task3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "Cohort 5 Screening Tasks\n",
    "\n",
    "Task 3 -  Find best results\n",
    "\n",
    "Tic - tac - toe\n",
    "\n",
    "\n",
    "X | O | O \n",
    "X | ? | ?\n",
    "O | ? | ?\n",
    "\n",
    "qubit representation will be\n",
    "\n",
    "q0 q1 q2\n",
    "q3 q5 q6\n",
    "q4 q7 q8\n",
    "\n",
    "\n",
    "Finding the winning combinations can be done by only one oracle call \n",
    "applying the grover search after that will rotate state of the system towards solutions linear combination vector\n",
    "and absolute values of amplitudes for the solutions eigenstates will be increased\n",
    "\n",
    "</pre>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make the necessary imports\n",
    "import matplotlib as plt\n",
    "import numpy as np\n",
    "from numpy import pi\n",
    "from qiskit import *\n",
    "import math\n",
    "from qiskit import Aer\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "from qiskit.circuit.library import QFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7fa0ae50b740>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create the circuit, we do not need to represent the previous filled qubits\n",
    "circuit = QuantumCircuit(5, 5)\n",
    "\n",
    "# we will use the grover search to find the solutions\n",
    "# put the 4 qubits we seek for the solution in superposition\n",
    "circuit.h(range(4))\n",
    "\n",
    "# and the last qubit to state |-> for the grover\n",
    "circuit.x(4)\n",
    "circuit.h(4)\n",
    "\n",
    "circuit.barrier()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "Grover search has two steps \n",
    "Step 1: Grocer oracle which flips the state that is a solution to the search, so using the phase kickback (addition mod 2)\n",
    "which leads to :\n",
    "</pre>\n",
    "\n",
    "$$\\ket{x}\\ket{-} \\xrightarrow[]{O} (-1)^{f(x)} \\ket{x} \\ket{-}$$\n",
    "\n",
    "<pre>\n",
    "where f(x) is 1 for the solutions, so the flip is done only for the solutions\n",
    "\n",
    "Step 2: Grover operator which performs a conditional phase shift for all computations basis vectors, except for 1st basis vector |0..0>:\n",
    "</pre>\n",
    "\n",
    "$$ U = 2 \\ket{\\psi} \\ket{\\psi} - I$$\n",
    "\n",
    "<pre>\n",
    "So the grover iteration will be combined to operator :\n",
    "</pre>\n",
    "\n",
    "$$ G = (2 \\ket{\\psi} \\ket{\\psi} - I) O$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# NAME: grover_oracle\n",
    "# DESC: Applies the grover oracle in the circuit\n",
    "def grover_oracle() :\n",
    "    # create the sub circuit that will be converted to a gate\n",
    "    circuit = QuantumCircuit(5)\n",
    "\n",
    "    # combination 3 x in the main diagonal\n",
    "    # qubits 0, 1 must be |1> and qubits 2, 3 must be |0>, thus the x gates\n",
    "    circuit.x([2, 3])\n",
    "    circuit.mct([0, 1, 2, 3], 4)\n",
    "    circuit.x([2, 3])\n",
    "\n",
    "    # combination 3 x in the middle row\n",
    "    # qubits 0, 1 must be |1> and qubits 2, 3 must be |0>\n",
    "    circuit.x([1, 2])\n",
    "    circuit.mct([0, 1, 2, 3], 4)\n",
    "    circuit.x([1, 2])\n",
    "\n",
    "    # convert to gate and return\n",
    "    return circuit.to_gate(label = 'Grover Oracle')\n",
