2e Mon Sep 17 00:00:00 2001
From: Aleks Kissinger <aleks0@gmail.com>
Date: Wed, 18 Dec 2024 11:21:58 +0000
Subject: [PATCH] pauli webs and cnot tests

---
 demos/PauliWebs.ipynb | 9047 ++++++++++++++++++++++++++++++++++++++++-
 pyzx/pauliweb.py      |   86 +-
 2 files changed, 8952 insertions(+), 181 deletions(-)

diff --git a/demos/PauliWebs.ipynb b/demos/PauliWebs.ipynb
index 84236966..75c05e97 100644
--- a/demos/PauliWebs.ipynb
+++ b/demos/PauliWebs.ipynb
@@ -10,77 +10,8880 @@
     "sys.path.insert(0,os.path.expanduser('~/git/pyzx')) # git version\n",
     "sys.path.insert(0,'/workspaces/pyzx')\n",
     "import pyzx as zx\n",
-    "from pyzx.pauliweb import preprocess, compute_pauli_webs"
+    "from pyzx.pauliweb import PauliWeb, compute_pauli_webs"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This notebook demonstrates using PyZX's simplifier to construct the reduced ZX diagram of a random Clifford+T circuit, then using PyZX's gflow-finding algorithm to automatically associate each node `n` in the diagram to an integer `order[n]` and a Pauli web (a.k.a. _correlation surface_) `web[n]` with the following properties:\n",
+    "This notebook demonstrates using PyZX's methods for automatically computing and drawing (bounded) Pauli webs. A Pauli web (a.k.a. _correlation surface_) is a coloring of the edges of ZX-diagram with the following properties for every Z spider `v`:\n",
     "\n",
-    "1. the boundary of `web[n]` consists of `n` and inputs\n",
-    "2. `web[n]` connects to `n` by a single edge, which is the same colour as `n`\n",
-    "3. for non-Clifford nodes `m, n`, if `m` is in `web[n].vertices()` then `order[m] < order[n]`\n",
+    "- _all-or-nothing_: either no incident edges or all incident edges of `v` are labelled X or Y\n",
+    "- _parity_: an even number of incident edges of `v` are labelled Y or Z\n",
     "\n",
-    "The values of `web[n]` at non-Clifford nodes and at outputs should be enough data to deterministically implement the diagram via lattice surgery and either measure at the end or compute the updated Pauli frame."
+    "All X spiders satisfy analogous conditions, swapping the role of X and Z. A _bounded Pauli web_ is a Pauli web with a chosen set of spiders, called the _boundary_ where the parity condition is allowed to be violated.\n",
+    "\n",
+    "We say a spider `anti-commutes` with a Pauli web if it is touching an edge of a different colour.\n",
+    "\n",
+    "The function `compute_pauli_webs` automitically associates each non-input vertex `v` in the diagram to an integer `order[v]` giving a time-ordering, and one or two bounded Pauli webs, with the following properties:\n",
+    "1. the boundary of the web consists of only `v` itself and inputs\n",
+    "2. Z spiders have a web `zweb[v]` with a Z-colored edge incident to `v`\n",
+    "3. X spiders have a web `xweb[v]` with a X-colored edge incident to `v`\n",
+    "4. output vertices have two webs `zweb[v]` and `xweb[v]` corresponding to both colors at `v`\n",
+    "5. for non-Pauli spiders `v, w`, if `v` anti-commutes with the Pauli web of `w` then `order[v] < order[w]`\n",
+    "\n",
+    "Under the hood, this is using PyZX's gflow-finding algorithm to compute a focussed gflow and translate this data into Pauli webs."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-MkhojJ4d\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-MkhojJ4d',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Here's a simple example of a single CNOT gate\n",
+    "\n",
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[2];\n",
+    "cx q[0], q[1];\n",
+    "\"\"\")\n",
+    "g = c.to_graph()\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "zx.draw(g, labels=True)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Qlp6stwV\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Qlp6stwV',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 3, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-qWMB22nJ\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-qWMB22nJ',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-omk09KlE\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-omk09KlE',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wW2HjYCA\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-wW2HjYCA',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 2, \"t\": \"Z\"}, {\"source\": 3, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# There are 4 interesting Pauli webs corresponding to the two outputs\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[4])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[5])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[4])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[5])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-r6IidzxG\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-r6IidzxG',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 3, \"t\": \"Z\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-RsQtsuBn\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-RsQtsuBn',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 2, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 2, \"t\": \"X\"}]}'), 200, 200, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# The CNOT example also has 2 more bounded Pauli webs, with boundaries on the two interior spiders.\n",
+    "# Since we aren't injecting magic states at these locations, we don't need these Pauli webs.\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[3])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[2])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-sDHG9pqb\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-sDHG9pqb',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 300, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Here's an example with three CNOT gates\n",
+    "\n",
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[3];\n",
+    "cx q[0], q[1];\n",
+    "cx q[1], q[2];\n",
+    "cx q[2], q[0];\n",
+    "\"\"\")\n",
