Quantum_Tic_Tac_Toe.ipynb

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    "colab": {
      "name": "Quantum_Tic_Tac_Toe.ipynb",
      "provenance": [],
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        "# Tiq Taq Toq\n",
        "\n",
        "*by [Afrad Muhamed Basheer](Afrad.M.Basheer@student.uts.edu.au)* \n",
        "\n",
        "*contact: Afrad.M.Basheer@student.uts.edu.au*\n",
        "\n",
        "*Team: Entanglement*\n",
        "\n",
        "*Poster Link: https://drive.google.com/file/d/1QErZT5G0u_JxoWZJiMJi1vXe5ftnAdPD/view?usp=sharing*\n",
        "\n",
        "Introducing Tiq Tac Toq, the tic tac toe game meant to be played on quantum computers. Analgous to the \"classical\" Tic Tac Toe game, Tiq Tac Toq also requires players to \"mark\" one spot in a 3 x 3 grid, where each spot is represented by 1 qubit, by applying a gate from a pre-defined set of gates. Once all gates are applied, we measure all 9 qubits, and the resulting board, with '1's and '0's is analyzed in the same way a normal Tic Tac Toe game is analyzed; horizontal,  vertical and diagonal patterns results in points for the players. Some additional constraints and features are also incorporated to increase the \"coherence\" of the game. We provide implementation of the game in both Qiskit as well as TheQ."
      ]
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        "# Rules\n",
        "\n",
        "\n",
        "1. We shall refer to both the players as player 0 and player 1. As we menttioned earlier, each square of the 3 x 3 grid is represented by a single qubit. Players take turn to mark a square by applying a gate on the qubit. After all gates are applied, we measure all 9 qubits. The resultant board of 9 qubits in the 0 or 1 state, is the final state of the board. Player 0 gains points for each winning pattern of 0's on the board, that is, three 0's aligned vertically, horizontally or diagonally. Same goes for player 1 as well. Note that no player can choose to mark a qubit which is already marked, just like a normal tic-tac-toe.\n",
        "\n",
        "2. Before the game starts, one pair of qubits, randomly chosen without the players' knowldege, are chosen to be entangled. Let's call them control qubit and target qubit. The idea is to construct the final quantum circuit in such a manner that if the control qubit results in 0 after measurement, the target qubit also results in 0 and same should happen for 1. \n",
        "3. Each qubit is indexed in the following manner. \n",
        "\n",
        "\n",
        "![qubit_index.png](data:image/png;base64,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)\n",
        "4. Every qubit, except the target qubit, will be initialized in the $|+\\rangle$ state. Since the players do not know which qubit is the target qubit, from their perspective, every qubit is initialized in the $|+\\rangle$ state.\n",
        "5. Each player gets to choose a square/qubit to apply a $\\mathbf{R_Y}(2 \\theta)$ rotation gate. The $\\mathbf{R_Y}(\\theta)$ gate has the form \n",
        "\\begin{equation}\n",
        "  \\mathbf{R_Y}(\\theta) = \n",
        "  \\begin{bmatrix}\n",
        "    cos(\\frac{\\theta}{2}) & -sin(\\frac{\\theta}{2}) \\\\\n",
        "    sin(\\frac{\\theta}{2}) & cos(\\frac{\\theta}{2}) \n",
        "  \\end{bmatrix}\n",
        "\\end{equation}\n",
        "Hence, for any rotation angle $\\theta > 0$, $\\mathbf{R_Y}(2\\theta)$ rotates a vector by angle $\\theta$ in the counter-clockwise direction on an x-y plane, and for any rotation angle $\\theta < 0$, $\\mathbf{R_Y}(2\\theta)$ rotates a vector by angle $\\theta$ in the clockwise direction on an x-y plane. Note that, from the players' perspectives, all qubits are initialized in the $| + \\rangle$ state, which is equal to $\\frac{1}{\\sqrt{2}} |0 \\rangle + \\frac{1}{\\sqrt{2}} |1 \\rangle$ or $\\begin{bmatrix} \\frac{1}{\\sqrt{2}} \\\\ \\frac{1}{\\sqrt{2}}\\end{bmatrix}$. So, on the first quadrant of an x-y plane, all qubits are represented by the point $(\\frac{1}{\\sqrt{2}}, \\frac{1}{\\sqrt{2}})$, which is situated at $\\frac{\\pi}{4}$ radian from the x-axis.\n",
