GHZ-Game.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The GHZ-Game\n",
    "\n",
    "\n",
    "### Solve \"unsolvable\" problems using Quantum Computers\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Usage instructions for the user interface\n",
    "\n",
    "* \"Shift Enter\" executes the interactive cells (might need to click the cell, first)\n",
    "* Execute all the interactive cells (\"In [1]:\", etc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First we need to install some prerequisits. You do not have to understand them for now (just click on the cells and press \"Shift Enter\"):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#import prerequisites\n",
    "import qiskit\n",
    "from ipywidgets import interact\n",
    "from qiskit.providers.aer import QasmSimulator, StatevectorSimulator, UnitarySimulator\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.visualization import plot_state_qsphere\n",
    "from qiskit.tools.visualization import plot_histogram, plot_bloch_multivector, plot_bloch_vector, plot_state_qsphere\n",
    "from GHZGame.ghzGame import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# create the quantum circuit with the chosen coin moves\n",
    "q = QuantumRegister(3) # create a quantum register with one qubit\n",
    "# create a classical register that will hold the results of the measurement\n",
    "c = ClassicalRegister(3) \n",
    "qc = QuantumCircuit(q, c) # creates the quantum circuit\n",
    "backend = BasicAer.get_backend('qasm_simulator') # define the backend, here a Quantum simulator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Let's play a game!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We form two teams of three players. Your team is called \"Team Einstein\" and your team members are Alice and Bob (and you, of course). The other team is called \"Team Schrödinger\" and - as the name indicates - will be able to exploit quantum mechanics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The rules for this game are as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Each player thinks of a color (red or blue) and a shape (star or rectangle)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The game master than asks either all players for a color or one for a color and two for a shape. In total, four different kinds of questions can be asked:\n",
    "\n",
    "\n",
    "1. Color, color, color\n",
    "2. Color, shape, shape\n",
    "3. Shape, color, shape\n",
    "4. Shape, shape, color\n",
    "\n",
    "Which of the four sets of questions is used, is chosen randomly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Once the questions are asked, the team members are not allowed to communicate anymore. Before that, the team members are allowed to agree on a strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- In the case that all players are asked for a color (1.), the team wins if an even number of people answered with red. Otherwise (when two are asked for a shape and only one for a color) they win if an uneven number of players answered with either red or star depending on the question they were asked. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example:\n",
    "\n",
    "Question: Color, color, color\n",
    "\n",
    "Answer: red, red, blue\n",
    "> right answer, even number of red.\n",
    "\n",
    "Question: Color, shape, shape\n",
    "\n",
    "Answer: red, star, rectangle\n",
    "> wrong answer, even number of red and star, should be uneven.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "If you think about a *real* object that will answer the question about color and shape, each team member could  choose to think of one of the following four objects.  You are allowed to change your mind as often as you want as long as you do not know whether your team members were asked for a color or a shape:\n",
    "![title](GHZGame/shapes.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Make your choices:\n",
    "(The 0 or 1 inside the brakets of the drop down fields below show the corresponding bit value. 0 is interpreted as red or star and 1 as blue or rectangle.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your team can now discuss which values each of you will say when asked either for the color or the shape of your object.\n",
      "\n",
      "Alice:\n"
     ]
    },
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      "text/plain": [
       "interactive(children=(Dropdown(description='AlicesColor', options={'red (1)': 1, 'blue (0)': -1}, value=1), Dr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bob:\n"
     ]
    },
    {
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      },
      "text/plain": [
       "interactive(children=(Dropdown(description='BobsColor', options={'red (1)': 1, 'blue (0)': -1}, value=1), Drop…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "You:\n"
     ]
    },
    {
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       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='YourColor', options={'red (1)': 1, 'blue (0)': -1}, value=1), Drop…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "print ('Your team can now discuss which values each of you will say when asked either for the color or the shape of your object.')\n",
    "print ('')\n",