+    "g = c.to_graph()\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-WP22uqEC\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-WP22uqEC',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 4, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 4, \"t\": \"X\"}, {\"source\": 9, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 9, \"t\": \"X\"}]}'), 300, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-7oJvrLPn\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-7oJvrLPn',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 6, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 6, \"t\": \"X\"}]}'), 300, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-KuLidNJt\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-KuLidNJt',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 8, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 8, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 8, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 8, \"t\": \"X\"}, {\"source\": 8, \"target\": 11, \"t\": \"X\"}, {\"source\": 11, \"target\": 8, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 4, \"target\": 7, \"t\": \"X\"}, {\"source\": 7, \"target\": 4, \"t\": \"X\"}]}'), 300, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-dEbN96bU\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-dEbN96bU',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"I\"}, {\"source\": 0, \"target\": 4, \"t\": \"I\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}, {\"source\": 7, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 7, \"t\": \"Z\"}, {\"source\": 7, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 7, \"t\": \"Z\"}]}'), 300, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-oUQDUZXv\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-oUQDUZXv',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 10, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 10, \"t\": \"Z\"}]}'), 300, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-cCRJ28GH\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-cCRJ28GH',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 11, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 11, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 8, \"t\": \"Z\"}, {\"source\": 8, \"target\": 5, \"t\": \"Z\"}]}'), 300, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "zx.draw(g, labels=True, pauli_web=xwebs[9])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[10])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[11])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[9])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[10])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[11])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-zbkpu55T\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-zbkpu55T',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
+       "  10.0, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-VIxPEAam\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-VIxPEAam',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 450, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Here's an example with more CNOT gates\n",
+    "\n",
+    "c = zx.qasm(\"\"\"\n",
+    "qreg q[3];\n",
+    "cx q[0], q[1];\n",
+    "cx q[1], q[2];\n",
+    "cx q[0], q[2];\n",
+    "cx q[2], q[1];\n",
+    "cx q[0], q[1];\n",
+    "cx q[2], q[0];\n",
+    "\"\"\")\n",
+    "g = c.to_graph()\n",
+    "\n",
+    "zx.draw(g)\n",
+    "\n",
+    "# Adjacent spiders of the same color need to be fused for the Pauli web computation to work.\n",
+    "# We can accomplish this with spider_simp:\n",
+    "zx.spider_simp(g, quiet=True)\n",
+    "\n",
+    "# This is not a fundamental problem, it just requires more case distinctions for compute_pauli_webs\n",
+    "# to handle unfused spiders.\n",
+    "\n",
+    "order, zwebs, xwebs = compute_pauli_webs(g)\n",
+    "\n",
+    "zx.draw(g, labels=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-snIpKXz5\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-snIpKXz5',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 15, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 15, \"t\": \"X\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"I\"}, {\"source\": 1, \"target\": 3, \"t\": \"I\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"I\"}, {\"source\": 2, \"target\": 5, \"t\": \"I\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}]}'), 450, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-i3lQpKxn\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-i3lQpKxn',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 16, \"t\": \"X\"}, {\"source\": 6, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 6, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 6, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 6, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"X\"}, {\"source\": 6, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 6, \"t\": \"X\"}]}'), 450, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-rd7rs7d5\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-rd7rs7d5',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 10, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 17, \"t\": \"X\"}, {\"source\": 17, \"target\": 10, \"t\": \"X\"}, {\"source\": 10, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 10, \"t\": \"X\"}, {\"source\": 5, \"target\": 2, \"t\": \"I\"}, {\"source\": 2, \"target\": 5, \"t\": \"I\"}, {\"source\": 4, \"target\": 0, \"t\": \"X\"}, {\"source\": 0, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 4, \"t\": \"X\"}, {\"source\": 3, \"target\": 1, \"t\": \"X\"}, {\"source\": 1, \"target\": 3, \"t\": \"X\"}, {\"source\": 4, \"target\": 13, \"t\": \"X\"}, {\"source\": 13, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 9, \"t\": \"X\"}, {\"source\": 9, \"target\": 4, \"t\": \"X\"}]}'), 450, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-1V9ngvb6\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-1V9ngvb6',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 13, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 13, \"t\": \"Z\"}, {\"source\": 13, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 13, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-XWa50rKo\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-XWa50rKo',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 9, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 9, \"t\": \"Z\"}, {\"source\": 9, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 9, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"I\"}, {\"source\": 0, \"target\": 4, \"t\": \"I\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-wHaPWXJ7\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-wHaPWXJ7',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 250, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 100, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 400, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 400, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"I\"}, {\"source\": 0, \"target\": 4, \"t\": \"I\"}, {\"source\": 3, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 3, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 6, \"t\": \"Z\"}, {\"source\": 6, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 5, \"t\": \"Z\"}, {\"source\": 17, \"target\": 10, \"t\": \"Z\"}, {\"source\": 10, \"target\": 17, \"t\": \"Z\"}]}'), 450, 250, 50,\n",
+       "  10.0, false, true, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "zx.draw(g, labels=True, pauli_web=xwebs[15])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[16])\n",
