diff --git a/examples/dbi/dbi_group_commutators_evolution_oracles_and_gci_transpiling.ipynb b/examples/dbi/dbi_group_commutators_evolution_oracles_and_gci_transpiling.ipynb
index b306551982..c0577fc300 100644
--- a/examples/dbi/dbi_group_commutators_evolution_oracles_and_gci_transpiling.ipynb
+++ b/examples/dbi/dbi_group_commutators_evolution_oracles_and_gci_transpiling.ipynb
@@ -11,7 +11,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "765f8da6",
+   "id": "173074d1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -25,10 +25,103 @@
     "    print(reduce(str.__add__, out[0]))"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "eb3a4f7f",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "@pytest.mark.parametrize(\"nqubits\", [3])\n",
+      "def test_double_bracket_iteration_eval_dbr_unitary(backend, nqubits):\n",
+      "    h0 = random_hermitian(2**nqubits, backend=backend)\n",
+      "    d = backend.cast(np.diag(np.diag(backend.to_numpy(h0))))\n",
+      "    dbi = DoubleBracketIteration(\n",
+      "        Hamiltonian(nqubits, h0, backend=backend),\n",
+      "        mode=DoubleBracketGeneratorType.group_commutator,\n",
+      "    )\n",
+      "\n",
+      "    for s in np.linspace(0,.01,NSTEPS):\n",
+      "        u = dbi.eval_dbr_unitary(s,mode = DoubleBracketRotationType.single_commutator)\n",
+      "        v = dbi.eval_dbr_unitary(s, mode = DoubleBracketRotationType.group_commutator)\n",
+      "\n",
+      "        assert np.linalg.norm( u - v ) < 10 * s * np.linalg.norm(h0) * np.linalg.norm(d)\n",
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "print_function_source_code(test_double_bracket_iteration_eval_dbr_unitary)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "ceb004ac",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import qibo\n",
+    "backend = qibo.backends.construct_backend(\"numpy\")\n",
+    "nqubits = 3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "50a41bdc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "numpy"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "backend"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "c0e53a8d",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "ename": "UnboundLocalError",
+     "evalue": "local variable 'operator' referenced before assignment",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mUnboundLocalError\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[0;32m/tmp/ipykernel_9225/3866532243.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtest_double_bracket_iteration_eval_dbr_unitary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbackend\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnqubits\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m~/Projects_git/DBI_qibo/qibo/examples/dbi/../../tests/test_models_dbi.py\u001b[0m in \u001b[0;36mtest_double_bracket_iteration_eval_dbr_unitary\u001b[0;34m(backend, nqubits)\u001b[0m\n\u001b[1;32m     61\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     62\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m.01\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mNSTEPS\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 63\u001b[0;31m         \u001b[0mu\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meval_dbr_unitary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDoubleBracketRotationType\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msingle_commutator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     64\u001b[0m         \u001b[0mv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meval_dbr_unitary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mDoubleBracketRotationType\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgroup_commutator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     65\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m~/Projects_git/DBI_qibo/qibo/src/qibo/models/dbi/double_bracket.py\u001b[0m in \u001b[0;36meval_dbr_unitary\u001b[0;34m(self, step, mode, d)\u001b[0m\n\u001b[1;32m    139\u001b[0m             )\n\u001b[1;32m    140\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 141\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0moperator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    142\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    143\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mstaticmethod\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mUnboundLocalError\u001b[0m: local variable 'operator' referenced before assignment"
+     ]
+    }
+   ],
+   "source": [
+    "test_double_bracket_iteration_eval_dbr_unitary(backend, nqubits)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "cdf50e7c",
+   "id": "02929afc",
    "metadata": {},
    "outputs": [
     {
@@ -64,7 +157,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "8688a26d",
+   "id": "de085a6e",
    "metadata": {},
    "outputs": [
     {
@@ -80,10 +173,32 @@
     "set_backend('numpy')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "b33d65d0",
+   "metadata": {},
+   "source": [
+    "# Show that double bracket iteration group commutator and dbi converge for small s BHMM\n",
+    "\n",
+    "This is testing the following:\n",
+    "\n",
+    "`dbi` runs $V = e^{-sW}$ and rotates $H_1 = V^\\dagger H_0 V$.\n",
+    "\n",
+    "`gci` runs $Q = GC$ and rotates $J_1 = Q^\\dagger H_0 Q$.\n",
+    "\n",
+    "`dbi2` runs $R = GC$ and rotates $K_1 = R^\\dagger H_0 R$.\n",
+    "\n",
+    "We assert that gci and dbi2 should be within machine precision for the correct sorting.\n",
+    "$$||J_1-K_1||\\le2 ||H_0||\\,||R-Q||\\le \\epsilon$$\n",
+    "\n",
+    "We assert that gci and dbi should be within the approximation bound of the GC\n",
+    "$$||J_1-H_1||\\le2 ||H_0||\\,||R-V||\\le C ||H_0|| s^{3/2}$$\n"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "1add4aa2",
+   "id": "99b58bba",
    "metadata": {},
    "outputs": [],
    "source": [