    "\n",
    "print ('Alice:')\n",
    "interact(Alice, AlicesColor={'red (1)':1,'blue (0)':-1}, AlicesShape={'star (1)':1,'rectangle (0)':-1})\n",
    "\n",
    "print ('Bob:')\n",
    "interact(Bob, BobsColor={'red (1)':1,'blue (0)':-1}, BobsShape={'star (1)':1,'rectangle (0)':-1})\n",
    "\n",
    "print ('You:')\n",
    "interact(You, YourColor={'red (1)':1,'blue (0)':-1}, YourShape={'star (1)':1,'rectangle (0)':-1})\n",
    "print ('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If you are confident with your choices try it out here. Do you have a 100% winning strategie that gives the correct answer for each of the four sets of questions? (\"If you loose once, you will stay in prison forever\".)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Round  1 , Question  1\n",
      "Team Einstein was wrong, Team Schrödinger was right\n",
      "Round  2 , Question  2\n",
      "Both teams were right\n",
      "Round  3 , Question  3\n",
      "Both teams were right\n",
      "Round  4 , Question  4\n",
      "Both teams were right\n"
     ]
    }
   ],
   "source": [
    "# runs the experiment for both teams, asking all four questions.\n",
    "runExperiment()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Why has the other team a 100% winning strategie while your team does not?\n",
    "\n",
    "To find out what they do differently you talk to team Schrödinger and their team member Erwin explains what they did."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Bob: \n",
    "\"*How did you do that? Isn't it impossible to constantly win this game? I mean look at this, we tried to solve it mathematically and the problem is unsolvable, you must have cheated!*\"\n",
    "\n",
    "(For easier calculations we replaced 0 for blue and rectangle with -1)\n",
    "    \n",
    "\n",
    "    \n",
    "   ![title](GHZGame/proof1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Erwin (from team Schrödinger): \n",
    "\"*Yes, you are right, but we did not cheat! We used so-called qubits and entanglement and with that it is possible to always win.*\"\n",
    "\n",
    "Bob: \n",
    "\"*What exactly is that and how does it work?*\"\n",
    "    \n",
    "Erwin: \n",
    "\"*Each of us had a qubit. You can imagine them as a little sphere with a vector pointing in \n",
    "    one direction. This vector describes the state the qubit is currently in.*\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_bloch_vector([1,0,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Erwin: \n",
    "\"*However - as you know from quantum mechanics - you cannot see in which state the qubit is, but \n",
    "    need to measure it to find out something about its state. The result of a measurement is always \n",
    "    either 0 or 1. These values correspond to the shape and color of the objects in such a way that we \n",
    "    answered with red or star whenever measuring 1 and accordingly with blue or rectangle when measuring 0.\n",
    "    For example, when asked for the color of your object and you are measuring a 0 you answer blue. For a 1 \n",
    "    your answer would be red.*\n",
    "    \n",
    "*The vector in the sphere above, is in a position other than 0 (top of the sphere) or 1 (at the bottom). When \n",
    "    measuring, you would still get one of these results. In this case, it would be 0 with 50% probability \n",
    "    and 1 with 50% probability. The actual result for a single measurement is random.*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Erwin: \n",
    "\"*So we used qubits that were entangled with each other and different \"observables\" of a quantum object. Normally, a Quantum Computer measures the Z-basis of a qubit but we measured X when asked for a color and when asked for a shape we measured Y. The result for the Y measurement in the example above \n",
    "    would always be 1, instead of the 50% probability of 0 or 1 when measuring the Z-value. \n",
    "    I will explain later why exactly this works but as all three of our qubits were entangled, we got the correct answer for all cases.*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Bob: \n",
    "\"*But isn't that against the rule to not communicate with each other after the question was asked?*\"\n",
    "    \n",
    "Erwin: \n",
    "\"*No it is not because the qubits do not communicate with each other. They are just correlated in \n",
    "    such a way that they cannot be seen as independent. We can just try it out :) Before we start we \n",
    "    need to bring all our three qubits into the so-called GHZ-state. This is an entangled state that creates \n",
    "    dependencies between the qubits. To do so, we need to apply the following Quantum circuit:*\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 394.558x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this circuit is explained in more detail later on.\n",
    "qc = QuantumCircuit(q, c)\n",
    "# create GHZ state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "qc.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Erwin:  \n",
    "\"*The first gate we see in the circuit above is the H-gate which brings the qubit into a \n",
    "            Superposition. When measured it has a 50% probability of beeing 0 and a 50% probability of beeing 1.*\"\n",