+    "zx.draw(g, labels=True, pauli_web=xwebs[17])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[15])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[16])\n",
+    "zx.draw(g, labels=True, pauli_web=zwebs[17])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Foib6n1h\"></div>\n",
+       "<script type=\"module\">\n",
+       "var d3;\n",
+       "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
+       "// PyZX - Python library for quantum circuit rewriting \n",
+       "//        and optimisation using the ZX-calculus\n",
+       "// Copyright (C) 2018 - Aleks Kissinger and John van de Wetering\n",
+       "\n",
+       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
+       "// you may not use this file except in compliance with the License.\n",
+       "// You may obtain a copy of the License at\n",
+       "\n",
+       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
+       "\n",
+       "// Unless required by applicable law or agreed to in writing, software\n",
+       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
+       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
+       "// See the License for the specific language governing permissions and\n",
+       "// limitations under the License.\n",
+       "\n",
+       "// styling functions\n",
+       "function nodeColor(t) {\n",
+       "    if (t == 0) return \"black\";\n",
+       "    else if (t == 1) return \"#ccffcc\";\n",
+       "    else if (t == 2) return \"#ff8888\";\n",
+       "    else if (t == 3) return \"yellow\";\n",
+       "    else if (t == 4) return \"black\";\n",
+       "    else if (t == 5) return \"black\";\n",
+       "    else if (t == 6) return \"#ccffcc\";\n",
+       "}\n",
+       "\n",
+       "function edgeColor(t) {\n",
+       "    if (t == 1) return \"black\";\n",
+       "    else if (t == 2) return \"#08f\";\n",
+       "    else if (t == 3) return \"gray\";\n",
+       "}\n",
+       "\n",
+       "function webColor(t) {\n",
+       "    if (t == 'X') return \"#ff8888\";\n",
+       "    else if (t == 'Y') return \"#88ff88\";\n",
+       "    else if (t == 'Z') return \"#44aa44\";\n",
+       "    else if (t == 'I') return \"#eee\";\n",
+       "}\n",
+       "\n",
+       "function nodeStyle(selected) {\n",
+       "    return selected ? \"stroke-width: 2px; stroke: #00f\" : \"stroke-width: 1.5px\";\n",
+       "}\n",
+       "\n",
+       "var symbolGround = {\n",
+       "    draw: function(context, size){\n",
+       "        let s = size/2;\n",
+       "\n",
+       "        context.moveTo(0,-s);\n",
+       "        context.lineTo(0,0);\n",
+       "\n",
+       "        context.moveTo(-s,0);\n",
+       "        context.lineTo(s,0);\n",
+       "\n",
+       "        context.moveTo(-2*s/3,s/3);\n",
+       "        context.lineTo(2*s/3,s/3);\n",
+       "\n",
+       "        context.moveTo(-s/3,2*s/3);\n",
+       "        context.lineTo(s/3,2*s/3);\n",
+       "    }\n",
+       "}\n",
+       "\n",
+       "function showGraph(tag, graph, width, height, scale, node_size, auto_hbox, show_labels, scalar_str) {\n",
+       "    var ntab = {};\n",
+       "\n",
+       "    var groundOffset = 2.5 * node_size;\n",
+       "\n",
+       "    graph.nodes.forEach(function(d) {\n",
+       "        ntab[d.name] = d;\n",
+       "        d.selected = false;\n",
+       "        d.previouslySelected = false;\n",
+       "        d.nhd = [];\n",
+       "    });\n",
+       "\n",
+       "    var spiders_and_boundaries = graph.nodes.filter(function(d) {\n",
+       "        return d.t != 3;\n",
+       "    });\n",
+       "\n",
+       "    graph.links.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "        s.nhd.push(t);\n",
+       "        t.nhd.push(s);\n",
+       "    });\n",
+       "\n",
+       "    graph.pauli_web.forEach(function(d) {\n",
+       "        var s = ntab[d.source];\n",
+       "        var t = ntab[d.target];\n",
+       "        d.source = s;\n",
+       "        d.target = t;\n",
+       "    });\n",
+       "\n",
+       "    var shiftKey;\n",
+       "\n",
+       "    // SETUP SVG ITEMS\n",
+       "\n",
+       "    var svg = d3.select(tag)\n",
+       "    //.attr(\"tabindex\", 1)\n",
+       "        .on(\"keydown.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "        .on(\"keyup.brush\", function() {shiftKey = d3.event.shiftKey || d3.event.metaKey;})\n",
+       "    //.each(function() { this.focus(); })\n",
+       "        .append(\"svg\")\n",
+       "        .attr(\"style\", \"max-width: none; max-height: none\")\n",
+       "        .attr(\"width\", width)\n",
+       "        .attr(\"height\", height);\n",
+       "\n",
+       "    var web = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"web\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.pauli_web)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return webColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 7px\");\n",
+       "\n",
+       "    var link = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"link\")\n",
+       "        .selectAll(\"line\")\n",
+       "        .data(graph.links)\n",
+       "        .enter().append(\"path\")\n",
+       "        .attr(\"stroke\", function(d) { return edgeColor(d.t); })\n",
+       "        .attr(\"fill\", \"transparent\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\");\n",
+       "\n",
+       "    var brush = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"brush\");\n",
+       "\n",
+       "    var node = svg.append(\"g\")\n",
+       "        .attr(\"class\", \"node\")\n",
+       "        .selectAll(\"g\")\n",
+       "        .data(graph.nodes)\n",
+       "        .enter().append(\"g\")\n",
+       "        .attr(\"transform\", function(d) {\n",
+       "            return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "        });\n",
+       "\n",
+       "    // Draw a ground symbol connected to the node.\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", \"M 0 0 L 0 \"+(groundOffset))\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "    node.filter(function(d) { return d.ground; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"style\", \"stroke-width: 1.5px\")\n",
+       "        .attr(\"fill\", \"none\")\n",
+       "        .attr(\"d\", d3.symbol().type(symbolGround).size(node_size*1.5))\n",
+       "        .attr(\"transform\", \"translate(0,\"+groundOffset+\")\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.t != 3 && d.t != 5 && d.t != 6; })\n",
+       "        .append(\"circle\")\n",
+       "        .attr(\"r\", function(d) {\n",
+       "            if (d.t == 0) return 0.5 * node_size;\n",
+       "            else if (d.t == 4) return 0.25 * node_size;\n",
+       "            else return node_size;\n",
+       "        })\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    var hbox = node.filter(function(d) { return d.t == 3; });\n",
+       "\n",