        "\n",
        "![init_board_values.PNG](data:image/png;base64,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)\n",
        "\n",
        "  The rotation angle $\\theta$ should be one of 0, $\\frac{\\pi}{4}$, $\\frac{\\pi}{8}$, $\\frac{\\pi}{16}$. The states are represented in the first quadrant of an x-y plane, that is, a state \n",
        "\\begin{equation}\n",
        "  | \\phi \\rangle = a_0 | 0 \\rangle + a_1 | 1 \\rangle\n",
        "\\end{equation}\n",
        "   where $a_0, a_1 \\geq 0$, is represented by the point $(a_0, a_1)$. So $|0\\rangle$ is $(1, 0)$ and $|1\\rangle$ is $(0, 1)$. Player 0 would like to rotate the vector downwards (towards $x$-axis) and player 1 would like to rotate the vector upwards (towards $y$-axis). This means that for player 0, an input choice of $\\theta$ would result in applying a gate $\\mathbf{R_Y}(-2\\theta)$ and for player 1, an input choice of $\\theta$ would result in applying the gate $\\mathbf{R_Y}(2\\theta)$. \n",
        "  \n",
        "\n",
        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)\n",
        "\n",
        "\n",
        "  Now we explain the reason why both players rotate in this manner. The closer the state of the qubit gets to the $x$-axis, the $x$ coordinate of the state would become more and more greater than the $y$ coordinate of the state and hence, the amplitude associated with $| 0 \\rangle$ would be higher compared to the amplitude associated with $| 1 \\rangle$. This would imply that the probability of the qubit being marked 0 after measurement is higher than the probability of the qubit being marked 1. Similarly, the closer the state of the qubit gets to the $y$-axis, the probability of the qubit being marked 1 after measurement is higher than the probability of the qubit being marked 0. An example of a board with gates applied to all qubits is given below.\n",
        "\n",
        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)\n",
        "  \n",
        "  Here, player 0 has played in even indexed qubits and player 1 has played in odd indexed qubits. \n",
        "\n",
        "\n",
        "4. Throughout one round, the sum of rotation angles one player can apply is capped at $\\frac{\\pi}{2}$. This forces players to strategically apply rotations on qubits. For example, from a player's perspective, a $\\frac{\\pi}{4}$ rotation on any qubit completely guarantees that qubit for the player. But, because of this restriction, players can only do two such rotations per round, and even if one does that, then that player cannot rotate any other qubit to any degree throughout the round. After each move a player makes, their remaining angle usage will be displayed.\n",
        "\n",
        "![3pi2.PNG](data:image/png;base64,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)\n",
        "\n",
        "5. Now, as we discussed before, player 0 would like to increase the amplitude of $| 0 \\rangle$ and player 1 would like to increase the amplitude of $|1\\rangle$. We bring an extra feature by allowing each player to choose one qubit/square to apply an $\\mathbf{X}$ gate, just before the round starts. Players don't know what the opponent's choice of $\\mathbf{X}$ gate qubit is. The $\\mathbf{X}$ gate is applied after all the rotation gates are applied. So, on the qubit that a player has chosen to apply an $\\mathbf{X}$ gate, the amplitudes get interchanged. For example, let the qubit be in state \n",
        "\\begin{equation}\n",
        "  | \\phi \\rangle = a_0 | 0 \\rangle + a_1 | 1 \\rangle\n",
        "\\end{equation}\n",
        "where $a_0 > a_1 \\geq 0$. So, the probability of the qubit being marked 0 after the final measurement is higher than the probability of the qubit being marked 1. But, after applying an $\\mathbf{X}$ gate, the state becomes\n",