    "\n",
    "\"*The other gates we see look different. They are called CNOT-gates and operate on 2 qubits. \n",
    "            The qubit with the dot is the control bit and the other one with the cross sign is the target \n",
    "            bit. If the control bit is one an X-gate is applied to the target bit. Otherwise nothing happens.*\"\n",
    "            \n",
    "(An X-gate cannot be found in the picture above. The X-gate is similar to a NOT-gate used on classical computers. When applied to a qubit in state $ \\;\\;|1\\rangle $ it becomes $ \\;\\;|0\\rangle $ and the other way around.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Erwin:  \"*On a Quantum Computer you can only measure what \n",
    "            points in the direction of the Z-axis. Therefore, we need to make the state vector point in the  direction to derive information about the X or Y basis. When you are asked for the color (corresponds to x value) of your qubit you need to apply an \n",
    "            H-gate and measure the state afterwards. Applying the H-gate turns your state vector 180° around the \n",
    "            Z-axis and 90° around the Y-axis and therefore, enables you to read out the X-value.* \n",
    "            \n",
    "*When asked for\n",
    "            the shape you apply the sdg-gate followed by an H-gate and measure afterwards. This corresponds to \n",
    "            a Y measurement (shape) as the sdg gate turns the object by 270° around the Z-axis so that the \n",
    "            shape of the object is now pointing towards X. When applying an H-gate afterwards, it turns the \n",
    "            object 180° around the Z-axis and 90° around the Y-axis so that it is now pointing towards Z which is the only axis we are able to measure.*\n",
    "            \n",
    "*You can try to reconstruct the movements of a single qubit using the visualization below. Whether \n",
    "            the top or bottom side of the dice is revealed in a measurement is randomly chosen. In the initial \n",
    "            GHZ-state the dice is pointing up with a black side so that a color is pointing towards X and a\n",
    "            shape towards Y.*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![title](GHZGame/visualization.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Erwin:  \n",
    "\"*The results for each player seems to be perfectly random, but all three results in fact are \n",
    "            strongly correlated and not independent. This is caused by the entanglement. The Bloch Sphere\n",
    "            visualization can only be used for a single qubit, but not for the entire (entangled) system \n",
    "            of multiple qubits. However the so-called QSphere shows that the measurement results of the GHZ-State can only be |000> or |111> with equal probability:*\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "backend = BasicAer.get_backend('statevector_simulator') # the device to run on\n",
    "result = execute(qc, backend).result()\n",
    "psi = Statevector.from_instruction(qc)\n",
    "plot_state_qsphere(psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "To measure the Y-basis of a quantum state, the following quantum circuit can be used:\n"
     ]
    },
    {
     "data": {
      "image/png": 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TEOlifDIUAL1793bb3tTUhMPhcB12ANhsNioqKnA6nW63LS8vJygoiGHDhtGzZ0+Sk5Nd102YMIGTJ0926MxOp1OXO/By/dffX18LbeVzoYiOjgagsrLSbXtOTg41NTWuE5kAaWlp1NbWsmPHDte2y5cvs3nzZpKTk4mIiGh1/2vXrmXGjBmeGV6ki/K5k5kxMTHY7Xays7OxWq3069ePvLw812cirg9FamoqEydOJCMjg5ycHPr06cO6deuoqqoiNze31X2/8MILHD9+nPfff7/Tno9IV+BzK4qAgAC2bNmCzWZj8eLFZGRkEB0dzdKlSwkMDHQ7kWmxWCgqKmL69OmsWLGC1NRUTp8+zc6dO92CAvDSSy+xdetWtm/fTnh4eGc/LRG/5nMrCoDY2Fh2797tti09PZ3hw4cTFhbmtr1nz56sX7+e9evX3/T+XnjhBYqLi9m1axc9e/b0xMgiXZpPhuJGDh48yPjx49u9X3l5Ob/61a8YNGgQSUlJru2lpaUdN5xIF+cXoWhsbKSyspIlS5a0e1+bzdaus7si0ppfhKJ79+5cuXLF22OI3LF87mSmiPgehUJEjBQKETFSKETESKEQESOFQkSMFAoRMVIoRMRIoRARI4VCRIwUChExUihExEihEBEjhUJEjBQKETFSKETESKEQESOFQkSMFAoRMVIoRMRIoRARI4VCRIwUCh8zZcoURo0axYgRI5g5cyZnz5719kjiISUlJdhsNgYPHsz8+fN9+ldSKBQ+ZsuWLZSWlnL06FH69+/Pa6+95u2RxANaWlqYP38+W7Zs4fjx45w9e5Y//elP3h7rphQKH3PXXXcBV19IFy5cwGKxeHki8YQPPviAvn37Mnz4cAAyMzN5++23vTzVzSkUPuhHP/oRvXr14uOPP+app57y9jjiAdXV1dxzzz2uvw8YMIDPPvvMixPdml/8SsE7TUFBAZcuXSIzM5O8vDyefPJJb48kQNOFi/znf22j+TvnEn795ts3/POjk37IkHv73/C+/O334WpF4aNCQkKYM2cOBQUF3h5F/l9Yt1AG39uXmtN11Jyuc23/7p9rTtcREGBh0MB+N72ve+65x20FUVVVRf/+N46KL1AofMi3335LTU0NcPUcRVFRETabzctTyfWSxo+mR0SY8XapD08g4Bbnl+6//36qq6upqKgA4I9//COPPfZYh83Z0bp8KL744gvmzp1LZGQk3bt355FHHqG8vNzbY93Qt99+y/Tp07Hb7djtdpqbm3n22We9PZZcJzQkmEcSx93yNvZhMdzbv/ctbxMYGMiGDRuYOXMmgwYNonv37qSnp3fkqB3K4vS3g6V2aGpqYvTo0bS0tJCdnU14eDjZ2dkcO3aM0tJSn17qfZfT6dQ7ID6ixenkt5sK+Pyr2lbXBQUGsuLfZmO9q4cXJvOcLr2i2LBhA5WVlRQUFDBz5kweffRR3nnnHZqbm8nOzvb2eO3yl6272bHnA2+PIUCAxcK0hx+84XUTx43ocpGALhCKo0eP8uMf/5jo6Gi6devGkCFDyMrKAqCwsJDRo0e7HedHRkaSmprqVycJa07XUVpx/JbHvNK57runD/ZhMW7bekSEkTR+tJcm8iy/DsWhQ4cYP3485eXlvPrqqxQXF/PMM8/w5ZdfAlBWVkZcXFyr/eLi4vjyyy+pq6trdZ0veu9/DhMaEkz8AyO8PYpcJyXphwQFBrr+/kjiOEJDgr04kef49econnrqKSIiIvjrX//q+kQjXP2UG0B9fT2RkZGt9rNara7ro6Kivvccz7zyxve+j7Z48debOuVx5PbkFTvIK3Z4e4x2Wb1yQZtu57crivPnz7N3717mzp3rFgkR6Xh+u6JoaGigpaXllu9cWK1WGhoaWm2vr693Xd8R2lrl9qo5Xcev33ybhyeMYfLE+z3yGPL9fVXbwN3RrVeuXYnfhiIyMpKAgAA+//zzm97GZrPd8DMT5eXl9O7du0MOO8Dzhx7v7T/Me/sPe/Qx5M7U5Q89wsPDSUhIIDc396Y/syEtLY3Dhw/z0UcfubZ98803vPPOO8yYMaOTJhXxf379gatDhw6RkJDAwIED+fnPf87AgQOpqqpi7969bNiwgfPnzzNq1CgsFovbB64qKiooLS11+7/3fM2fCnbxj1PVrFw8j/Buod4eR+5wfruiABg7diwHDhxgyJAhLF++nEcffZSXX36Zvn37AldXHbt372bUqFFkZmYyc+ZMwsLCKCkp8elI1Jyuo6zyJA/dP0KREJ/g1yuKrqq88hTv7j7Avz/xmEIhPkGh8FEtLS0EBPj1gk+6EIVCRIz0LUtEjBQKETFSKETESKEQESOFQkSMFAoRMVIoRMRIoRARI4VCRIwUChExUihExEihEBEjhUJEjBQKETFSKETESKEQESOFQkSMFAoRMVIoRMRIoRARI4VCRIwUChExUihExEihEBEjhUJEjBQKETFSKETE6P8ADD9k3IRaLPEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 334.358x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print (\"To measure the Y-basis of a quantum state, the following quantum circuit can be used:\")\n",