+       "    hbox.append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    // draw a triangle for d.t == 5\n",
+       "    node.filter(function(d) { return d.t == 5; })\n",
+       "        .append(\"path\")\n",
+       "        .attr(\"d\", \"M 0 0 L \"+node_size+\" \"+node_size+\" L -\"+node_size+\" \"+node_size+\" Z\")\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\")\n",
+       "        .attr(\"transform\", \"translate(\" + (-node_size/2) + \", 0) rotate(-90)\");\n",
+       "\n",
+       "    // draw a square for Z box: d.t == 6\n",
+       "    node.filter(function(d) { return d.t == 6; })\n",
+       "        .append(\"rect\")\n",
+       "        .attr(\"x\", -0.75 * node_size).attr(\"y\", -0.75 * node_size)\n",
+       "        .attr(\"width\", node_size * 1.5).attr(\"height\", node_size * 1.5)\n",
+       "        .attr(\"fill\", function(d) { return nodeColor(d.t); })\n",
+       "        .attr(\"stroke\", \"black\")\n",
+       "        .attr(\"class\", \"selectable\");\n",
+       "\n",
+       "    node.filter(function(d) { return d.phase != ''; })\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", 0.7 * node_size + 14)\n",
+       "        .text(function (d) { return d.phase })\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"12px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#00d\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "\n",
+       "    if (show_labels) {\n",
+       "        node.append(\"text\")\n",
+       "            .attr(\"y\", -0.7 * node_size - 8)\n",
+       "            .text(function (d) { return d.name; })\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "            .attr(\"font-size\", \"10px\")\n",
+       "            .attr(\"font-family\", \"monospace\")\n",
+       "            .attr(\"fill\", \"#999\")\n",
+       "            .attr('style', 'pointer-events: none; user-select: none;');\n",
+       "    }\n",
+       "\n",
+       "    // Display the chosen data fields over the node.\n",
+       "    node.filter(d => d.vdata.length > 0)\n",
+       "        .append(\"text\")\n",
+       "        .attr(\"y\", d => -0.7 * node_size - 14 - 10 * d.vdata.length)\n",
+       "        .attr(\"text-anchor\", \"middle\")\n",
+       "        .attr(\"font-size\", \"8px\")\n",
+       "        .attr(\"font-family\", \"monospace\")\n",
+       "        .attr(\"fill\", \"#c66\")\n",
+       "        .attr('style', 'pointer-events: none; user-select: none;')\n",
+       "        .selectAll(\"tspan\")\n",
+       "        .data(d => d.vdata)\n",
+       "        .enter()\n",
+       "        .append(\"tspan\")\n",
+       "        .attr(\"x\", \"0\")\n",
+       "        .attr(\"dy\", \"1.2em\")\n",
+       "        .text(x => x.join(\": \"));\n",
+       "\n",
+       "    if (scalar_str != \"\") {\n",
+       "        svg.append(\"text\")\n",
+       "            .text(scalar_str)\n",
+       "            .attr(\"x\", 60).attr(\"y\", 40)\n",
+       "            .attr(\"text-anchor\", \"middle\")\n",
+       "    }\n",
+       "\n",
+       "    function update_hboxes() {\n",
+       "        if (auto_hbox) {\n",
+       "            var pos = {};\n",
+       "            hbox.attr(\"transform\", function(d) {\n",
+       "                // calculate barycenter of non-hbox neighbours, then nudge a bit\n",
+       "                // to the NE.\n",
+       "                var x=0,y=0,sz=0;\n",
+       "                for (var i = 0; i < d.nhd.length; ++i) {\n",
+       "                    if (d.nhd[i].t != 3) {\n",
+       "                        sz++;\n",
+       "                        x += d.nhd[i].x;\n",
+       "                        y += d.nhd[i].y;\n",
+       "                    }\n",
+       "                }\n",
+       "\n",
+       "                offset = 0.25 * scale;\n",
+       "\n",
+       "                if (sz != 0) {\n",
+       "                    x = (x/sz) + offset;\n",
+       "                    y = (y/sz) - offset;\n",
+       "\n",
+       "                    while (pos[[x,y]]) {\n",
+       "                        x += offset;\n",
+       "                    }\n",
+       "                    d.x = x;\n",
+       "                    d.y = y;\n",
+       "                    pos[[x,y]] = true;\n",
+       "                }\n",
+       "\n",
+       "                return \"translate(\"+d.x+\",\"+d.y+\")\";\n",
+       "            });\n",
+       "        }\n",
+       "    }\n",
+       "\n",
+       "    update_hboxes();\n",
+       "\n",
+       "    var link_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = d.target.x, y1 = d.source.y, y2 = d.target.y;\n",
+       "        if (d.num_parallel == 1) {\n",
+       "            return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        } else {\n",
+       "            var dx = x2 - x1, dy = y2 - y1;\n",
+       "            var midx = 0.5 * (x1 + x2), midy = 0.5 * (y1 + y2);\n",
+       "            var pos = (d.index / (d.num_parallel-1)) - 0.5;\n",
+       "            var cx = midx - pos * dy;\n",
+       "            var cy = midy + pos * dx;\n",
+       "            return `M ${x1} ${y1} Q ${cx} ${cy}, ${x2} ${y2}`;\n",
+       "            // return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "        }\n",
+       "    };\n",
+       "    link.attr(\"d\", link_curve);\n",
+       "\n",
+       "\n",
+       "    var web_curve = function(d) {\n",
+       "        var x1 = d.source.x, x2 = (x1 + d.target.x)/2, y1 = d.source.y, y2 = (y1 + d.target.y)/2;\n",
+       "        return `M ${x1} ${y1} L ${x2} ${y2}`;\n",
+       "    }\n",
+       "    web.attr(\"d\", web_curve);\n",
+       "\n",
+       "    // EVENTS FOR DRAGGING AND SELECTION\n",
+       "\n",
+       "    node.on(\"mousedown\", function(d) {\n",
+       "        if (shiftKey) {\n",
+       "            d3.select(this).selectAll(\".selectable\").attr(\"style\", nodeStyle(d.selected = !d.selected));\n",
+       "            d3.event.stopImmediatePropagation();\n",
+       "        } else if (!d.selected) {\n",
+       "            node.selectAll(\".selectable\").attr(\"style\", function(p) { return nodeStyle(p.selected = d === p); });\n",
+       "        }\n",
+       "    })\n",
+       "        .call(d3.drag().on(\"drag\", function(d) {\n",
+       "            var dx = d3.event.dx;\n",
+       "            var dy = d3.event.dy;\n",
+       "            // node.filter(function(d) { return d.selected; })\n",
+       "            //     .attr(\"cx\", function(d) { return d.x += dx; })\n",
+       "            //     .attr(\"cy\", function(d) { return d.y += dy; });\n",
+       "            node.filter(function(d) { return d.selected; })\n",
+       "                .attr(\"transform\", function(d) {\n",
+       "                    d.x += dx;\n",
+       "                    d.y += dy;\n",