        "\\begin{equation}\n",
        "  \\mathbf{X} | \\phi \\rangle = a_0 |1\\rangle + a_1 |0\\rangle\n",
        "\\end{equation}\n",
        "  Now, we see that the probability of the qubit being marked 1 after the final measurement is higher than the probability of the qubit being marked 0. So, $\\mathbf{X}$ gate is like a mine. When a player tries to increase the probability for their mark on a qubit which their opponent has decided to apply an $\\mathbf{X}$ gate in, they are actually decreasing that probability. \n",
        "6. After all squares are marked with rotations, we move on to the quantum circuit.\n",
        "7. First we apply Hadamard gates on all qubits except the target qubit.\n",
        "8. Then we apply all the chosen rotation gates on the chosen qubits, except for target qubit.\n",
        "9. Then we apply the $\\mathbf{X}$ gates, if it is not on the target qubit. If it is, we don't apply that $\\mathbf{X}$ gate.\n",
        "10. Then we apply a CNOT gate with the control qubit as control and target qubit as target. Now whatever is the result of the control qubit after measurement, the target qubit will also have the same result. For example, let the control qubit $|ctrl \\rangle$ be in the state $a_0 | 0 \\rangle + a_1 | 1 \\rangle$, then, since no gates are applied to the target qubit $| tar \\rangle$, both of these qubits can be represented as\n",
        "\n",
        "\\begin{equation}\n",
        "\\begin{split}\n",
        "  | ctrl \\rangle \\otimes |tar \\rangle &= (a_0 | 0 \\rangle + a_1 | 1 \\rangle) \\otimes | 0 \\rangle \\\\\n",
        "  &= a_0 | 00 \\rangle + a_1 | 10 \\rangle\n",
        "  \\end{split}\n",
        "\\end{equation}\n",
        "\n",
        "  Now, after applying the CNOT gate, we get\n",
        "\n",
        "\\begin{equation}\n",
        "  CNOT | ctrl \\rangle \\otimes | tar \\rangle = a_0 | 00 \\rangle + a_1 | 11 \\rangle\n",
        "\\end{equation}\n",
        "\n",
        "  Therefore, the CNOT forces the target qubit to have the same result as the control qubit. An example of a final circuit, with qubit 0 being the control qubit and qubit 8 being the target qubit, will look like this.\n",
        "\n",
        "\n",
        "![circuit.png](data:image/png;base64,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)\n",
        "11. Then we measure all the qubits. Each player gets 1 point for 1 winning pattern on the board. For example:\n",
        "\n",
        "\n",
        "![results_mat.png](data:image/png;base64,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)\n",
        "12. Players play 4 rounds with the same 2 qubits chosen for entanglement with CNOT gates. So, based on the results of each round, players have to figure out which qubits are entangled and try to take advantage of it. Player 0 plays first in the even rounds and player 1 plays first in the odd rounds.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NQhQ-57ZYkRb"
      },
      "source": [
        "# Qiskit Installation\n",
        "\n",
        "Run the cell below to install qiskit, if you haven't yet. If you plan to play the game on TheQ, ignore this."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9iDSkQNNs6gb"
      },
      "source": [
        "!pip install qiskit --quiet\n",
        "from qiskit import *"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aVP6Bx2Ho-Dn"
      },
      "source": [
        "# Import required packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b1wzcsB6n9F-"
      },
      "source": [
        "# This is first cell to run before executing the game.\n",
        "\n",
        "import numpy as np\n",
        "import random\n",
        "import getpass\n",
        "import sympy as sp\n",
        "from sympy.abc import pi, x\n",
        "from sympy import symbols\n",
        "import math\n",
        "import matplotlib as mpl"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bI51kUzN9R1c"