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "# If measuring the X or Z-value, this step is not necessary:\n",
    "#apply sdg-gate to qubit 0. Vector moves 90° counterclockwise around the Z-axis (e.g. from y-basis to x-basis)\n",
    "qc.sdg(q[0]) \n",
    "# If measuring the Z-value, this step is not necessary:\n",
    "#apply H-gate to qubit 0. Vector moves 180° around the Z-axis and 90° around the Y-axis (e.g. from x-basis to z-basis)\n",
    "qc.h(q[0]) \n",
    "#create measurement gate for qubit 0\n",
    "qc.measure(q[0],c[0]) \n",
    "#draw the circuit\n",
    "qc.draw(output='mpl') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    Can you modify the cell above to build a Quantum circuit that is suitable for an X measurement by \n",
    "    commenting out or deleting the line that is not necessary? \n",
    "\n",
    "    Can you do the same for a Z-measurement? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "    A quantum circuit that can be used when your team is asked for the XYY-values, therefore, could look like\n",
    "    this:\n",
    "    (XYY means that Alice (player 1) is asked for the color while Bob and you (player 2 and 3) are asked for \n",
    "    a shape.\n",
    "    1 -> red or star\n",
    "    0 -> blue or rectangle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 695.558x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "# create GHZ state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "\n",
    "# measure each qubit accordingly\n",
    "qc.h(q[0]) #apply H-gate to the first qubit (for x-value, player 1)\n",
    "qc.sdg(q[1]) #apply sdg-gate to the second qubit\n",
    "qc.h(q[1]) #apply H-gate to the second qubit (for y-value, player 2)\n",
    "qc.sdg (q[2]) #apply sdg-gate to the third qubit\n",
    "qc.h(q[2]) #apply H-gate to the third qubit (for y-value, player 3)\n",
    "qc.measure(q,c) #create measurement gates for all qubits\n",
    "qc.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    In this case the measurement results are distributed as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "# create GHZ state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "\n",
    "# measure each qubit accordingly\n",
    "qc.h(q[0]) #apply H-gate to the first qubit (for x-value, player 1)\n",
    "qc.sdg(q[1]) #apply sdg-gate to the second qubit\n",
    "qc.h(q[1]) #apply H-gate to the second qubit (for y-value, player 2)\n",
    "qc.sdg (q[2]) #apply sdg-gate to the third qubit\n",
    "qc.h(q[2]) #apply H-gate to the third qubit (for y-value, player 3)\n",
    "qc.draw(output='mpl') #draw the circuit\n",
    "result = execute(qc, backend).result()\n",
    "psi = Statevector.from_instruction(qc)\n",
    "plot_state_qsphere(psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# So now let's play again, using this new strategy\n",
    "\n",
    "To generate a random question execute the next cell:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The question your team is getting asked is:\n",
      "Color, shape, shape\n"
     ]
    }
   ],
   "source": [
    "question = randomQuestion()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Try to build a quantum circuit that can be used to answer these questions on the next slide and provide the right answers to your team members (if you need  help use the previous cells as examples or continue to the next cells):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 153.758x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #creates a new Quantum circuit\n",
    "\n",
    "#TODO: create GHZ-state (try not to use the predefined function)\n",
    "\n",
    "#TODO: apply gates according to the question above\n",
    "\n",
    "qc.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Now let's test your Quantum circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'000': 100}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# runs your quantum circuit 100 times on a simulator\n",
    "simulate(qc, q, c, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you can check your results for yourself. You get several different answers and this can be correct as the requirements of an even or uneven number of ones or zeros can be satisfied in multiple ways."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Do you think your answers were right? Check it here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hmmm... There might still be a mistake.\n"
     ]
    }
   ],
   "source": [
    "# compares whether the measurement results from your circuit correspond to the question asked\n",