    "\n",
    "# NAME: grover_operator\n",
    "# DESC: Applies the grover operator \n",
    "def grover_operator(nqubits):\n",
    "    circuit = QuantumCircuit(nqubits)\n",
    "    \n",
    "    # apply hadamard gates\n",
    "    circuit.h(range(nqubits))\n",
    "\n",
    "    # Apply transformation |00..0> -> |11..1> (X-gates)\n",
    "    for qubit in range(nqubits):\n",
    "        circuit.x(qubit)\n",
    "    \n",
    "    circuit.h(nqubits-1)\n",
    "    # multi-controlled gate\n",
    "    circuit.mct(list(range(nqubits - 1)), nqubits - 1)\n",
    "    circuit.h(nqubits-1)\n",
    "    \n",
    "    # Apply transformation |11..1> -> |00..0>\n",
    "    for qubit in range(nqubits):\n",
    "        circuit.x(qubit)\n",
    "    \n",
    "    # apply hadamard gates\n",
    "    circuit.h(range(nqubits))\n",
    "\n",
    "    # We will return the diffuser as a gate\n",
    "    gate = circuit.to_gate(label = 'Grover')\n",
    "\n",
    "    return gate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "Only one grover iteration is needed\n",
    "initial state of the system in the geometric intepretations is :\n",
    "</pre>\n",
    "\n",
    "$$\\ket{\\psi} = \\sqrt((N - M) / N) \\ket{a} + \\sqrt(M/N) \\ket{b} $$\n",
    "\n",
    "<pre>\n",
    "Search solutions are M = 2 and the number of eigenstates in the 4 qubit composite system are N = 16\n",
    "This means that angle between state and non solution state is approx 20.7 degrees\n",
    "oracle will send state 69 degrees above vector a axis\n",
    "then grover operator will send state to 3 * 20.7 / 2 = 31.1 degrees above vector a axis, closer to solution b vector\n",
    "\n",
    "Grover iteration needed are computed with the following formula and it turns out we need only 1.\n",
    "</pre>\n",
    "\n",
    "$$R = CI(\\dfrac{\\arccos(\\sqrt(M / N))}{\\theta}) = CI(\\dfrac{69.3}{31.1}) = CI(2.2) = 2$$\n",
    "\n",
    "<center>\n",
    "or\n",
    "</center>\n",
    "\n",
    "$$R \\leq \\dfrac{\\pi}{4} \\sqrt{\\dfrac{N}{M}} = 2.2$$\n",
    "\n",
    "So we need 2 grover iteration to get as close as possible to the search solutions vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1230.4x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2 grover iteration are needed\n",
    "grover_iterations = 2\n",
    "\n",
    "for i in range(grover_iterations) :\n",
    "    # apply grover oracle\n",
    "    circuit.compose(grover_oracle(), qubits = range(5), inplace = True)\n",
    "\n",
    "    # apply grover operatior \n",
    "    circuit.append(grover_operator(4), range(4))\n",
    "\n",
    "    circuit.barrier()\n",
    "\n",
    "# measure the 4 qubits we are interested\n",
    "circuit.measure(range(4), range(4))\n",
    "\n",
    "# draw the circuit\n",
    "%matplotlib inline\n",
    "circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# then we simulate the circuit and see the results\n",
    "simulator = simulator = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "# execute the simulation with 1000 shots\n",
    "result = execute(circuit, backend = simulator, shots = 1000).result()\n",
    "\n",
    "# get counts and print the histogram\n",
    "counts = result.get_counts()\n",
    "\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "After getting the results from the simulation, we see as expected only two solutions with higher probabilities\n",