      },
      "source": [
        "# Some required functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TR7GeUZu9QiB"
      },
      "source": [
        "# This is the second cell required to run before executing the game.\n",
        "\n",
        "# The divisor functions helps in displaying the board after each move.\n",
        "\n",
        "def divisor(index, val, choices):\n",
        "  if index not in choices:\n",
        "    return x\n",
        "  elif val == 0:\n",
        "    return 0\n",
        "  else:\n",
        "    return (val).as_integer_ratio()[0] * pi/(val).as_integer_ratio()[1]\n",
        "    \n",
        "\n",
        "# This function is required to receive input from players\n",
        "\n",
        "def get_player_input(player, player_limit, chosen_qubits):\n",
        "    player_qubit = input(\"\\n Enter qubit for player %d [0-8]\\n\" % player)\n",
        "    \n",
        "    # Check for exit or bad moves\n",
        "    if player_qubit == 'exit':\n",
        "      return ('exit',0)\n",
        "    elif int(player_qubit) in chosen_qubits:\n",
        "      print('\\n Chosen qubit is already marked. Please choose a differnet qubit! \\n')\n",
        "      return get_player_input(player, player_limit, chosen_qubits)\n",
        "    elif int(player_qubit) not in list(range(9)):\n",
        "      print('\\n Please chose an integer [0-8] or type \"exit\" \\n')\n",
        "      return get_player_input(player, player_limit, chosen_qubits)\n",
        "    else:\n",
        "      player_qubit = int(player_qubit)\n",
        "      player_good_theta = False\n",
        "      while not player_good_theta:\n",
        "\n",
        "         player_choice = input(\"\\n Player %d enter theta: \\n 0 for 0 rad,\\n 4 for π/4 rad, \\n 8 for π/8 rad, \\n 16 for π/16 rad, \\n Enter 'exit' to stop the game and see measurement results. \\n\" %player)\n",
        "         if player_choice not in ['0','4','8','16','exit']:\n",
        "            print ('wrong theta, please chose from {0,4,8,16,exit}')\n",
        "         elif player_choice == 'exit':\n",
        "            return ('exit',0)\n",
        "         else:\n",
        "            player_choice = int(player_choice)\n",
        "            if player_choice == 0:\n",
        "               player_good_theta = True\n",
        "            elif player_limit + 1/player_choice <= 1/2:\n",
        "               player_good_theta = True\n",
        "            else:\n",
        "              print(\"\\n Maximum angle exceeded \\n\")\n",
        "              print(\"\\n Player {} remaining angle usage: \".format(player))\n",
        "              if 0.5 - player_limit == 0:\n",
        "                sp.pprint(0)\n",
        "              else:\n",
        "                sp.pprint((0.5 - player_limit).as_integer_ratio()[0] * pi/(0.5 - player_limit).as_integer_ratio()[1])\n",
        "    return (player_qubit,player_choice)\n",
        "    \n",
        "\n",
        "# This funciton is used to display the angles as plots on the first quadrant.\n",
        "def rot_graph(thetas):\n",
        "  pi0 = np.pi\n",
        "  ori = [0,0]\n",
        "  thet = thetas\n",
        "  thetas = [x * pi0 for x in thetas]\n",
        "\n",
        "  fig = mpl.pyplot.figure(figsize = (6,6),constrained_layout=True)\n",
        "\n",
        "  for i in range(9):\n",
        "    ax = fig.add_subplot(3,3,i+1)\n",
        "    circ = mpl.pyplot.Circle((0, 0), radius=1, edgecolor='b', facecolor='None')\n",
        "    th = thetas[i]\n",
        "    th1 = (thet[i]).as_integer_ratio()[0]\n",
        "    th2 = (thet[i]).as_integer_ratio()[1]\n",
        "    if th1 == 1:\n",
        "      a = r'\\frac{\\pi}{%d}' %th2\n",
        "    else:\n",
        "      a = r'\\frac{%d\\pi}{%d}' %(th1 ,th2)\n",
        "    col = 'r'\n",