    "circuitCheck(qc, q, c, question)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Need some help? \n",
    "(Otherwise skip this cell)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qqsLcuXPRvXt3mJmZwc/PD4cOHRI6Fj3hzBX5ILSWJL4q/2rJ7fvyDwActNZ+7777rtARiFRmbGyM1157DVlZWbh9+zays7ORkZGBH374Afn5+aiqqsLOnTsxduxYhRJ3dHREZmYmPvvsM7z6ait/cLSUqItbJpNh0qRJ2LlzJ9asWYO0tDTY2toiJCQEp06dEjoe/X81tcAONd76OfcqcO6q+tanq1JSUoSO0C6Zn7+BPevC8PuZvUh9LxB/XDohdCTqIMHBwcjPz8eXX34Jf39/GBsbIz8/Hz/88AN++uknXLlyBV26dMHkyZOxb98+HDlyBG5ubg2l3bdvX5w8eRLp6elCvxSViHpw2u7du5GVlYX09HRMmDABgPwUF6lUipiYGNH+T+lszhYDVffUu86DBYDUWb3rJO1RVVqIQ9uicC3/IB7dr4axuRXseg/FhDe+hr6BEQAgcMYnuHXjMv73zXKMjdgqbOAnpL4XiJ4ewRg2ealS00l577//PpYsWQIAOHv2LD766COkpKTg1q1bCvM5OjpixowZWLBgAZ555hmcPHkSN2/ehL29PU6ePIng4GBUVopz0IzWbnHX1dVhzZo16Nu3L0xMTDBo0CBkZWWhf//+mDNnDgBg165dsLGxwfjx4xuWMzIyQlhYGDIyMnDnzh2h4tNjjrWyi1wV50uAW2r+MEDaY9cHz8Lc0gF/+SAfkZtvY9qyI+jpOQ4yHiPRaWvWrMGSJUvw6NEjvP322/D29saWLVsalTYAXLt2De+//z7c3NyQnJwMExMT2Nvb4/Lly6IubUCLi3v27NlYuXIlIiIisGfPHkybNg3h4eEoLCzEkCFDAAA5OTmQSqWNBiF4eHigpqYG58+fFyI6PUYmA4rKNbPuKxpar67Q1utB37tdjsqSfAwcMxfGZl0hkUjQxcYZnmPmwsDQWOh4JJAXX3wRf//73/Hw4UNMnjwZcXFxqK2tbXU5CwsLDB36511a7Ozs0K1bN01G1TitLO7k5GRs3boVaWlpeOuttxAUFISYmBgMHz4cNTU1GDx4MACgoqICVlZWjZa3trZueJyEdfu+fDS4Jly7qZn16orc3FyhIzTJtIsNbJyl+HHz68g7+AXKr57jlraOs7S0xMaNGwEAixcvVvow6JPHtP/73//C1NQUn332mSbjapxWHuOOjY3F+PHjERAQoDDd1dUVhoaG8PT0bNP63n33XWzbtg0XLlzA9u3b1X4f4pZOO9B1Xe36YOaHFxSmtTZyvLnHF32l+PPyle9j7PbodqRTj4X/kZeKNr0PFi9e3Oo8CQkJrc6XkJCgrkgNXoo5AGe3wFbmycTJ9LU4tTcR5cU5MDa3xKCQNzBs8lKFf2d9QxNYOQxQ6nmzsjLxt7FBGsv8pKO7VuFE+hqFaY/uV6OnR3Cb1tOe3KqIiksCIH8/P/69kGbPng07OzscPHiwocBb82RpBwcHQyaTYcyYMfDz84O/vz9+/vlnhWWysrIEe61t+XCqdVvcxcXFyMnJwdSpUxs9VlRUBKlUCmNj+e4ya2vrJo9T1G9p1295jx8/Hnv37uW1mQVQV/NQY+uurdHQpjwJzrSLLfxejsUrq05i7qabGBkWj6Pf/hPnfv63wnzmlvbweWGJQClbNmxSDCI33VT4cuw3UuhYohQZGQkAWL16tVIF11RpV1ZW4ubNm/j0008V1ilGWrfFXVxcDACwt7dXmH7v3j1kZWU1jB4HAKlUirS0NMhkMoVPSbm5uTAwMMCAAfJP4iNGjNBoZu7Ga15dHbBkO/DwsUNRT24516vf0m7u8Set/3A5huxY3q586lCfV5veB8qM70hISGgY6NmctWvXqitSg08y2nZva0NjM7j7z8Tp/Z/gxu/ZKj9vQEAgUt9T7f9RWzOrU3tyq2LJ6k0A5O/nx7/vKIGBgQrjL3r16oU+ffqgvLwce/bsaXX55kq73hdffIFly5ZhzJgxjZYNCAhAZmamWl6HJmndFretrS0AoKCgQGF6fHw8SkpKGgamAcCkSZNQVlaGffv2NUx79OgRtm3bhuDgYJibm3dMaGqWnh7gZK2ZdffQ0Hp1xYoVK4SO0KT7dypx+Ou3UXYlB7U1j1BXW4Pfju5AeXEOnPqPEjoedbD6MU3Hjh1DXV1di/O2VtoAUFhYiPLycnTr1g09evTQWG5N0rotbhcXF3h6eiI2NhbW1tZwcnJCampqw2CEx4t74sSJGDVqFGbNmoX4+Hg4ODhg3bp1KCoqQnJyslAvgZ4wqAdwSc03onLoCnTrot516ppp06YJHaFJ+vpGuHurFN9/NAV3bpZAT88AT3V7GgHTP0bfZxofQqPOzcnJCQBw8eLFFudTprTrXbhwATY2NnB0dMSVK+24DrNAtK649fT0kJKSgoiICERGRsLGxgYzZszA/PnzER0drTAwTSKRIC0tDVFRUXjzzTdRXV0Nb29v7N+/X6HgSVjDXIDvTwOPWj9zQ2l+/QAtGgsmSm5ubsjLyxM6RiOGJuYI+esWoWO0S+jSzDZNp+Zt3LgRX3zxRatb2127dsVTTz2l1MVVxo0bh9raWtFe60PrihsA+vXrhwMHDihMmz59Otzd3WFqaqow3dLSEklJSUhKSurIiNQGZsZAiBRIP6Oe9dk9BTzTRz3rIiLtVltb2+QFVp6Ul5eHgIAAlJaWtnpxlaqqKnXFE4TWHeNuzvHjx1Xein7nnXfg7OyMI0eOICIiAs7Ozq3udiH1GiNVzzFpPQkQPhww1G//uoioc8nPzxf1FdGUJYrirq6uRkFBQcMghbZauXIliouL8eDBA5SXl6O4uBh9+nCTrSPp6wGvBwC2LRyXXvRVyyPKJQBeHQ48bav2eDopMDBQ6AhEpAKt3FX+JAsLC6UubUfarasZ8EYI8MWhtp9aY2YEhPsCA8U5CFQrKXshCyLSLqLY4qbOo6spMD8YeGko8JRJ6/PrSYAhTwNvP8/SVjcxX4CCSJeJYoubOhc9CTCqPzCiL3D2CnDuGlBcAZRXy29KYmYMOFkBvbsBPr3lW+qkfmK40AQRNcbiJsHo6wFeveRfRESkHO4qJyIiEhEWN5GO0saLrxBR67irnEhHbd++XZDLnjpZdfhTtvt5hcos9HMLwcvLq83LFBaVAABcejoofN8Rzy0EFjeRjlq2bJkgxT1laIc/ZbuJMbNYJSYmtnmZ+ruYxUXNUfi+s+KuciIiIhFhcRMREYkIi5tIR23YsEHoCESkAhY3kY6SSqVCRyAiFbC4iXRUQECA0BGISAUsbiIiIhFhcRPpKB8fH6EjEJEKWNxEOurYsWNCRyAiFbC4iYiIRITFTUREJCIsbiIdlZqaKnQEIlIBi5uIiEhEWNxEOio0NFToCESkAt4djIg61DfHgauVHf+8Tlaq3+Vr0aJFyM7OVmseZXl5eal0xyzqvFjcRNShrlYCF0uFTtE22dnZyMrKEjoGEQDuKifSWfPnzxc6AhGpgMVNpKMWLFggdAQiUgGLm0hFD2uAovI/f759X7gsqvD39xc6AhGpgMe4idrgzgPgaCFwrBAoqQJksj8fe2cHYGkGePYA/PoCdl2Fy6mMGzduCB2BiFTA4iZSQp0MOFwAfJct39Juzs27wM/58i/fPsCkwYCpUYfFJCIdwOImasWDR8C/DwLnS9q23P8uypeJCAIcLDUSrV3c3d2FjkBEKuAxbqIWPKwBkg60vbTr3bwLfJIBXK9Sby512LFjh9AR6Aldu2r58RXSCqIv7qqqKsydOxfdu3eHmZkZ/Pz8cOjQIaFjUSexOxsobOVQcOKr8q/m3H0IfH4QqKlVa7R2e/fdd4WO0ClJJBKEhIRg1apV2Lt3L06fPo3s7Gzs3bsXq1atQnBwMCQSSaPl5s2bh/z8fEilUgFSk5iIurhlMhkmTZqEnTt3Ys2aNUhLS4OtrS1CQkJw6tQpoeORyF26ARzMV8+6SqqA/TnqWZe6pKSkCB2hU5FIJJgzZw5+++037N+/H9HR0Rg3bhw8PT0xaNAgjBs3DtHR0cjIyEBBQQH++te/NhT4vHnzsH79etjZ2WH48OECvxLSdqI+xr17925kZWUhPT0dEyZMACA/xUUqlSImJgbp6ekCJyQx+yEXkLU+m9J+zgfGuAPGhmpcqQ5IfS8QPT2CMWzyUqWmC8HZ2RlffPEFgoKCAACXL19GcnIyjh49ikuXLkEikeDpp5/GsGHD8Morr8DV1RWbNm1CWFgYfvzxR6xatQqA/Nz6zZs3C/lSSAS0dou7rq4Oa9asQd++fWFiYoJBgwYhKysL/fv3x5w5cwAAu3btgo2NDcaPH9+wnJGREcLCwpCRkYE7d+4IFZ9ErqIaOHdVveu8/wg4cVm96yThubi44PDhwwgKCkJpaSnCw8PRp08fREdH49tvv23YVf7tt98iOjoaLi4uCA8PR2lpKUaPHq1Q2uvXrxf41ZAYaG1xz549GytXrkRERAT27NmDadOmITw8HIWFhRgyZAgAICcnB1KptNHxIg8PD9TU1OD8+fNCRKdO4Lc/1Lu1Xa/gugZWqiJee7v9LCwssG/fPvTs2ROHDx+GVCrFtm3bUFdX1+wydXV12LZtGz788MOGaaWlpdi6dWsHJKbOQCuLOzk5GVu3bkVaWhreeustBAUFISYmBsOHD0dNTQ0GDx4MAKioqICVlVWj5a2trRseJ1JFsYbeOpparypyc3OFjiB68fHxcHV1xenTpzF+/HiUlZUptdy8efOwevVqAMDVq1fRvXt3xMXFaTIqdSJaeYw7NjYW48ePR0BAgMJ0V1dXGBoawtPTU+l1VVZWYvr06SgoKICpqSns7OywYcMGuLq6qi1vUyNESdyeW7gDrj5TFKa1NHK8pccXffXn99cr7kEiMWtnutYtXry41XkSEhJanS8hIUFdkRq8FHMAzm6BbVrm6K5VOJG+RmHao/vV6OkRrPQ6srIy8bexQW163pZIpVJERkbi4cOHeO2111BdXa3UcvUD0QD57vGDBw/i+PHjWLBgATZs2IC8vLwncmd16N+YqLgkAPK/a49/r83EmPlJMpny+/i0bou7uLgYOTk5mDp1aqPHioqKIJVKYWxsDEC+ZV1