+       "                    return \"translate(\" + d.x + \",\" + d.y +\")\";\n",
+       "                });\n",
+       "\n",
+       "            update_hboxes();\n",
+       "\n",
+       "            link.filter(function(d) { return d.source.selected || d.target.selected ||\n",
+       "                    (auto_hbox && d.source.t == 3); })\n",
+       "                .attr(\"d\", link_curve);\n",
+       "            web.filter(function(d) { return d.source.selected || d.target.selected; })\n",
+       "                .attr(\"d\", web_curve);\n",
+       "        }));\n",
+       "\n",
+       "    brush.call(d3.brush().keyModifiers(false)\n",
+       "        .extent([[0, 0], [width, height]])\n",
+       "        .on(\"start\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(\n",
+       "                        d.selected = d.previouslySelected = shiftKey &&\n",
+       "                        d.selected);\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"brush\", function() {\n",
+       "            if (d3.event.sourceEvent.type !== \"end\") {\n",
+       "                var selection = d3.event.selection;\n",
+       "                node.selectAll(\".selectable\").attr(\"style\", function(d) {\n",
+       "                    return nodeStyle(d.selected = d.previouslySelected ^\n",
+       "                        (selection != null\n",
+       "                            && selection[0][0] <= d.x && d.x < selection[1][0]\n",
+       "                            && selection[0][1] <= d.y && d.y < selection[1][1]));\n",
+       "                });\n",
+       "            }\n",
+       "        })\n",
+       "        .on(\"end\", function() {\n",
+       "            if (d3.event.selection != null) {\n",
+       "                d3.select(this).call(d3.event.target.move, null);\n",
+       "            }\n",
+       "        }));\n",
+       "}\n",
+       "\n",
+       "\n",
+       "showGraph('#graph-output-Foib6n1h',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 26.666666666666668, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 26.666666666666668, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 26.666666666666668, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 53.333333333333336, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 53.333333333333336, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 80.0, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 80.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 106.66666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": 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{\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, 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\"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"49\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"50\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"51\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"52\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"53\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"55\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"56\", \"target\": \"60\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"57\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"59\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"62\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"61\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 133.33333333333334, 26.666666666666668,\n",
+       "  5.333333333333334, false, false, '');\n",
+       "</script>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Generate a random CNOT, H, T circuit\n",
+    "random.seed(1330)\n",
+    "c = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=40)\n",
+    "# for g in c.gates: print(g)\n",
+    "zx.draw(c)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "CNOT(0,1)\n",
-      "CNOT(1,0)\n",
-      "CNOT(2,0)\n",
-      "HAD(2)\n",
-      "CNOT(2,1)\n",
-      "HAD(2)\n",
-      "CNOT(1,0)\n",
-      "CNOT(0,2)\n",
-      "CNOT(1,2)\n",
-      "T(0)\n",
-      "T(1)\n",
-      "HAD(2)\n",
-      "T(2)\n",
-      "HAD(1)\n",
-      "HAD(0)\n",
-      "CNOT(0,2)\n",
-      "CNOT(0,2)\n",
-      "CNOT(1,0)\n",
-      "T(2)\n",
-      "HAD(2)\n",
-      "HAD(1)\n",
-      "CNOT(1,0)\n",
-      "CNOT(0,1)\n",
-      "CNOT(2,1)\n",
-      "T(0)\n",
-      "CNOT(2,0)\n",
-      "T(0)\n",
-      "T(0)\n",
-      "T(0)\n",
-      "CNOT(2,0)\n",
-      "CNOT(0,2)\n",
-      "T(2)\n",
-      "T(1)\n",
-      "T(1)\n",
-      "T(0)\n",
-      "HAD(1)\n",
-      "T(1)\n",
-      "CNOT(1,0)\n",
-      "CNOT(1,2)\n",
-      "CNOT(1,0)\n"
-     ]
-    },
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-1NvgQylw\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-w4Z8BbjY\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -443,9 +9246,9 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-1NvgQylw',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 26.666666666666668, \"y\": 53.333333333333336, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 26.666666666666668, \"y\": 80.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 26.666666666666668, \"y\": 106.66666666666667, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 53.333333333333336, \"y\": 80.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 53.333333333333336, \"y\": 53.333333333333336, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 80.0, \"y\": 53.333333333333336, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 80.0, \"y\": 80.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 106.66666666666667, \"y\": 53.333333333333336, \"t\": 2, \"phase\": 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{\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"16\", \"t\": 1, 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{\"source\": \"23\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"33\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 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\"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"59\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"61\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"60\", \"target\": \"62\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"61\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 800.0, 133.33333333333334, 26.666666666666668,\n",
-       "  5.333333333333334, false, false, '');\n",
+       "showGraph('#graph-output-w4Z8BbjY',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 350, 250, 50,\n",
+       "  10.0, false, true, '');\n",
        "</script>"
       ],
       "text/plain": [
@@ -456,37 +9259,11 @@
      "output_type": "display_data"
     }
    ],
-   "source": [
-    "# Generate a random CNOT, H, T circuit\n",
-    "random.seed(1330)\n",
-    "c = zx.generate.CNOT_HAD_PHASE_circuit(qubits=3, depth=40)\n",