        "    pts = mpl.pyplot.scatter(np.cos(th), np.sin(th), color = col)\n",
        "    xy =[np.cos(th), np.sin(th)]\n",
        "    mpl.pyplot.plot([0,np.cos(th)], [0,np.sin(th)])\n",
        "    ax.add_patch(circ)\n",
        "    mpl.pyplot.xlim(0, 1)\n",
        "    mpl.pyplot.ylim(0, 1)\n",
        "    mpl.pyplot.title(\"$%s$ radian\" %a)\n",
        "    mpl.pyplot.xticks([])\n",
        "    mpl.pyplot.yticks([])\n",
        "    mpl.pyplot.xlabel(\"Player 0\")\n",
        "    mpl.pyplot.ylabel(\"Player 1\")\n",
        "  fig.tight_layout(pad=0.7)\n",
        "  mpl.pyplot.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YB7nKJI8toxU"
      },
      "source": [
        "## Let's start the game"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NAIf91b6qIEO"
      },
      "source": [
        "# Run this cell to play the game. \n",
        "\n",
        "\n",
        "# Generate a random pair of qubits to be entangled\n",
        "r1 = np.random.randint(9)\n",
        "r2 = np.random.randint(9)\n",
        "while r1 == r2:\n",
        "  r2 = np.random.randint(9)\n",
        "  \n",
        "# Uncomment the line below to see which qubits are entangled. In the real game, this will not be shown to the players.\n",
        "#print(\"Control aubit: {} \\nTarget qubit: {}\".format(r1, r2))\n",
        "\n",
        "# Dsiplay the board with indices of the qubits\n",
        "print(\"\\n Index of the qubits \\n \\n \")\n",
        "sp.pprint(sp.Matrix([['____', 0, '____', 1, '____', 2, '____'], \n",
        "          ['____', 3, '____', 4, '____', 5, '____'], \n",
        "          ['____', 6, '____', 7, '____', 8, '____']]))\n",
        "\n",
        "# Initialize the scores\n",
        "player_scores = [0, 0]\n",
        "\n",
        "# The game runs for only 4 rounds. \n",
        "for round in range(4):\n",
        "\n",
        "  # Initialize the quantumand classical registers\n",
        "  qr = QuantumRegister(9)\n",
        "  cr = ClassicalRegister(9)\n",
        "  qc = QuantumCircuit(qr, cr)\n",
        "\n",
        "  # Apply Hadamard gates on all qubits except target qubit to initialize them to the \"+\" state\n",
        "  for i in range(9):\n",
        "    if i != r2:\n",
        "      qc.h(i)\n",
        "\n",
        "  # Some more required initializaions \n",
        "  chosen_qubits = []\n",
        "  limit0 = 0\n",
        "  limit1 = 0\n",
        "  print(\"\\n Round: {}\".format(round + 1))\n",
        "  board_values = [1/4] * 9\n",
        "  x = symbols('+')\n",
        "  # Display the initial state of the board\n",
        "  print(\"\\n\\n\\n Initial state of the board \\n \\n\")\n",
        "  sp.pprint(sp.Matrix([['____', divisor(0, board_values[0], chosen_qubits), '____', divisor(1, board_values[1], chosen_qubits), '____', divisor(2, board_values[2], chosen_qubits), '____'], \n",
        "            ['____', divisor(3, board_values[3], chosen_qubits), '____', divisor(4, board_values[4], chosen_qubits), '____', divisor(5, board_values[5], chosen_qubits), '____'], \n",
        "            ['____', divisor(6, board_values[6], chosen_qubits), '____', divisor(7, board_values[7], chosen_qubits), '____', divisor(8, board_values[8], chosen_qubits), '____']]))\n",
        "\n",
        "  rot_graph([1/4] * 9)\n",
        "\n",
        "  # Players input where to apply an X gate\n",
        "  X_gate0 = getpass.getpass(prompt = \"\\n Player {}, Enter qubit for X gate [0-8]\".format(round % 2))\n",
        "  X_gate1 = getpass.getpass(prompt = \"\\n Player {}, Enter qubit for X gate [0-8]\".format((round + 1) % 2))\n",
        "\n",
        "\n",
        "  # Only 9 squares in total. So only 9 moves allowed in each round.\n",
        "  while len(chosen_qubits) <= 9:\n",
        "    #print (chosen_qubits)\n",
        "\n",
        "    # Take the first player's move for rotation target\n",
        "    (player0_qubit, player0_choice) = get_player_input(round % 2, limit0, chosen_qubits)\n",