Z2fjGvvVb2tbW1pBIJFi0aBEKCgpw+vRpPP/885g1a5ZmXwSJn8Z+6cX1x0RbDJsUg8hNNxW+HPuNFDRTZGQkAGDz5s3IyVHulIEnS3v9+vU4c+YMtmzZorBOopZo3RZ3cXExAMDe3l5h+r1795CVldUwehyQf+JNS0uDTCZT+HSVm5sLAwMDDBgwAObm5ggO/vNT+YgRIxAfH6/WzG35pETi8PWvwJELitMe33J+XP2WdnOPP87W0qRD3i/KjO9ISEhoGOjZnLVr16orUoNPMoS5H3dAQCBS31Pt3z4wMLDRmICwsDAAwMaNG5VaR1OlXW/jxo2YO3cuwsPD8be//e2J3AHIzMxUKbcqlqzeBED+d+3x77WZGDO3h9Ztcdva2gIACgoKFKbHx8ejpKSkYWAaAEyaNAllZWXYt29fw7RHjx5h27ZtCA4Ohrm5eaP1JyYmYvLkyZoJT52Gc+OhE+pZr7Vm1quKFStWCB1BtHr37g0bGxtcv35dqa3tlkobAM6cOYMbN27A1tYWvXr10khm6jy0bovbxcUFnp6eiI2NhbW1NZycnJCamtpwTvbjxT1x4kSMGjUKs2bNQnx8PBwcHLBu3ToUFRUhOTm50bpXrFiBCxcu4Keffuqw10Pi1MdOM+t16aaZ9api2rRpQkcQrfqrm50+fbrVeVsr7XrZ2dkICQmBVCrF77//rr6w1OloXXHr6ekhJSUFERERiIyMhI2NDWbMmIH58+cjOjpaYWCaRCJBWloaoqKi8Oabb6K6uhre3t7Yv3+/QsEDwHvvvYfdu3cjIyMDZmaaHxxE4mbfFejdTX71NHXR1wOGuahvfe3l5ubWaCCUNgpdmtmm6R3h4sWLWLFiRaM9g0/y8PBQqrQB4PPPP8cvv/yCwsJCtWalzkfrihsA+vXrhwMHDihMmz59Otzd3WFqaqow3dLSEklJSUhKSmp2fStWrEB6ejoyMjJgaWmpicjUCQW5qbe4h7kAFibqWx8JJy8vD8uXL291vpycHCxcuBC1tbWtXlzlq6+UGCRBBC0t7qYcP34cvr6+bV4uNzcXy5cvR58+fRAYGNgwPTs7W33hqFPy7AEM6gmcLmr/urqaAhO9278eEp+PP/5Y6AjUyYiiuKurq1FQUIB58+a1eVmpVNqpRxeSZk31Aa5VAjduNz9Pa6PJDfSA6X6AmZF6s7XX4x9kiUg8RFHcFhYWqK3Vsnsikk6wMAHmBwMbfwT+uNX25Q31gf/zB1w1NNitPZQ9jYmItIvWnQ5GpG0szYA3JwCj+rVtOZduwD+eA9wcNZOrvXixDyJxEsUWN5HQjA2Al3wAX1fgUIH8Ll8PaxrPJwHQ3wHw6wtInQE9Lb5QWkde1IOI1IfFTdQGTlbAy88AoT7A9Sr58e8HNfJTvbo/JX/chPfbJiINYnETqUBfT17SThq6whoRUXN4jJtIR4nh4itE1BiLm0hHbd++XegIRKQC7ion0lHLli0T5HrlQh1eaM/zenl5qbRcYVGJws8uPR067Lmp82JxE1GHmjJU6ARtl5iYqNJy9beYrBcX1fJtVImUwV3lREREIsLiJtJRGzZsEDoCEamAxU2ko+rvKU1E4sLiJtJRAQEBQkcgIhWwuImIiESExU1ERCQiPB2MqBMaMGBAq/MsW7ZMqfmISLtwi5tIRy1fvlzoCESkAhY3ERGRiLC4iYiIRITFTUREJCIsbiIiIhFhcRMREYkIi5uIiEhEWNxaZuzYsfDy8sLAgQMRGhqKW7duCR2JiDrYlStXMGbMGLi5uUEqleLtt98WOpJSMjMzIZVK4erqitdffx21tbVCR2rVwoUL4ezsDAMD8VzWhMWtZVJSUpCdnY2zZ8/C2dkZa9euFToSEXUwAwMDrF69Gnl5eTh16hQOHTqEXbt2CR2rRXV1dXj99deRkpKCCxcu4NatW/jPf/4jdKxWTZ06FcePHxc6RpuwuLVM165dAch/Ce7fvw+JRCJwIiLqaA4ODhg6dCgAwMjICN7e3igqKhI4VcuOHTsGR0dHuLu7AwBmz56NHTt2CJyqdSNHjoS9vb3QMdqExa2FXnzxRXTv3h35+fn4+9//LnQcIhJQRUUFvv32W4SEhAgdpUXFxcXo0aNHw889e/bElStXBEzUeYlnp74O2blzJx4+fIjZs2cjNTUVM2fOFDoSESlh949HcLHoWrOPf/TvP7dA+/RyxPOjh7e4vocPHyI0NBQLFy7U2HXlr/1RhpT0rEbTH89a/71EAvxlyjhYPmXRaH6ZTKaRfE2RyWTY/n0mrt+oUJjeVGYAGOTWB4G+Xh0VT+O4xa2ljIyMEBYWhp07dwodhYiUNGRgP1y/UYGS0nKUlJY3erx++vUbFRg6sH+L66qtrcUrr7wCLy8vje55c7SzRRdzs0aZn/y+pLQcTnbdmixtAOjRo4fCFnZRURGcnZ01klkikWCIRz+lMpdVVsFb2lcjOYTC4tYit2/fRklJCQD5Me60tDRIpVKBUxGRshy622DYoNa3jJ/xcoN9N+sW55kzZw66dOmCDz/8UF3xmvX8aF/otTKextjIEGP9hzb7+NChQ1FcXIxz584BALZs2YIpU6aoNefjXJ92gptrr1bnC/T1Qtcu5hrLIYROX9zXrl1DeHg4rKysYGFhgXHjxiE3N1foWE26ffs2XnjhBXh6esLT0xM1NTVYunSp0LGIqA1CRg2FsZFhs4+bGBshZGTzBQgAhw8fxmeffYbjx4/D29sbXl5e+Pjjj9UdtUF3Wyv4DnZvcZ7RI7zRxdys2cf19fWxefNmhIaGok+fPrCwsMD06dPVHVXBc0G+0Ndrvsa6djGHv49ni+uIiIiAs7Mzamtr4ezsjPnz56s7ptpJZB15YKKD3bt3D97e3qirq0NsbCzMzMwQGxuL8+fPIzs7W2O7cTRBJpNxhDmRSPx89AzSD/yvyceeG+2LUa2UiRDu3LuPNZu+xr37Dxo9Zm3ZBW/OngYDA30BkrXs+5/+h4PHzjT5WPjE0Rjk7trBiTSvU29xb968GQUFBdi5cydCQ0Px7LPP4rvvvkNNTQ1iY2OFjtcmX+8+gH0/HxM6BhEpYcQQKWysnmo03da6K4YP1s7DX+amJgj2G9LkY88G+mplaQPyPQHmpiaNpvdysoOnWx8BEmme6Iv77NmzeOmll2BrawsTExP07dsXMTExAIBdu3bB29tb4TixlZUVJk6cKKpBXyWl5cg+d6HVY1BEpB0M9PXxbJBvo+nPBfnCQF87CxAAfL3d0c3aUmFa7x4OkPZ7WpA8yjA1MUbIqMaHHp4fM7zT7qUUdXGfOHECvr6+yM3NxQcffID09HQsWbIE169fBwDk5OTAw8Oj0XIeHh64fv06yssbj/rURj8ePgljI0P4+QwUOgoRKcndtRf69HJs+Lnv004Y0KengIlap6+vh+dH//mBQwJxFKDPoAGws7Vq+HmwR1/0cOguYCLNEvUx7sDAQJw7dw6//fZbwxXHHmdkZIR58+YhMTFRYfq//vUvzJkzBwUFBejbt/2nCSxZvand6yAiIt0VFzVH6XlFu8V99+5dHDx4EOHh4U2WNhERUWck2iunVVZWoq6ursWR4dbW1qisrGw0vaKiouFxdWjLJ6W2KCktx0f/3oExIwY3eQyHiLRf9Z17kEgkMDdrPIBKm/1RVqmw+1kMKm7eQhdzMxgairbalCLaV2dlZQU9PT1cvXq12XmkUmmT52zn5ubC3t4eNjY2asmi6V3lP/5yEj/+clKjz0FERMLRiV3lZmZm8Pf3R3JycrP3rJ40aRJOnjyJvLy8hmk3b97Ed999h8mTJ3dQUiIiIvUR9eC0EydOwN/fH7169cI//vEP9OrVC0VFRTh48CA2b96Mu3fvwsvLCxKJROECLOfOnUN2drbCnWy0zX92ZuC3y8WIinwFZibGQschIiItIdotbgAYMmQIjhw5gr59+2Lx4sV49tlnsWrVKjg6yk/BMDMzw4EDB+Dl5YXZs2cjNDQUpqamyMzM1OrSLiktR07BJYwcOpClTURECkS9xd1Z5RZcxvcHjmDBjCksbiIiUsDi1lJ1dXXQa+Hi+UREpJtY3ERERCLCTToiIiIRYXETERGJCIubiIhIRFjcREREIsLiJiIiEhEWNxERkYiwuImIiESExU1ERCQiLG4iIiIRYXETERGJCIubiIhIRFjcREREIsLiJiIiEhEWNxERkYiwuImIiESExU1ERCQiLG4iIiIRYXETERGJCIubiIhIRFjcREREIsLiJiIiEhEWNxERkYiwuImIiESExU1ERCQiLG4iIiIRYXETERGJCIubiIhIRP4fx9cLG6UhxCcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 635.358x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q, c) #create a new Quantum circuit\n",
    "\n",
    "#creates GHZ-state\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.cx(q[0],q[1]) #entangle the first two qubits\n",
    "qc.cx(q[0],q[2]) #entangle the first and the last qubit\n",
    "qc.barrier() #visual seperation (optional)\n",
    "\n",
    "#TODO: apply gates according to the question above - choose the right ones\n",
    "qc.sdg(q[0]) #apply sdg-gate to the first qubit\n",
    "qc.h(q[0]) #apply H-gate to the first qubit\n",
    "qc.sdg(q[1]) #apply sdg-gate to the second qubit\n",
    "qc.h(q[1]) #apply H-gate to the second qubit\n",
    "#qc.sdg (q[2]) #apply sdg-gate to the third qubit\n",
    "qc.h(q[2]) #apply H-gate to the third qubit \n",
    "\n",
    "#Hint: only h-gate for x-value, both gates for y-value\n",
    "\n",
    "\n",
    "qc.measure(q,c) #create measurement gates for all qubits\n",