    "the two cases are : X in the main diagonal and x in the middle row\n",
    "</pre>\n",
    "\n",
    "$$\\ket{1100}, \\ket{1001}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "If we were to start one step earlier and the oponent has not yest chosen, by this situation:\n",
    "\n",
    "X | O | O \n",
    "X | ? | ?\n",
    "? | ? | ?\n",
    "\n",
    "The new qubit representation will now be:\n",
    "X | O | O \n",
    "X | q0 | q1\n",
    "q2 | q3 | q4\n",
    "\n",
    "This means that we may have more winning probabilities which are based on opponents choise (entangled with the opponent choice)\n",
    "</pre>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7fa0a85f7780>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create the new circuit\n",
    "circuit = QuantumCircuit(6, 6)\n",
    "\n",
    "# put the 4 qubits we seek for the solution in superposition\n",
    "circuit.h(range(5))\n",
    "\n",
    "# put the last qubit in state |-> as previously for the phase kickback\n",
    "circuit.x(5)\n",
    "circuit.h(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# out new oracle is needed\n",
    "def grover_oracle2() :\n",
    "    circuit = QuantumCircuit(6)\n",
    "\n",
    "    # this winning case is when we have x in the middle row\n",
    "    circuit.x([2, 3, 4])\n",
    "    circuit.mct([0, 1, 2, 3, 4], 5)\n",
    "    circuit.x([2, 3, 4])\n",
    "\n",
    "    # this winning case is when we have x in the main diagonal\n",
    "    circuit.x([1, 2, 3])\n",
    "    circuit.mct([0, 1, 2, 3, 4], 5)\n",
    "    circuit.x([1, 2, 3])\n",
    "\n",
    "    # this winning case is when we have x in the 1st column\n",
    "    # this winning can have 4 different winning states \n",
    "    circuit.x([0, 1, 3])\n",
    "    circuit.mct([0, 1, 2, 3, 4], 5)\n",
    "    circuit.x([0, 1, 3])\n",
    "\n",
    "    circuit.x([0, 1, 4])\n",
    "    circuit.mct([0, 1, 2, 3, 4], 5)\n",
    "    circuit.x([0, 1, 4])\n",
    "\n",
    "    circuit.x([0, 3, 4])\n",
    "    circuit.mct([0, 1, 2, 3, 4], 5)\n",
    "    circuit.x([0, 3, 4])\n",
    "\n",
    "    circuit.x([1, 3, 4])\n",
    "    circuit.mct([0, 1, 2, 3, 4], 5)\n",
    "    circuit.x([1, 3, 4])\n",
    "    \n",
    "    return circuit.to_gate(label = 'Grover Oracle')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GjBkFLrd48WL9/ve/18SJE/O9Dtz169dzfLEOMJppSlxqaqoSExM1evToHPOnTZumadOmGZQKAGB2SUlJatGihUOfmwOciWlKnJeXFz9gAIBiwd8XmJFTfrEBAAAA+aPEAQAAmBAlDgAAwIQocQAAACZEiQMAADAhShwAAIAJUeIAAABMyDTXiTOKX+WyuW8AMJu7+T9NDx09IUnyr1crx+3i3i9QFChxBejb2ugEAABHxMTEFHqdyTPmS5JemzQix23ADDidCgAAYEKUOAAAABOixAEAAJgQJQ4AAMCEKHEAAAAmRIkDAAAwIUocAACACVHiAAAATIgSBwAAYEKUOAAAABOixAEAAJgQJQ4AAMCEKHEAAAAmVM7oAM4uNl46dt6YfftVlvq2NmbfAIDiN27cOCUkJBiy79DQUMXExBiybxQNSlwBjp2XDp4yOgUAoDRKSEiQzWYzOgZMitOpAAAAJkSJAwAAMCFKHAAAgAlR4gAAAEyIEgcAAGBClDgAAAATosQBAGAylSpVUrNmzRQUFKTq1avnu6yLi4sGDBhQQslQkihxAACYQHBwsN577z3t379fFy5c0E8//aQ9e/bo119/1bFjx7R06VJ16dIlxzouLi7629/+pqVLl+qll14yKDmKi1OXuKysLM2aNUuNGzeWh4eHQkJCZLPZ1KRJE40YMcLoeAAAFLvatWtr9erV2rlzp0aNGqWAgAClpaVp3759+umnn5SSkqLatWtrwIABWr9+vbZt26aQkBB7gRs0aJBSUlK0bt06o58KiphT/48Nw4cPV2xsrKZOnaqwsDBt3rxZgwYN0unTpzV+/Hij4+Vq+fQI1WveVW37vODQfPw2H3wxSVv2/UunLyTJw91L9zZ9SE89