        "    \n",
        "    # Check for exit\n",
        "    if player0_qubit == 'exit':\n",
        "      break    \n",
        "    \n",
        "    # If rotated then increase the used rotation for the first player\n",
        "    if player0_choice in [0,4,8,16]:\n",
        "      if player0_choice != 0:\n",
        "        limit0 += 1/player0_choice\n",
        "        board_values[player0_qubit] = (board_values[player0_qubit] + (((-1) ** (round + 1)) * (1/player0_choice)))\n",
        "    \n",
        "    # Record which square was played\n",
        "    chosen_qubits.append(player0_qubit)\n",
        "    \n",
        "    sp.pprint(sp.Matrix([['____', divisor(0, board_values[0], chosen_qubits), '____', divisor(1, board_values[1], chosen_qubits), '____', divisor(2, board_values[2], chosen_qubits), '____'], \n",
        "                      ['____', divisor(3, board_values[3], chosen_qubits), '____', divisor(4, board_values[4], chosen_qubits), '____', divisor(5, board_values[5], chosen_qubits), '____'], \n",
        "                      ['____', divisor(6, board_values[6], chosen_qubits), '____', divisor(7, board_values[7], chosen_qubits), '____', divisor(8, board_values[8], chosen_qubits), '____']]))\n",
        "    rot_graph(board_values)\n",
        "\n",
        "    # Display remaining angle usage \n",
        "\n",
        "    sp.pprint(\"\\n Player {} remaining angle usage: \".format(round % 2))\n",
        "    if 0.5 - limit0 == 0:\n",
        "      sp.pprint(0)\n",
        "    else:\n",
        "      sp.pprint((0.5 - limit0).as_integer_ratio()[0] * pi/(0.5 - limit0).as_integer_ratio()[1])\n",
        "\n",
        "    # Apply rotation\n",
        "    if player0_qubit != r2 and player0_choice!=0:\n",
        "      qc.u3( ((-1) ** (round + 1)) * 2 * math.pi/player0_choice, 0, 0, player0_qubit)\n",
        "\n",
        "    \n",
        "    if len(chosen_qubits) == 9:\n",
        "      break\n",
        "\n",
        "    # Take second player's move for rotation target\n",
        "    (player1_qubit, player1_choice) = get_player_input((round + 1) % 2, limit1, chosen_qubits)\n",
        "\n",
        "    # Check for exit\n",
        "    if player1_qubit == 'exit':\n",
        "      break    \n",
        "    \n",
        "    # If rotated then increase the used roatation\n",
        "    if player1_choice in [0,4,8,16]:\n",
        "      if player1_choice != 0:\n",
        "        limit1 += 1/player1_choice\n",
        "        board_values[player1_qubit] = (board_values[player1_qubit] + (((-1) ** (round)) * (1/player1_choice)))\n",
        "\n",
        "    # Record which square was played\n",
        "    chosen_qubits.append(player1_qubit)\n",
        "    \n",
        "    sp.pprint(sp.Matrix([['____', divisor(0, board_values[0], chosen_qubits), '____', divisor(1, board_values[1], chosen_qubits), '____', divisor(2, board_values[2], chosen_qubits), '____'], \n",
        "                      ['____', divisor(3, board_values[3], chosen_qubits), '____', divisor(4, board_values[4], chosen_qubits), '____', divisor(5, board_values[5], chosen_qubits), '____'], \n",
        "                      ['____', divisor(6, board_values[6], chosen_qubits), '____', divisor(7, board_values[7], chosen_qubits), '____', divisor(8, board_values[8], chosen_qubits), '____']]))\n",
        "    rot_graph(board_values)\n",
        "\n",
        "    # Apply rotation\n",
        "    print(\"\\n Player {} remaining angle usage:\".format((round + 1) % 2))\n",
        "    if 0.5 - limit1 == 0:\n",
        "      sp.pprint(0)\n",
        "    else:\n",
        "      sp.pprint((0.5 - limit1).as_integer_ratio()[0] * pi/(0.5 - limit1).as_integer_ratio()[1])\n",
        "    \n",
        "    if player1_qubit != r2 and player1_choice!=0:\n",
        "      qc.u3(((-1) ** (round)) * 2 * math.pi/player1_choice, 0, 0, player1_qubit)\n",
        "\n",