    "qc.draw(output='mpl') #draw the circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To check your answer return to the previous slide."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Copy the following code in the cell above:\n",
      "\n",
      "\n",
      "qc.h(q[0])\n",
      "qc.sdg(q[1])\n",
      "qc.h(q[1])\n",
      "qc.sdg(q[2])\n",
      "qc.h(q[2])\n"
     ]
    }
   ],
   "source": [
    "# prints out the correct code for your questions\n",
    "correctAnswer(question)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "You: \n",
    "\"*Cool it works, and with this Quantum strategy the team can always win, no matter which question is asked. But still I don't really understand why and how?!*\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Background Information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Entangled qubits have a strong dependency. Therefore, their states cannot be described individually but only in a correlated manner.\n",
    "In the GHZ state, for example, when performing an XXX-measurement only the results $\\;\\; |000\\rangle, |011\\rangle,  |101\\rangle $ and $ \\;\\;|110\\rangle $ occur.\n",
    "The fascinating thing is each qubit when observed individually (for example when only looking at the first qubit), behaves perfectly random. But when considering the whole system a dependency becomes obvious. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A commonly known entangled state is the Bell state.The state can be $\\;\\frac{|00\\rangle + |11\\rangle}{\\sqrt{2}}\\;\\;$. When measuring the first qubit in state 1 we can already say with certainty that the result of the second measurement will also be 1, as a state with mixed results cannot occur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "But let's go back to our Experiment. We remember the GHZ-state from above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 394.558x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(q,c)\n",
    "ghz_state(qc,q).draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Which outcomes do you expect when executing this circuit, using the z-axis as measurement basis?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) All 8 possible states equally mixed (|000>, |001>, |010>, ..., |110>, |111>)\n",
      "(b) A random distribution across all 8 states (|000>, |001>, |010>, ..., |110>, |111>)\n",
      "(c) Measurement result in 50% is state |000> and in 50% is state |100>\n",
      "(d) Measurement result in 50% is state |000> and in 50% is state |111>\n",
      "\n",
      "No, try again!\n"
     ]
    }
   ],
   "source": [
    "quiz()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now try it out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(simulate(qc, q, c, 100)) # Visualise the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Interestingly the only results that you get are either $ \\;\\;|000\\rangle $ or $ \\;\\;|111\\rangle $ with roughly 50/50 probability (Increase the number of shots to get more accurate results - closer to 50%).\n",
    "This is because q0 is brought into a superposition. In case it is 0 the two CNOT gates do not change the value of the other two qubits. If it is 1 both of the other values (which initially were 0) are flipped to 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This becomes obvious when looking at the state which can be written as $\\;\\;|GHZ\\rangle=\\frac{|000\\rangle + |111\\rangle}{\\sqrt{2}}\\;\\;$ and only consists of these two basis states."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And why can it be used to answer the questions of the experiment above?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When measuring on the XXX-basis, we apply a Hadamard-gate to each of the qubits.\n",
    "A Hadamard-gate can be described with the following matrix:\n",
    "\n",
    "$$ H=\\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to apply the H-gate 3 times (one time on each qubit) we can use the tensor product. For the tensor product A⨂B each block aij*B is calculated. For the tensor product of three Hadamard gates this means:\n",
    "$$ H⨂H⨂H=\\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} $$\n",
    "$$=  \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} H & H \\\\ H & -H \\end{pmatrix}=   \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} ⨂\\frac 1 {2}\\begin{pmatrix} 1 & 1 & 1 & 1 \\\\ 1 & -1 & 1 & -1 \\\\ 1 & 1 & -1 & -1 \\\\ 1 & -1 & -1 & 1 \\end{pmatrix}$$\n",
    "$$= \\frac 1 {2\\sqrt{2}} \\begin{pmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\\\ 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\\\ 1 & 1 & -1 & -1 & 1 & 1 & -1 & -1 \\\\ 1 & -1 & -1 & 1 & 1 & -1 & -1 & 1 \\\\ 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\\\ 1 & -1 & 1 & -1 & -1 & 1 & -1 & 1 \\\\ 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\\\ 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1\\end{pmatrix}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The states $ \\;\\;|0\\rangle $ and $ \\;\\;|1\\rangle $ can also be represented by the vectors $ \\;\\;|0\\rangle=\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}|1\\rangle=\\begin{pmatrix} 0 \\\\ 1 \\end{pmatrix} \\;\\;$\n",
    "\n",
    "Therefore, the GHZ state can also be represented as a vector:\n",