NEPenlWMjgYn4ug4SUzepiXro7Xn8EalXb+iShV81dgvTL06jlHLgC55bB0oPj169NCSJUvk4+OjlJQULVq0SB9//LF27dqljIwMSZLFYlHjxo01YMAAjRo1Sq1atdKPP/6oXbt2KSwsTCkpKerevbt++OEHg58NiprTHolbsmSJFi1apNWrV2vixImKjIzUlClT1L59e2VkZKhVq1ZGR4QTsFpdNHnQJ1rx8lnN++NOnbmYrNf/MdToWHAyjoyTbYlfa9w7HVW7aiO9MzZeq6df0vzxu9Wl5eP6fs/KXLebkXm9BNIbv08Y48EHH9Tq1avl4+Ojzz//XE2bNtXYsWO1fft2e4GTpOzsbCUmJmratGkKDAzU22+/LVdXV4WFhSktLY0CV4o5bYmLjo5Wjx49FB4enmN+QECAXF1dFRwcrPPnz6tnz54KDAxUSEiIunXrpgMHDhiUGEYY/mC0AvxaqpyLq3y8qumRTmO162Cc0bHgZBwZJ3Njo3R/qyf0dM+Zql65niwWizw9Kqpz8KN6ps9bkqQJ70Xo3c/G6aVFfdT7BW8tt81WZmaG/vb1Kxr8V3898mJlPTfvfh0+uUeSdOTkT3pwspsupJ627yc7O1uD/+qvr+I/liSlpV/RvM8nanB0Q/V9sYr+/EEPHTvzv99jue0TpV/dunW1dOlSubq6as6cOerVq5dOnDhR4HppaWmqWrWq/b6Hh4fc3d2LMyoM5JQlLjk5WXv27FH//v3veOzo0aMKCgqSu7u7LBaLxo0bp8TERO3cuVM9e/bUsGHDDEgMZ7HjwHr51w4xOgac3O3jJPl0oo6fPajI0EEFrrvuxwXq0+kPWjXtovp0+oP+aXtd32xbrFeHr9E/XjypFg07a/L8B3Q5LUUNagapUe1Qfbvj7/b1dx6MU8rlM7ov+MbvtzeWP62k0z9r7rM/6B8vnlTTevdq6oKeOY643b5PlH4ffPCBvL29tXLlSk2YMMGhdW7/DNyHH34oSVqwYIE8PT2LMy4M4rQlTpJq1qyZY/7Vq1dls9nsp1J9fHzUtWtX++MdOnTQ4cOHHdqHxWJxaLLZ4gqdf+tnr+q9ET45puOJmwq9HZstzuGcZWEq6L3YuGuF/vXD+xrd681Cv9YoOkaP27sZJzePlPlW8rPP2/zTavWZ6qPeUyvpd3/2sM/vHNxPLQO6yGKxyMPNU+t+XKgBkZNUr3pTuZVz1xNdX5TV6qIt+76QJHVvPUzrflxoX3/djwsVHjJAHm6eunj5jL7d8an+8Mi7qlyxhlzLuWnwAy/p7KUT+vnoljz3afRrnNd00+23nXkyOrPNZrtjjN57773q3r27zp8/r1GjRuU7nm+6vcB1795dUVFR2rlzp/z9/fXEE0/csY7NZjP89WfKe0w6wilLnK+vryQpMTExx/yZM2fqxIkTCgsLy3W9mJgY9enTp7jjFaht7ymKmn8hx1Q7sJPRsUo1285lemP503pl6Go1rsPnJZG7vMZJpQo3fuecuZBsn9chqJdWTbugV5/8Qtczrtnn16jcIMc2T19IUs3KDe33rVaralRuoNMXkiRJkS0HKfl0ovYnb9eVtEvatHuFerR5UpJ08tyNf3SOmBOsPlN91Geqj/q+VEWZmdd16r/r57ZPlG6jR4+WJM2bN0+nTp0qcPncCtwPP/ygjIwMzZgxI8c2Ubo45bdT/f39FRwcrOjoaFWpUkV+fn5avny51qxZI0m5lriXX35ZBw4c0LfffuvQPrKzsx1a7q2vpYMF/wwVi/DwCC2f7ljOsiB+qXTL31i7tT8u1PzPJ+iVYZ+recOOJR8MOYSHRyj7PePG7d2MkzrVAlWrir827FyqVoFd71z5FlZLzn/7VvOpq5Pnj9jvZ2Vl6dfzR1TNp64kyau8jzo076Ov4hfJv3aIqlWup2YN2kuSqleuL0laNGm/fLyqObxPo1/jvEyeMV/Sjd+vt952ZkZnjoiIuONoXPfu3SVJCxcuzG2VHPIqcDetWLFCly5dUkhIiGrUqKFff/3V/lh4eLji4uKK5onAEE55JM5qtWrZsmUKCgpSVFSUhg0bJl9fX40ZM0YuLi4KDg7Osfz06dP1r3/9S2vXruW8fxmzctNczf/XRP316XUUOOSpoHFisVj07CPvaP22v+mDLybp1IUkZWdnKy39ivbdclozN91aD9U/42Yq+XSirmek69P1ryozM0P33vOQfZnurYfp2x2fas0P89W99f8+t1vZq7q6tHxcc1eO1pmLxyRJqVcvaNPulbp6LbWInj3MxM/PTzVq1NC5c+fuOBt1u4IKnCSlp6dr27ZtknI/AAJzc8ojcZIUGBioDRs25Jg3ePBgNWvWTOXLl7fPe/nll7VmzRp9/fXX8vHxKeGUMNq7n42Vi7WcJr4fmWP+56/yBxD/48g4adO0h94Ys0lL1kdrdEwrXUu/Ih+v6mrk11Kvj8z7CP9jEc/pesY1Tf6gmy6nXVSj2qF67emvVMHD275Mq8Zd5e7mqcRj2/Ty0M9yrP/Hfh9oybfRmvB+hM5fOikvDx81b9hZYU26FdGzh5nUq1dP0p0fJ7qdIwXupl9++UURERH2baP0cNoSl5v4+Hi1a9fOfv+nn37SX/7yFzVq1EgRERH2+QkJCSUf7r/6vRBXqPn4bb5+3blP1cA5ODpOmtRto78Mzf2acJI0OyrujnnlXFw1pPvLGtL95TzXs1qt+nTK0Vwf83Dz1LAe0zWsx3SH94nSa8eOHQoMDFRmZma+y1WtWlVt27Z16EK+r7zyit544w2HLlECczFNiUtNTVViYmKOD2cGBQU5/ectAABwVFpamvbv31/gcqdOnVJkZKRq1aqlrVu35rvs8ePHiyoenIxpSpyXl1eB/zIBAKCsSEpKUlJSUsELotRyyi82AAAAIH+UOAAAABOixAEAAJgQJQ4AAMCEKHEAAAAmRIkDAAAwIUocAACACZnmOnFG8atcNvcNACh+oaGhd7XeoaM3/vcF/3q1ctwuiX3DeVDiCtC3tdEJAAClVUxMzF2tN3nGfEnSa5NG5LiNsoXTqQAAACZEiQOQp8Vf/UV/mtfV6BgAgFxwOhVlQmLyNi1ZH609hzcq7foVVargq8Z+YerVcYxaBnQxOl6BsrKyFLsxRmt//Egnzx2Wm2t5hfhHaGiPaapfo5nR8QAABuBIHEq9bYlfa9w7HVW7aiO9MzZeq6df0vzxu9Wl5eP6fs/KPNfLyLxeginz3+esfw7Tio1zNOrhN7TylQv6YMIeVa5YQ8++da8OHd+V6zrZ2dnKzMwozrgAAANxJA6l3tzYKN3f6gk93XOmfZ6nR0V1Dn5UnYMftc+b8F6EGtUO1a/njyjhwLca1OV59Q+fqE+/jdZX8YuUevW8AvxaaXTvN9WwZnMdOfmTomJaaskLx+TjVU3SjeL0f6810uAHXlK31kOUln5FH697UZt2r9DltItqUretnnnkbfn5BuS5z4FdJufIv+fwJn29bbFmjYpTSKNwSVJV71r6Q993dfTUPr3/+XjNHPmNJOmB5yyK6hWjb7b/Tf85+ZNeH7VBaemXtfDL55V8JlEu1nJqGXC/RveZq8pe1SXdKI7/jHtdX2/7WGdTjsunQnU99dAM3Rfc747XsqDnAwAoORyJQ6mWfDpRx88eVGToIIeWX/fjAvXp9AetmnZRfTr9Qf+0va5vti3Wq8PX6B8vnlSLhp01ef4DupyWogY1g9Sodqi+3fF3+/o7D8Yp5fIZ3RfcX5L0xvKnlXT6Z8199gf948WTalrvXk1d0DPHEbfb93m7LT+vUbVKdewF7lb3t3pCOw/F6dr1q/Z5a7d+pBd+/w+tfjVVAX4t5VbOXc888raWv3Ra88fv1tmU43r3s7H25ReufUHrt3+iqU8s02fTUjQ7yqY6voG5vj6OPB8AQMmgxKFUu5B6WpLkW8nPPm/zT6vVZ6qPek+tpN/92SPH8p2D+6llQBdZLBZ5uHlq3Y8LNSBykupVbyq3cu56ouuLslpdtGXfF5Kk7q2Had2PC+3rr/txocJDBsjDzVMXL5/Rtzs+1R8eeVeVK9aQazk3DX7gJZ29dEI/H92S5z5vdzH1tKrekv9WVb1rKysrU5eunLPP6x8+UbV9G8nF6iK3cu5q3rCTmtRtIxeXcqriXVOPRfxJCfvXS7px5HD15nc0oufr8q8dLIvFomo+deRfO/jOHA4+HwBAyeB0Kkq1ShV8JUlnLiSrXvWmkqQOQb20atoF7Tm8SX98t3OO5WtUbpDj/ukLSapZuaH9vtVqVY3KDXT6QpIkKbLlIL3/+XjtT94uP9/G2rR7hWaMuHFq8+S5w5KkEXNyFqLMzOs69d/1c9vnHc/Bq5rOXjyW62NnU47LanVRRc8q/9telZzbS0zepgVfPq9Dx3fq2vUryla2rl5LlSRduHxaaemX5ZfHkbdbOfp8AAAlgxKHUq1OtUDVquKvDTuXqlVgwZfKsFpyHpyu5lNXJ88fsd/PysrSr+ePqJpPXUmSV3kfdWjeR1/FL5J/7RBVq1xPzRq0lyRVr1xfkrRo0n77Z+Yc2eft2jTpoaXf/lW7D21UC/+cpfPbHZ8q2D9c7q7l89zeq38fqPta9NPUwctUwcNbP+z9l6YufFiS5FOhmjxcPXXszH7VqdY43xyOPh8AQMngdCpKNYvFomcfeUfrt/1NH3wxSacuJCk7O1tp6Ve0z4FTgN1aD9U/42Yq+XSirmek69P1ryozM0P33vOQfZnurYfp2x2fas0P89W99TD7/Mpe1dWl5eOau3K0zvz3SFrq1QvatHul/UiYI4L971OXlo/rr0t+r+2J3+h6RrrOpZzU26ue1c9Ht2hkz1n5rn8lLUUVPCrJ072iTp0/qqUbXsvx+jzcYbQ+/OJPOnxyj7Kzs3X6QnKu33gtqucDACgaHIlDqdemaQ+9MWaTlqyP1uiYVrqWfkU+XtXVyK+lXh/5bb7rPhbxnK5nXNPkD7rpctpFNaodqtee/koVPLzty7Rq3FXubp5KPLZNLw/9LMf6f+z3gZZ8G60J70fo/KWT8vLwUfOGnRXWpFuhnsOfBi5W7Hdv6J3P/qBfzx+RWzkPBfuHa+6zP6hhzeb5rvvHR+dr3r8m6O/rp6tu9abq2mqwfjryvf3xYT1eVXn3ivrLoj46d+mkqlSsqacempnr5+KK6vkAAH47S3Z2drbRIQBHxC+VLiQbnQIF8akjtR5o3P7Lwjgx+jXOixn/P08zZpbMmxtFi9OpAAAAJsTp1ALExkvHzhuzb7/KUt/WxuwbAIC8jBs3TgkJCSW+39DQUMXExJT4fp0VJa4Ax85LB08ZnQIAAOeRkJAgm81mdIwyj9OpAAAAJkSJAwAAMCFKHAAAgAlR4gAAAEyIEgcAAGBClDgAAAATosQBAACn4+rqanQEp8d14gAAQLHx8PBQt27d1KZNGzVv3lyenp5KS0vTvn37FB8fr7Vr1yo1NfWOdVavXq34+Hg9//zzBiV3fpQ4AABQ5CpVqqTnn39ew4cPV9WqVe94vFevXpKklJQULV68WNOmTdOpU6fsBe6BBx5QixYtFBMTo1OnuOp+bpy6xGVlZWnOnDmaN2+ekpKS1KRJE82dO1cjRoxQeHi45s+fb3TEOyyfHqF6zbuqbZ8XHJqP327Bl1O0YcenSrlyVm7lPNTC/z6NeniOqleuZ3Q0OBHGCVByunfvro8++kh+fn6SpG3btmndunVKSEjQxYsX5eXlpZCQEHXp0kWdOnXSM888o0GDBmns2LEaMmSIHnjgAZ08eVJdunShwOXDqUvc8OHDFRsbq6lTpyosLEybN2/WoEGDdPr0aY0fP97oeHASXcMGa0DEn1ShfCWlpV/RorUv6NW/D9Sbz2w2OhqcCOMEKBnDhg3Thx9+KKvVqn//+98aN26ctm7desdysbGxeumll9S8eXPNnj1b3bp10yeffCJJ9gK3b9++ko5vKk5b4pYsWaJFixYpLi5O4eHhkqTIyEht375dsbGxatWqlcEJ4SzqVW9qv52tbFksViWd/sXARHBGjBOg+D300EP2Avfyyy/rlVdeUVZWVr7r7NmzR71799aOHTvUtOmNn9O5c+dS4BzgtCUuOjpaPXr0sBe4mwICAuTq6qrg4GBJUp8+fXTo0CG5uLjI1dVV0dHR6tq1qxGRYaBvd3yqN2OjdCUtRS7Wchr18ByjI8EJMU6A4lOlShV7gXvxxRc1bdo0h9a7+Rm4pk2b6uLFi6pUqZImT56sTz75RElJScWc2tyc8hIjycnJ2rNnj/r373/HY0ePHlVQUJDc3d0lSYsWLdKuXbu0Y8cOzZs3T48++qgyMzML3IfFYnFostniCp1/62ev6r0RPjmm44mbCr0dmy3O4ZxlYcrvvejS8nF9Nu2i/jH1hAZ3+4sa1mpR6NcbRcPocVsWxonRr3Fe002333bmyYyZnSG3zWa7Y1y+9NJLqlmzpr777jtNnz7dobF865cYTp48qfbt2ys2Nlbe3t56/fXXcxn7NsNf+5J6bx3htCVOkmrWrJlj/tWrV2Wz2XKcSvXx8bHfvnjxoiwWi7Kzs0skZ17a9p6iqPkXcky1AzsZmqmsqOJdU7+792m9sKCnUq6cMzoOnBTjBChaXl5eGjp0qCTpmWeecejv8O0F7uZn4P7whz8oIyNDffv2Va1atYo5ubk5ZYnz9fWVJCUmJuaYP3PmTJ04cUJhYWE55o8ZM0b+/v569NFHtWLFCpUrV/BZ4uzsbIem8PCIIntehRUeHuFwzrIwOfpeZGZmKC39ss6mHC/eNwi5MnrcloVxYvRrnNd00+23nXkyY2ZnyH37R5169eolb29vfffdd9q9e3eBYzivAidJx44d06pVq+Tq6qqBAwfeNvbDDX/tS+q9dYRTljh/f38FBwcrOjpaixcv1vr16xUVFaUFCxZI0h0l7p133tGhQ4cUGxur55577o6LBqL0ysrK0qrv39b51BtfQT99IVlvrxyjmpUbqF61pgWsjbKCcQIUr7Zt20qSvvzyywKXza/A3XRzO23atCn6sKWIU5Y4q9WqZcuWKSgoSFFRURo2bJh8fX01ZswYubi42L/UcLvw8HBZrVZ9//33JZwYRtr68xqNmNVcDz9fQc++da/c3Tw1Y8Q3cnFx2u/twACME6D4tGhx4/OlO3bsyHc5RwrcrdvJ6+89bnDa316BgYHasGFDjnmDBw9Ws2bNVL58eUlSamqqzp49q/r160u68aYfPHhQ99xzT4nnvanfC3GFmo/fxmq1Knr4GqNjwMkxToDitW7dOh05ckT79+/Pd7m33nqrwAInSUlJSVq4cKGOHTtWHHFLDactcbmJj49Xu3bt7PcvX76sAQMGKDU1VeXKlZOHh4c++eQT1avHFdgBACgpM2fOdGi5V155Rc2aNdNTTz2V73Xgzpw5oyeffLKo4pVapilxqampSkxM1OjRo+3zatSooR9++MHAVAAAwFFJSUnq2LGj0TFKDdOUOC8vL4eu/wYAAFAWOOUXGwAAAJA/ShwAAIAJUeIAAABMiBIHAABgQpQ4AAAAE6LEAQAAmBAlDgAAwIRMc504o/hVLpv7BgAgL6GhoYVe59DRE5Ik/3q1ctwu7v2WZpS4AvRtbXQCAACcS0xMTKHXmTxjviTptUkjctzG3eN0KgAAgAlR4gAAAEyIEgcAAGBClDgAAAATosQBAACYECUOAADAhChxAAAAJkSJAwAAMCFKHAAAgAlR4gAAAEyIEgcAAGBClDgAAAATosQBAACYUDmjAzi72Hjp2Hlj9u1XWerb2ph9AwBQmowbN04JCQmG7Ds0NFQxMTFFvl1KXAGOnZcOnjI6BQAA+C0SEhJks9mMjlGkOJ0KAABgQpQ4AAAAE6LEAQAAmBAlDgAAwIQocQAAACZEiQMAADAhShwAAEAuXFxcFBQUpK5du+r+++9XUFCQXFxc8lzex8dHY8aMKbF8XCcOAADgv1xcXNSrVy+NGjVKnTp1kqenZ47Hr1y5oo0bN+r999/X559/rszMTEk3CtzXX3+t1q1by8PDQ7Nnzy72rE59JC4rK0uzZs1S48aN5eHhoZCQENlsNjVp0kQjRowwOh4AAChF2rZtq927dys2NlbdunWTp6enDh06pPXr12v9+vU6dOiQPD091b17d61cuVI7d+5U69atcxS4AwcO6B//+EeJ5HXqEjd8+HBNmzZNI0eO1JdffqnHHntMgwYN0qFDhxQWFmZ0vFwtnx6hraumOzwfRScrK0tj3+6gB56z6PSFZKPjwEkxTgDkZvz48dq8ebPuueceHTx4UGPHjlW1atXUqFEjde3aVV27dlWjRo1UrVo1jRs3TgcPHlRQUJB++OEHe5k7cOCAIiMjlZxcMr9bnLbELVmyRIsWLdLq1as1ceJERUZGasqUKWrfvr0yMjLUqlUroyPCyazY+IbcXT0LXhBlGuMEwO0mTpyo2bNny8XFRTNmzFBQUJDmzp2rM2fO3LHsmTNn9Oabb6p58+aaO3euXFxcVK9ePZ05c6ZEC5zkxCUuOjpaPXr0UHh4eI75AQEBcnV1VXBwcI758+fPl8Vi0fLly0syJpxE8ulEfb75XY3oOcvoKHBijBMAt+vUqZNmzJihrKwsDRkyRJMnT9a1a9cKXM/Dw0MdOnSw369SpYrq1q1bnFHv4JQlLjk5WXv27FH//v3veOzo0aMKCgqSu7u7fd7+/fu1cOFCtWvXriRjwklkZWVp1j+f1Iies+RV3sfoOHBSjBMAt3Nzc9OCBQtktVoVHR2txYsXO7Te7Z+Be/vtt2W1WrVw4UK5uroWc+r/cdoSJ0k1a9bMMf/q1auy2Ww5TqVmZGToySef1HvvvZej2BXEYrE4NNlscYXOv/WzV/XeCJ8c0/HETYXejs0W53DOsjDl9V6s3PSmqlSsqU4tHin0a4yiZ/S4LQvjxOjXOK/ppttvO/NkxsxmzW10ZpvNdsfPUr9+/dS4cWPt27dP06ZNc+jn7/YCFxkZqQkTJuiXX35RkyZN1Ldv31x+Zm2Ffp0c4ZQlztfXV5KUmJiYY/7MmTN14sSJHF9qmDZtmh588EGFhoaWZMR8te09RVHzL+SYagd2MjpWqXTszAEt/262nunzttFR4MQYJwByExUVJUmaM2eO0tPTC1w+twKXnJys9PR0vfHGGzm2WRKcssT5+/srODjYfmhz/fr1ioqK0oIFCyTJXuK2bNmib7/9VpMmTSr0PrKzsx2awsMjivKpFUp4eITDOcvClNt7sefwJl1MPa2nZzfXoy/5anTMjaO0I+cEa/Xmd0v4HYNk/LgtC+PE6Nc4r+mm228782TGzGbNbXTm2z9j7+npaf+y5JIlSwr8ucurwN306aefKjMzUx07dpSHh8dtP7PhhX6dHOGUF/u1Wq1atmyZRo4cqaioKFWtWlVDhgzRmDFj9Pzzz9u/1LBhwwYdPHhQjRo1kiSdPHlSe/fu1X/+8x9NmDDByKeAEhIe8phaNe5qv3/6YrLGvt1ef336K9Wr3tTAZHAmjBMAtwsJCZGLi4t27typy5cv57tsQQVOki5duqR9+/apefPmCg4O1tatW4szviQnLXGSFBgYqA0bNuSYN3jwYDVr1kzly5eXJE2ePFmTJ0+2Px4REaFnnnlG/fr1K9GsMI6Hm6c83P53uYjMrAxJUpWKNVXe3cuoWHAyjBMAt6tdu7Yk6eDBg/ku50iBu+nAgQNq3ry5fdvFzWlLXG7i4+Od/huo/V6IK9R8FK2aVRro69cLdzgaZQ/jBMDKlSvl7e1d4HJeXl6qXLmyQxfy/b//+z9JKvDIXlExTYlLTU1VYmKiRo8enecycXFxJRcIAACYVlZWli5dulTgcsnJyYqMjFR2dnaBF/J1ZHtFyTQlzsvLy/6fzAIAAJSUpKQkoyPkyim/nQoAAID8UeIAAABMiBIHAABgQpQ4AAAAE6LEAQAAmBAlDgAAwIQocQAAACZkmuvEGcWvctncN2BWFasbnaD4lYXnCBS10NDQu1rv0NETOe7716tVYvsuCCWuAH1bG50AQGE06WJ0AgDOKCYm5q7Wmzxjfo77r00aUQRpiganUwEAAEyIEgcAAGBClDgAAAATosQBAACYECUOAADAhChxAAAAJkSJAwAAMCFKHAAAgAlR4gAAAEyIEgcAAGBClDgAAAATosQBAACYECUOAADAhMoZHcDZTfhlr3ZeumTIvkMqVtTsJs3uat3YeOnY+SIO5AC/ylLf1iW/XwAAyhpKXAF2Xrqk786fMzpGoR07Lx08ZXQKAABQXDidCgAAYEKUOAAAABOixAEAAJgQJQ4AAMCEKHEAAAAmRIkDAAAwIUocAACACVHiAAAATIgSBwAAYEJOXeKysrI0a9YsNW7cWB4eHgoJCZHNZlOTJk00YsQIo+PlKvv6dV0f9Ywy532QY37mylW6/sQQZaemGpQsf8unR2jrqukOz3cWM5cOVY9Jrnp4ipd9Wr35XaNjAQBQ7Jz6v90aPny4YmNjNXXqVIWFhWnz5s0aNGiQTp8+rfHjxxsdL1cWV1eVm/ycMp4dJ0vbNrK2DFX24cPKWvCxXF59RRYvL6MjljoPtB6iCf0/NDoGAAAlymlL3JIlS7Ro0SLFxcUpPDxckhQZGant27crNjZWrVq1Mjhh3iwN6sv65BBlznpDlrfeUMZrr8va+2FZg1sYHQ0AAJQSTlvioqOj1aNHD3uBuykgIECurq4KDg6WJEVEROg///mPKlWqJEnq0aOHXnvttRLPeztrn97K3hqvjJFjpGq+sg4ZbHSkUmvT7hX6fnesvCv4qkNQbw1+4CWVd+eIJwCgdHPKz8QlJydrz5496t+//x2PHT16VEFBQXJ3d7fPe/3115WQkKCEhASHC5zFYnFoiouLu6vnYLFYZAluIV28KOv9XWRxdS30NuLi4hzOeftksxU+99bPXtV7I3xyTMcTNxVqGzbb3We+m+fUp9OzWvDcz1r+lzP6y5CV2nXIpjnLny70c0fRKc4xwOTc002333bmyYyZzZrbjJlvzVpSmQvDKY/EJScnS5Jq1qyZY/7Vq1dls9n04IMPGhGrULIPH1bWp0tlHdBfWZ98KmvnjrJUr250rHy17T1Fbfu8kGPe8ukRxoRxUGCdMPvtBjWDNOrhNzTx/QilD1gkt3Lu+awJAIC5OeWROF9fX0lSYmJijvkzZ87UiRMnFBYWlmP+lClT1KJFC/Xu3Vu7du1yaB/Z2dkOTREREYXOn51+/cbn4Pr2kcvwYbJ0bK/M1+coOyurUNuJiIhwOOftU3h44XMXhfDwu89cFM/JavnvkM7OLt4nijwV5xhgcu7ppttvO/NkxsxmzW3GzLdmLanMheGUR+L8/f0VHBys6OhoValSRX5+flq+fLnWrFkjSTlK3OLFi1W3bl1ZLBYtXbpU3bt314EDB1ShQgWj4itrwUJZypWTdfDvJUkuo0cpY+QYZa1YKZf+jxqWqzTakLBUbZr0kFd5HyWf3q95/5qg9s16yc3Vw+hoAAAUK6c8Eme1WrVs2TIFBQUpKipKw4YNk6+vr8aMGSMXFxf7lxokqV69evZzyAMHDpSbm5t++eUXo6Ira0eCstaslcvkP8lS7kZHtnh6ymXSRGUt/kTZhw8blq00+te/39f//dVfDz9fQX/+oJvuqddOEwcsNDoWAADFzimPxElSYGCgNmzYkGPe4MGD1axZM5UvX16SlJaWptTUVPvp1/Xr1+vSpUsKCAgo8bw3WVuGyro69s75zYNk/XylAYkc0++FuELNdxazo+KMjgAAgCGctsTlJj4+Xu3atbPfT0lJ0YMPPqj09HRZrVZ5e3tr9erV8vb2NjAlAABA8TNNiUtNTVViYqJGjx5tn1e9enVt27bNwFQAAADGME2J8/LyUmZmptExAAAAnIJTfrEBAAAA+aPEAQAAmBAlDgAAwIQocQAAACZEiQMAADAhShwAAIAJUeIAAABMyDTXiTNKSMWKpty3X+UiDOIk+61Yvfi2jaLD+wQAJYMSV4DZTZoZHeGu9G1tdIKi16SL0QkAAHAenE4FAAAwIUocAACACVHiAAAATIgSBwAAYEKUOAAAABOixAEAAJgQJQ4AAMCEKHEAAAAmRIkDAAAwIUocAACACVHiAAAATIgSBwAAYEKUOAAAABOixAEAAJgQJQ4AAMCEKHF5uHz5soYMGaImTZqoadOmmjdvntGRAKDUiouLU1BQkAICAvTUU08pMzPT6EgFGjt2rOrUqaNy5coZHcVhSUlJuv/++3XPPfcoKChIf/7zn42O5LBu3bopNDRULVq0UL9+/ZSSkmJ0JIeNGTOmWMYJJS4PEyZMUFBQkH755Rft27dPjzzyiNGRAKBUysrK0lNPPaVly5bpwIEDSklJ0SeffGJ0rAL1799f8fHxRscolHLlymnGjBnat2+fduzYoU2bNumzzz4zOpZDli1bpoSEBO3evVt16tTRnDlzjI7kkI0bNyo1NbVYtk2Jy8WlS5e0evVqjR8/XpJksVhUvXp1g1MBQOn0448/qnbt2mrWrJkkafjw4VqxYoXBqQrWqVMn1axZ0+gYhVKrVi21bt1akuTm5qaWLVvq6NGjBqdyTKVKlSTdKP1paWmyWCwGJyrYtWvXNHnyZM2aNatYtm/Jzs7OLpYtm9jOnTs1dOhQ3Xvvvdq6davq16+vmJgY1a9f3+hoAOA0dvy0X99t3WW/f+LUWUlSrepVc9yWpGpVKmlgr/tlzeUP74oVKxQbG6u///3vkqR9+/bp8ccf144dO4o8c9q1dH28Yp3SrqUXmFmSHunWSfX8auS7zXLlyikjI6PIs95q04+7tW1Pov1+frnr+9VQ7wc6Flhyzp07p9DQUH311Vdq2rRpkWdOSb2iv8WuU0ZmVoGZLRZpUK/7Va2KT77bfOSRR7Rx40a1aNFCn3/+uby8vIo897rvftTPB/9XbG9mvenW8dEsoL4e6Nw6z21NmTJFjRo10pNPPlks44QjcbnIyMhQQkKC+vXrp+3bt+vhhx/Wk08+aXQsAHAqwU0bycVq1YlTZ3P8obv99q+nz6lz2+BcC5wkleSxBA93N7UNaVpg5hOnzqqGb+UCC1xJaRPSVNfS0wvMffb8RXVq06LAApeenq5+/fpp7NixxVLgJMnby1PNm/g79FoH1PcrsMBJ0sqVK3X8+HHVqVNHy5cvL47Y6hAWpJRLl+/IfdPN+ZdSr6h9WFCe29m1a5e2bNmiYcOGFUtOiRKXqzp16qhq1arq2rWrJGngwIHatm2bwakAwLm4uFj1WM9IlSvnku9yXTq0Ut1aeX8kpW7dukpKSrLfP3r0qOrUqVNkOW8X2ixALZo0zHeZShUrqPcDHYstQ2G5u7nqsYciCyxnD3VpL9/KlfJdJjMzU48//rhCQ0M1YcKEoox5h85tWqhBnfxPOdesVkXdOrdxeJtubm4aOHCgVq5c+Vvj5apiBU890qNzgcv1ffA+eXmWz/Px77//Xnv37lXDhg3VoEEDZWZmqkGDBkX6hQxKXC5q1KihoKAgbd++XZL09ddfKygo77YNAGVV9ao+ejDi3jwfr1OrmiLbt8x3G61bt1ZycrL27t0rSfroo4/Ut2/fIs15K4vFoj7dO6uil2eey/T/XYTKe7gXW4a70aBOTYXfG5Ln400b1VPbkIKPqo0YMUIVK1bU7NmzizJerqzWG0Xf3c0118ddrI79Q+DSpUs6ceKEpBufiVu9enWx/l1uHthQYc0D83y8TXBTNQvI/yNWUVFROn78uI4cOaIjR47IxcVFR44ckbe3d5HlpMTl4b333tOYMWMUHBys2bNn68MPP5RUsof9AcAM2rcKUuMGfnfMdy3nogEPRcrFJf8/NS4uLvrwww/Vr18/NWrUSF5eXho8eHBxxZUkVSjvoX497sv1sY6tmysgl+dzu5EjR6pOnTrKzMxUnTp1NGbMmKKOeYeuncJyfCbrJs/y7nq0x30FHqn7/vvvtWDBAsXHx6tly5YKDQ3V3LlziyuuJKlKpYp6+P4OuT7W7b7Wqp3L87ndpUuX1KtXLwUHBys4OFgZGRl64YUXijpqDg937SAf7zs/c1elUkX17NKuWPftKL7YUEhxPyTo2MnTGvBwF5Vzyf9fDgBQVly8dFlvfLTM/oUBSer9QEe1b+XcZzFWfbVJP+zYa79fvaqPnh3SV66uznvtt19Pn9NbH69Uxi3X0nuizwNqXsApYiNlZ2frbyu/1t79R+zzGtSpqRGDespqdd7jSYeSTuiDTz/XzaJksVg08vGHCzxFXFKc95VzQteupeu7LTuVfj2DAgcAt6hUsYIe6dbJfj+wYR21a9nMwESO+V3EvfbPkFmtFg3o2cWpC5wk1ahWRd3D//cZslbNA526wEk3yk/fHp3tnyFzc3PVYw9FOHWBkyT/urXUuW2w/X74vSFOU+CkUlDidu/erUcffVS+vr7y8PBQ48aNNWXKlGLZ1+btP+lK2jV17RhWLNsHADMLaRagkHsaqbyHu/o9GG6K63jdLBMWi0VdO4bJr6av0ZEc0rF1C/nXqy0fby/16pr7qUpn4+VZXn0fvHEK++H726uKT9F9Nqw4devcRjWrVVGt6lXVtZNz/f039enUbdu26b777lPdunU1adIk1a9fX4cPH9bmzZv10Ucf5bvu5BnzSyglAACAY16bNMLhZZ37mHEBJkyYoAoVKmjLli32KzlLN672DQAAUJqZ9kjclStXVLFiRT3zzDN68803i3Vf166la8b7S1S3dnUN6/9gse4LAADAEaY9Enf+/HllZWXd9QUh7+Z06i+HkjgNCwAAik1hTqea9osNlStXltVq1bFjx4yOAgAAUOJMezpVkiIjI7V3717t37+/SK+AfKsN/96hdd/9qDGD+6hu7bz/2xgAAICSZNojcZI0a9Yspaamql27dlq0aJE2bNigjz/+WE899VSRbP/atXRt3LpLTfzrUuAAAIBTMe1n4iQpLCxM//73vzV16lT98Y9/VFpamurWrauBAwcWyfbPXbyk8uXduS4cAABwOqY+nVoSsrKynP6K0gAAoOyhxAEAAJgQh5gAAABMiBIHAABgQpQ4AAAAE6LEAQAAmBAlDgAAwIQocQAAACZEiQMAADAhShwAAIAJUeIAAABMiBIHAABgQpQ4AAAAE6LEAQAAmBAlDgAAwIQocQAAACZEiQMAADAhShwAAIAJUeIAAABMiBIHAABgQpQ4AAAAE6LEAQAAmBAlDgAAwIQocQAAACZEiQMAADAhShwAAIAJUeIAAABMiBIHAABgQpQ4AAAAE/p/aLyEl6BNv0oAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 808.997x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# apply grover oracle, only one iteration is needed in this case\n",
    "circuit.compose(grover_oracle2(), qubits = range(6), inplace = True)\n",
    "circuit.append(grover_operator(5), range(5))\n",
    "\n",
    "# measure the 5 qubits we are interested in \n",
    "circuit.measure(range(5), range(5))\n",
    "\n",
    "%matplotlib inline\n",
    "circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# then we simulate the circuit and see the results\n",
    "simulator = simulator = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "# execute the simulation with 1000 shots\n",
    "result = execute(circuit, backend = simulator, shots = 1000).result()\n",
    "\n",
    "# get counts and plot histogram\n",
    "counts = result.get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<pre>\n",
    "Finally after the quantum search the states that are the winning solution of the game are 6:\n",
    "</pre>\n",
    "$$\\ket{11000}$$\n",
    "$$\\ket{01100}$$\n",
    "$$\\ket{00110}$$\n",
    "$$\\ket{10001}$$\n",
    "$$\\ket{00101}$$\n",
    "$$\\ket{10100}$$"
   ]
  }
 ],
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