        "  # Apply CNOT and X gates\n",
        "  \n",
        "  if X_gate0 != r2:\n",
        "    qc.x(int(X_gate0))\n",
        "\n",
        "  if X_gate1 != r2:\n",
        "    qc.x(int(X_gate1))\n",
        "  qc.cx(r1, r2)\n",
        "\n",
        "  # Display circuit. This part is currently commented because in a normal game, the circuit should not be displayed as it will reveal the location of the CNOT gate. \n",
        "  # But if one wants to see the circuit, just uncomnnent the 2 lines below.\n",
        "\n",
        "  #print(\"The Circuit \\n \\n\")\n",
        "  #print(qc.draw())\n",
        "  \n",
        "\n",
        "  # Run quantum simulation\n",
        "  qc.measure(qr, cr)\n",
        "  backend = Aer.get_backend('qasm_simulator')\n",
        "\n",
        "  \n",
        "  job_sim = execute(qc, backend, shots = 1)\n",
        "  sim_result = job_sim.result()\n",
        "  counts = sim_result.get_counts(qc)\n",
        "  for key in counts:\n",
        "    results = key\n",
        "\n",
        "  # Display results of measured board (1's and 0's)\n",
        "  print(\"Result \\n\")\n",
        "  sp.pprint(sp.Matrix([['____', results[8], '____', results[7], '____', results[6], '____'], \n",
        "                      ['____', results[5], '____', results[4], '____', results[3], '____'], \n",
        "                      ['____', results[2], '____', results[1], '____', results[0], '____']]))\n",
        "  results = list(results)\n",
        "  print (\"Results:\")\n",
        "  \n",
        "  res = []\n",
        "  for rex_x in results:\n",
        "    res.append(int(rex_x))\n",
        "  results = res\n",
        "  results.reverse()\n",
        "  res_mat = np.reshape(np.array(results), (3, 3))\n",
        "\n",
        "  # Update scores from measured board\n",
        "\n",
        "  player0_score_temp = 0\n",
        "  player1_score_temp = 0\n",
        "  for i in range(3):\n",
        "    if len(set(res_mat[i,:])) == 1:\n",
        "      if res_mat[i,0] == (round % 2):\n",
        "        player0_score_temp += 1\n",
        "      else:\n",
        "        player1_score_temp += 1\n",
        "  for i in range(3):\n",
        "    if len(set(res_mat[:,i])) == 1:\n",
        "      if res_mat[0, i] == (round % 2):\n",
        "        player0_score_temp += 1\n",
        "      else:\n",
        "        player1_score_temp += 1\n",
        "  if len(set([res_mat[0, 0], res_mat[1, 1], res_mat[2, 2]])) == 1:\n",
        "    if res_mat[0, 0] == (round % 2):\n",
        "      player0_score_temp += 1\n",
        "    else:\n",
        "      player1_score_temp += 1\n",
        "\n",
        "  if len(set([res_mat[0, 2], res_mat[1, 1], res_mat[2, 0]])) == 1:\n",
        "    if res_mat[1, 1] == (round % 2):\n",
        "      player0_score_temp += 1\n",
        "    else:\n",
        "      player1_score_temp += 1\n",
        "  \n",
        "  # Print score updates\n",
        "  print(\"\\n Player {} gains {} points\\n\".format(round % 2, player0_score_temp))\n",
        "  print(\"\\n Player {} gains {} points\\n\".format((round + 1)% 2, player1_score_temp))\n",
        "  player_scores[round % 2] += player0_score_temp\n",
        "  player_scores[(round + 1) % 2] += player1_score_temp\n",
        "  print(\"\\n Player 0's current score is {} points\\n\".format(player_scores[0]))\n",
        "  print(\"\\n Player 1's current score is {} points\\n\".format(player_scores[1]))\n",
        "\n",
        "#End of all rounds display. Printing final scores and deciding the winner\n",
        "if player_scores[0] > player_scores[1]:\n",
        "  print(\"\\n Player 0 wins. \\n\")\n",
        "elif player_scores[0] < player_scores[1]:\n",
        "  print(\"\\n Player 1 wins. \\n\")\n",
        "else:\n",
        "  print(\"\\n Draw \\n\")\n",
        "print(\"\\n Player 0's score {} \\n\".format(player_scores[0]))\n",