-    "for g in c.gates: print(g)\n",
-    "zx.draw(c)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "KeyError",
-     "evalue": "58",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[3], line 10\u001b[0m\n\u001b[1;32m      6\u001b[0m g\u001b[38;5;241m.\u001b[39mnormalize()\n\u001b[1;32m      8\u001b[0m \u001b[38;5;66;03m# Compute the time-ordering on nodes (which is only important for the non-Clifford nodes) and compute the Pauli\u001b[39;00m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;66;03m# webs for every node.\u001b[39;00m\n\u001b[0;32m---> 10\u001b[0m order, zwebs, xwebs \u001b[38;5;241m=\u001b[39m \u001b[43mcompute_pauli_webs\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     12\u001b[0m \u001b[38;5;66;03m# Draw the simplified ZX diagram. Note blue edges correspond to edges with Hadamard gates\u001b[39;00m\n\u001b[1;32m     13\u001b[0m zx\u001b[38;5;241m.\u001b[39mdraw(g, labels\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n",
-      "File \u001b[0;32m~/git/pyzx/pyzx/pauliweb.py:191\u001b[0m, in \u001b[0;36mcompute_pauli_webs\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m    188\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    189\u001b[0m         ref \u001b[38;5;241m=\u001b[39m v\n\u001b[0;32m--> 191\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[43mg1\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtype\u001b[49m\u001b[43m(\u001b[49m\u001b[43mv\u001b[49m\u001b[43m)\u001b[49m \u001b[38;5;241m==\u001b[39m VertexType\u001b[38;5;241m.\u001b[39mZ: zwebs[ref] \u001b[38;5;241m=\u001b[39m pw\n\u001b[1;32m    192\u001b[0m     \u001b[38;5;28;01melif\u001b[39;00m g1\u001b[38;5;241m.\u001b[39mtype(v) \u001b[38;5;241m==\u001b[39m VertexType\u001b[38;5;241m.\u001b[39mX: xwebs[ref] \u001b[38;5;241m=\u001b[39m pw\n\u001b[1;32m    195\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m (order, zwebs, xwebs)\n",
-      "File \u001b[0;32m~/git/pyzx/pyzx/graph/graph_s.py:293\u001b[0m, in \u001b[0;36mGraphS.type\u001b[0;34m(self, vertex)\u001b[0m\n\u001b[1;32m    292\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mtype\u001b[39m(\u001b[38;5;28mself\u001b[39m, vertex):\n\u001b[0;32m--> 293\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mty\u001b[49m\u001b[43m[\u001b[49m\u001b[43mvertex\u001b[49m\u001b[43m]\u001b[49m\n",
-      "\u001b[0;31mKeyError\u001b[0m: 58"
-     ]
-    }
-   ],
    "source": [
     "# Convert to a ZX diagram and call the full_reduce procedure on it (PyZX's main ZX diagram optimisation pass)\n",
     "g = c.to_graph()\n",
     "zx.full_reduce(g)\n",
+    "zx.to_rg(g)\n",
     "\n",
     "# Normalise compacts the circuit visually and ensures every input/output is connected to a Z spider\n",
     "g.normalize()\n",
@@ -501,13 +9278,63 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{(16, 5): 'Y',\n",
+       " (5, 16): 'Y',\n",
+       " (5, 2): 'X',\n",
+       " (2, 5): 'Z',\n",
+       " (16, 43): 'Z',\n",
+       " (43, 16): 'Z',\n",
+       " (16, 58): 'Z',\n",
+       " (58, 16): 'X',\n",
+       " (16, 14): 'Y',\n",
+       " (14, 16): 'Y',\n",
+       " (3, 1): 'Z',\n",
+       " (1, 3): 'Z',\n",
+       " (3, 43): 'Z',\n",
+       " (43, 3): 'Z',\n",
+       " (3, 5): 'Y',\n",
+       " (5, 3): 'Y',\n",
+       " (3, 58): 'Z',\n",
+       " (58, 3): 'X',\n",
+       " (3, 54): 'Z',\n",
+       " (54, 3): 'Z',\n",
+       " (3, 14): 'Y',\n",
+       " (14, 3): 'Y',\n",
+       " (5, 43): 'X',\n",
+       " (43, 5): 'Z',\n",
+       " (5, 58): 'X',\n",
+       " (58, 5): 'X',\n",
+       " (5, 54): 'X',\n",
+       " (54, 5): 'Z',\n",
+       " (14, 58): 'X',\n",
+       " (58, 14): 'X'}"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pw = zwebs[43]\n",
+    "pw.half_edges()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-9pNvTZCn\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-m5O9iHKS\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -870,8 +9697,8 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-9pNvTZCn',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 300, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 300, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 300, \"y\": 250, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 300, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 400, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 400, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 400, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"65\", \"x\": 150, \"y\": 100, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"66\", \"x\": 150, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"67\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"68\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"69\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"70\", \"x\": 250, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"71\", \"x\": 350, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"72\", \"x\": 350, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"73\", \"x\": 300, \"y\": 300, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"74\", \"x\": 350, \"y\": 300, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"71\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"70\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"72\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"73\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"62\", \"target\": \"71\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"63\", \"target\": \"72\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"64\", \"target\": \"74\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"65\", \"target\": \"66\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"67\", \"target\": \"68\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"69\", \"target\": \"70\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"73\", \"target\": \"74\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 4, \"t\": \"X\"}, {\"source\": 4, \"target\": 54, \"t\": \"Z\"}, {\"source\": 54, \"target\": 4, \"t\": \"Z\"}, {\"source\": 5, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 54, \"t\": \"Z\"}, {\"source\": 54, \"target\": 5, \"t\": \"Z\"}, {\"source\": 68, \"target\": 67, \"t\": \"Z\"}, {\"source\": 67, \"target\": 68, \"t\": \"Z\"}, {\"source\": 68, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 68, \"t\": \"Z\"}]}'), 450, 350, 50,\n",