    "$$|GHZ\\rangle=\\frac{|000\\rangle + |111\\rangle}{\\sqrt{2}} = \\frac{|0\\rangle |0\\rangle |0\\rangle+ |1\\rangle |1\\rangle |1\\rangle}{\\sqrt{2}} $$\n",
    "$$ =\\frac {\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}⨂\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}⨂\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}+ \\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}}{\\sqrt{2}}$$\n",
    "$$ =\\frac {\\begin{pmatrix} 1 \\\\ 0\\end{pmatrix}⨂\\begin{pmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 0\\end{pmatrix}+ \\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 0\\\\ 0\\\\ 1\\end{pmatrix}⨂\\begin{pmatrix} 0 \\\\ 1\\end{pmatrix}}{\\sqrt{2}}$$\n",
    "$$ =\\frac 1 {\\sqrt{2}}\\left( {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 0\\end{pmatrix}+ \\begin{pmatrix} 0 \\\\ 0\\\\ 0\\\\ 0 \\\\0 \\\\0\\\\ 0\\\\ 1\\end{pmatrix}} \\right)\n",
    "= \\frac 1 {\\sqrt{2}} {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 1\\end{pmatrix}}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When applying three Hadamard-gates to the GHZ state:\n",
    "$$\\frac 1 {2\\sqrt{2}} \\begin{pmatrix} 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\\\\ 1 & -1 & 1 & -1 & 1 & -1 & 1 & -1 \\\\ 1 & 1 & -1 & -1 & 1 & 1 & -1 & -1 \\\\ 1 & -1 & -1 & 1 & 1 & -1 & -1 & 1 \\\\ 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 \\\\ 1 & -1 & 1 & -1 & -1 & 1 & -1 & 1 \\\\ 1 & 1 & -1 & -1 & -1 & -1 & 1 & 1 \\\\ 1 & -1 & -1 & 1 & -1 & 1 & 1 & -1\\end{pmatrix}*\\frac 1 {\\sqrt{2}} {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 1\\end{pmatrix}}= \\frac 1 {4} {\\begin{pmatrix} 2 \\\\ 0 \\\\0 \\\\2 \\\\ 0\\\\ 2\\\\ 2 \\\\ 0\\end{pmatrix}} $$\n",
    "$$= \\frac 1 {4} (2*|000\\rangle+0*|001\\rangle+0*|010\\rangle+2*|011\\rangle+0*|100\\rangle+2*|101\\rangle+2*|110\\rangle+0*|111\\rangle)$$\n",
    "$$= \\frac 1 {2} (|000\\rangle+|011\\rangle+|101\\rangle+|110\\rangle)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected only the results with an even number of ones occur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When measuring a Y-value we need an additional gate: $$ S^†= \\begin{pmatrix} 1 & 0 \\\\ 0 & -i \\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the YYX-measurement we would apply the sdg-gate to qubit 0 and 1 follwed by a Hadamard-gate on all three qubits. Therefore the following needs to be caluclated:\n",
    "\n",
    "$$HS^†⨂HS^†⨂H$$\n",
    "$$=\\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}\\begin{pmatrix} 1 & 0 \\\\ 0 & -i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix}\\begin{pmatrix} 1 & 0 \\\\ 0 & -i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} $$\n",
    "$$= \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & -i \\\\ 1 & i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & -i \\\\ 1 & i \\end{pmatrix}⨂ \\frac 1 {\\sqrt{2}} \\begin{pmatrix} 1 & 1 \\\\ 1 & -1 \\end{pmatrix} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When applying this measurement to the GHZ state:\n",
    "\n",
    "$$HS^†⨂HS^†⨂H *\\frac 1 {\\sqrt{2}} {\\begin{pmatrix} 1 \\\\ 0 \\\\0 \\\\0 \\\\ 0\\\\ 0\\\\ 0 \\\\ 1\\end{pmatrix}}= \\frac 1 {4} {\\begin{pmatrix} 0 \\\\ 2 \\\\2 \\\\0 \\\\ 2\\\\ 0\\\\ 0 \\\\ 2\\end{pmatrix}} $$\n",
    "$$= \\frac 1 {4} (0*|000\\rangle+2*|001\\rangle+2*|010\\rangle+0*|011\\rangle+2*|100\\rangle+0*|101\\rangle+0*|110\\rangle+2*|111\\rangle)$$\n",
    "$$= \\frac 1 {2} (|001\\rangle+|010\\rangle+|100\\rangle+|111\\rangle)$$\n",
    "\n",
    "only the results with an even number of zeros, and accordingly an even number of blue or rectangle, remain."
   ]
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    "\n",
    "## What does it change?"
   ]
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    "As we saw above, any strategy that is using pre-defined answers (i.e. \"local hidden variables\") cannot answer all four sets of questions correctly. But the procedure based on quantum mechanics and Entaglement, i.e. the GHZ state, was able to give a correct answer all the time. \n",
    "\n",
    "How can that be explained? \n",
    "\n",
    "The final pragraphs of Mermin's book \"Quantum Computer Science: An Introduction\" conclude: \"The best explanation anybody has come up with to this day is to insist that no explanation is needed beyond what one can infer from the laws of quantum mechanics. Those laws are correct. (...) One gets puzzled only if one tries to understand how the rules can work not only for the actual situation in which they are applied, but also in alternative situations that might have been chosen but were not. (...) A good motto for the quantum physicist and for future quantum computer scientists might be 'What didn’t happen didn't happen.'\""
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    "To learn more about Quantum Entanglement you can look at the Hardy's paradox here: https://mybinder.org/v2/gh/JanLahmann/Fun-with-Quantum/master?filepath=Hardys-Paradox.ipynb\n",
    "\n",
    "One use case entanglement is needed for is the so-called \"Quantum Teleportation\". You can learn what it is and find out more about Quantum Entanglement here: https://qiskit.org/textbook/ch-algorithms/teleportation.html"
   ]
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