+       "showGraph('#graph-output-m5O9iHKS',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 2, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/2\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 100, \"t\": 2, \"phase\": \"7\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 250, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"5\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"58\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\\u03c0\", \"ground\": false, \"vdata\": []}, {\"name\": \"62\", \"x\": 300, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"63\", \"x\": 300, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"64\", \"x\": 300, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"43\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"58\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"54\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"62\", \"t\": 2, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"58\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"54\", \"target\": \"63\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"58\", \"target\": \"64\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 16, \"t\": \"Y\"}, {\"source\": 5, \"target\": 2, \"t\": \"X\"}, {\"source\": 2, \"target\": 5, \"t\": \"Z\"}, {\"source\": 16, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 16, \"t\": \"X\"}, {\"source\": 16, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 16, \"t\": \"Y\"}, {\"source\": 3, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 43, \"t\": \"Z\"}, {\"source\": 43, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 5, \"t\": \"Y\"}, {\"source\": 5, \"target\": 3, \"t\": \"Y\"}, {\"source\": 3, \"target\": 58, \"t\": \"Z\"}, {\"source\": 58, \"target\": 3, \"t\": \"X\"}, {\"source\": 3, \"target\": 54, \"t\": \"Z\"}, {\"source\": 54, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 14, \"t\": \"Y\"}, {\"source\": 14, \"target\": 3, \"t\": \"Y\"}, {\"source\": 5, \"target\": 43, \"t\": \"X\"}, {\"source\": 43, \"target\": 5, \"t\": \"Z\"}, {\"source\": 5, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 5, \"t\": \"X\"}, {\"source\": 5, \"target\": 54, \"t\": \"X\"}, {\"source\": 54, \"target\": 5, \"t\": \"Z\"}, {\"source\": 14, \"target\": 58, \"t\": \"X\"}, {\"source\": 58, \"target\": 14, \"t\": \"X\"}]}'), 350, 250, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
       ],
@@ -886,7 +9713,7 @@
    "source": [
     "# Once the Pauli webs have been computed, a specific web can be highlighted by `zx.draw` by passing it in as\n",
     "# an optional argument. Note that webs change color when they cross Hadamard edges.\n",
-    "zx.draw(g, labels=True, pauli_web=webs[67])"
+    "zx.draw(g, labels=True, pauli_web=zwebs[43])"
    ]
   },
   {
@@ -900,13 +9727,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-yx7Oii5U\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-4UnBIBHv\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1269,7 +10096,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-yx7Oii5U',\n",
+       "showGraph('#graph-output-4UnBIBHv',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -1281,17 +10108,10 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[] []\n"
-     ]
-    },
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-Ry9D3F6l\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-n2FqkzWZ\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -1654,8 +10474,8 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-Ry9D3F6l',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 150, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 250, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 200, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 4, \"target\": 3, \"t\": \"Z\"}, {\"source\": 3, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 4, \"t\": \"Z\"}]}'), 300, 250, 50,\n",
+       "showGraph('#graph-output-n2FqkzWZ',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 150, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"1\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"2\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 200, 150, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
       ],
@@ -1679,7 +10499,7 @@
     "order, zwebs, xwebs = compute_pauli_webs(g)\n",
     "\n",
     "# highlight the web associated to the T spider\n",
-    "zx.draw(g, labels=True, pauli_web=webs[3])"
+    "zx.draw(g, labels=True, pauli_web=None)"
    ]
   },
   {
@@ -1691,13 +10511,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-VgYH9uE3\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-U2vZXqTu\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2060,7 +10880,7 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-VgYH9uE3',\n",
+       "showGraph('#graph-output-U2vZXqTu',\n",
        "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": 100, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": 150, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": 150, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": 200, \"y\": 200, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": 250, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": 250, \"y\": 150, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": 300, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": 300, \"y\": 100, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 100, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 150, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"3\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"5\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"6\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"7\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"8\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 400, 250, 50,\n",
        "  10.0, false, false, '');\n",
        "</script>"
@@ -2072,17 +10892,10 @@
      "metadata": {},
      "output_type": "display_data"
     },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[] []\n"
-     ]
-    },
     {
      "data": {
       "text/html": [
-       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-bFjisVXv\"></div>\n",
+       "<div style=\"overflow:auto; background-color: white\" id=\"graph-output-tSoikvKv\"></div>\n",
        "<script type=\"module\">\n",
        "var d3;\n",
        "if (d3 == null) { d3 = await import(\"https://cdn.skypack.dev/d3@5\"); }\n",
@@ -2445,8 +11258,8 @@
        "}\n",
        "\n",
        "\n",
-       "showGraph('#graph-output-bFjisVXv',\n",
-       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 350, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 450, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 450, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 450, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 350, \"y\": 300.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 350, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": 400, \"y\": 200, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": 400, \"y\": 250, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": 400, \"y\": 300, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 16, \"t\": \"Z\"}]}'), 500, 350, 50,\n",
+       "showGraph('#graph-output-tSoikvKv',\n",
+       "  JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": 50, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": 50, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": 50, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": 100, \"y\": 200, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": 350, \"y\": 200, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": 350, \"y\": 250, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": 350, \"y\": 300, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": 200, \"y\": 100, \"t\": 1, \"phase\": \"\\u03c0/4\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": 200, \"y\": 150, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": 110.00000000000001, \"y\": 300.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": 80.0, \"y\": 250.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"4\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": [{\"source\": 16, \"target\": 15, \"t\": \"Z\"}, {\"source\": 15, \"target\": 16, \"t\": \"Z\"}, {\"source\": 16, \"target\": 17, \"t\": \"Z\"}, {\"source\": 17, \"target\": 16, \"t\": \"Z\"}, {\"source\": 17, \"target\": 2, \"t\": \"Z\"}, {\"source\": 2, \"target\": 17, \"t\": \"Z\"}, {\"source\": 16, \"target\": 18, \"t\": \"Z\"}, {\"source\": 18, \"target\": 16, \"t\": \"Z\"}, {\"source\": 18, \"target\": 1, \"t\": \"Z\"}, {\"source\": 1, \"target\": 18, \"t\": \"Z\"}, {\"source\": 16, \"target\": 4, \"t\": \"Z\"}, {\"source\": 4, \"target\": 16, \"t\": \"Z\"}, {\"source\": 4, \"target\": 0, \"t\": \"Z\"}, {\"source\": 0, \"target\": 4, \"t\": \"Z\"}]}'), 400, 350, 50,\n",
        "  10.0, false, true, '');\n",
        "</script>"
       ],
@@ -2482,7 +11295,7 @@
     "order, zwebs, xwebs = compute_pauli_webs(g)\n",
     "\n",
     "# highlight the web associated to the T spider\n",
-    "zx.draw(g, labels=True, pauli_web=webs[15])"
+    "zx.draw(g, labels=True, pauli_web=zwebs[15])"
    ]
   },
   {
diff --git a/pyzx/pauliweb.py b/pyzx/pauliweb.py
index 551245c9..9908d382 100644
--- a/pyzx/pauliweb.py
+++ b/pyzx/pauliweb.py
@@ -50,7 +50,7 @@ def __init__(self, g: BaseGraph[VT,ET]):
         self.es: Dict[Tuple[VT,VT], str] = dict()
         self.vs: Set[VT] = set()
     
-    def add_edge(self, v_pair: Tuple[VT, VT], pauli: str):
+    def add_edge(self, v_pair: Tuple[VT, VT], pauli: str, spread_to_input: bool=False):
         s, t = v_pair
         self.vs.add(s)
         self.vs.add(t)
@@ -60,10 +60,18 @@ def add_edge(self, v_pair: Tuple[VT, VT], pauli: str):
         self.es[(s,t)] = multiply_paulis(t1, pauli)
         self.es[(t,s)] = multiply_paulis(t2, pauli if et == EdgeType.SIMPLE else h_pauli(pauli))
 
-    def add_vertex(self, v: VT):
+        if spread_to_input and ('Z' if self.g.type(t) == VertexType.Z else 'X') == pauli:
+            inp = self.g.inputs()
+            for v2 in self.g.neighbors(t):
+                if v2 in inp:
+                    self.add_edge((t, v2), pauli, spread_to_input=False)
+                    break
+
+
+    def add_vertex(self, v: VT, spread_to_input: bool=False):
         p = 'X' if self.g.type(v) == VertexType.Z else 'Z'
         for v1 in self.g.neighbors(v):
-            self.add_edge((v, v1), p)
+            self.add_edge((v, v1), p, spread_to_input=spread_to_input)
     
     def vertices(self):
         return self.vs
@@ -74,64 +82,6 @@ def half_edges(self) -> Dict[Tuple[VT,VT],str]:
     def __repr__(self):
         return 'PauliWeb' + str(self.vs)
 
-
-def preprocess(g: BaseGraph[VT,ET]):
-    #g.normalize()
-    #gadgetize(g)
-    #gadgets = set(v for v in g.vertices() if g.is_phase_gadget(v))
-    #boundary_spiders = set(v for v in g.vertices() if any(g.type(w) == VertexType.BOUNDARY for w in g.neighbors(v)))
-    #to_rg(g, init_z=None, init_x=gadgets)
-
-    in_circ = Circuit(len(g.inputs()))
-    for j,i in enumerate(g.inputs()):
-        e = g.incident_edges(i)[0]
-        v = next(iter(g.neighbors(i)))
-        p = g.phase(v)
-        ty = g.type(v)
-
-        # remove local cliffords from the inputs
-        if g.edge_type(e) == EdgeType.HADAMARD:
-            in_circ.add_gate('H', j)
-            g.set_edge_type(e, EdgeType.SIMPLE)
-        if p != 0:
-            g.set_phase(v, 0)
-            in_circ.add_gate("ZPhase" if ty == VertexType.Z else "XPhase", j, phase=p)
-
-    out_circ = Circuit(len(g.outputs()))
-    for j,o in enumerate(g.outputs()):
-        r = g.row(o)
-        g.set_row(o, r + 2)
-        e = g.incident_edges(o)[0]
-        v = next(iter(g.neighbors(o)))
-        p = g.phase(v)
-        ty = g.type(v)
-
-        # remove local cliffords from the outputs
-        if p != 0:
-            g.set_phase(v, 0)
-            out_circ.add_gate("ZPhase" if ty == VertexType.Z else "XPhase", j, phase=p)
-
-        if g.edge_type(e) == EdgeType.HADAMARD:
-            out_circ.add_gate('H', j)
-        g.remove_edge(e)
-
-        # introduce ID spiders at the outputs for computing pauli webs
-        if ty == VertexType.X:
-            v1 = g.add_vertex(VertexType.Z, qubit=g.qubit(o), row=r)
-            g.add_edge((v,v1), EdgeType.SIMPLE)
-        else:
-            v1 = v
-            g.set_row(v1, r)
-        
-        v2 = g.add_vertex(VertexType.X, qubit=g.qubit(o), row=r+1)
-
-        
-        g.add_edge((v1,v2), EdgeType.SIMPLE)
-        g.add_edge((v2,o), EdgeType.SIMPLE)
-    
-    return (in_circ, out_circ)
-
-
 def transpose_corrections(c: Dict[VT, Set[VT]]) -> Dict[VT, Set[VT]]:
     ct: Dict[VT, Set[VT]] = dict()
     for k,s in c.items():
@@ -172,16 +122,15 @@ def compute_pauli_webs(g: BaseGraph[VT,ET]) -> Tuple[Dict[VT, int], Dict[VT, Pau
     xwebs: Dict[VT, PauliWeb[VT,ET]] = dict()
     vset = g.vertex_set()
     corr_t = transpose_corrections(corr)
-    print(corr_t)
 
     for v,c in corr_t.items():
         pw = PauliWeb(g)
         for v1 in c:
             if v1 in vset:
-                pw.add_vertex(v1)
+                pw.add_vertex(v1, spread_to_input=True)
             elif v1 in out_edge:
                 o, vo = out_edge[v1]
-                pw.add_edge((o,vo), 'Z' if g1.type(v1) == VertexType.X else 'X')
+                pw.add_edge((o,vo), 'Z' if g1.type(v1) == VertexType.X else 'X', spread_to_input=True)
         if v in out_edge:
             # o, vo = out_edge[v]
             # pw.add_edge((o,vo), 'Z' if g1.type(v) == VertexType.Z else 'X')
@@ -192,5 +141,14 @@ def compute_pauli_webs(g: BaseGraph[VT,ET]) -> Tuple[Dict[VT, int], Dict[VT, Pau
         if g1.type(v) == VertexType.Z: zwebs[ref] = pw
         elif g1.type(v) == VertexType.X: xwebs[ref] = pw
 
+    for i in g.inputs():
+        v = next(iter(g.neighbors(i)))
+        pw = PauliWeb(g)
+        if g.type(v) == VertexType.Z:
+            pw.add_edge((v, i), 'Z')
+            zwebs[v] = pw
+        elif g.type(v) == VertexType.X:
+            pw.add_edge((v, i), 'X')
+            xwebs[v] = pw
 
     return (order, zwebs, xwebs)
\ No newline at end of file