        "print(\"\\n Player 1's score {} \\n\".format(player_scores[1]))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ucA5euiCWfDB"
      },
      "source": [
        "# Play Tiq-Taq-Toq on TheQ"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MGa8Pxe-eF-v"
      },
      "source": [
        "In this section, we present the required code to play Tiq-Taq-Toq on TheQ."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "midLsjzpguGn"
      },
      "source": [
        "## Required functions for simulating quantum circuits on TheQ."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RliJcz7UfpCf"
      },
      "source": [
        "# Server addresses should be stable, but may occasionally be offline\n",
        "import requests\n",
        "import json\n",
        "import math\n",
        "from google.colab import files\n",
        "#req_str = 'http://8b851bd5c0ec.ngrok.io/qsim/perform_operation'\n",
        "req_str = 'http://8fc11588c850.ngrok.io/qsim/perform_operation'\n",
        "#req_str_qasm = 'http://8b851bd5c0ec.ngrok.io/qsim/qasm'\n",
        "req_str_qasm = 'http://8fc11588c850.ngrok.io/qsim/qasm'\n",
        "# Define Create ciruit (these are the four core definitions for any circuit)\n",
        "# all circuits must be bookmarked by the create_circuit and destroy_circuit command\n",
        "\n",
        "# Initial_state is a binary integer to initalise all qubit, \n",
        "# most often initial_state=0.\n",
        "def create_circuit(qubits,initial_state):\n",
        "    data = {\n",
        "        'operation': 'create_circuit',\n",
        "        'num_qubits': qubits\n",
        "    }\n",
        "    result = requests.post(req_str, json=data)\n",
        "    json_obj = json.loads(result.content)\n",
        "    reg_id = json_obj['result']\n",
        "\n",
        "    data = {\n",
        "        'operation': 'set_state',\n",
        "        'register': reg_id,\n",
        "        'state': initial_state,\n",
        "        'complex_value': {'re': 1, 'im': 0}\n",
        "    }\n",
        "    result = requests.post(req_str, json=data)\n",
        "    return reg_id\n",
        "\n",
        "# Gates.  gate_name and params are specified from the list above\n",
        "def gate(register_id, gate_name, params):\n",
        "    data = {\n",
        "        'operation': 'gate',\n",
        "        'register': register_id,\n",
        "        'gate': gate_name\n",
        "    }\n",
        "    for k in params.keys():\n",
        "        data[k] = params[k]\n",
        "    result = requests.post(req_str, json=data)\n",
        "    json_obj=json.loads(result.content)\n",
        "    return json_obj['result']\n",
        "\n",
        "# params contain an array of qubit numbers to measure, 'lq2m': [0,1,3] would measure qubits 0, 1 and 3 and return the \n",
        "# corresponding 3-bit integer value from 0 to 7.\n",
        "def measure_qubit(register_id, params):\n",
        "    data = {\n",
        "        'operation': 'measure', \n",
        "        'register': register_id,\n",
        "    }\n",
        "    for k in params.keys():\n",
        "        data[k] = params[k]\n",
        "    result = requests.post(req_str, json=data)\n",
        "\n",
        "    json_obj = json.loads(result.content)\n",
        "    return json_obj['result']\n",
        "\n",
        "# Always call destroy_circuit to terminate simulation (turn off your QC)\n",
        "def destroy_circuit(register_id):\n",
        "  data = {\n",
        "        'operation': 'destroy_circuit', \n",
        "        'register': register_id\n",
        "  }\n",
        "  result = requests.post(req_str, json=data)\n",
        "\n",
        "# Print allows you to output the current computational state of the machine.\n",
        "def print_vector(register_id):\n",
        "  data = {\n",
        "        'operation': 'state_vector', \n",
        "        'register': register_id\n",
        "  }\n",
        "  result = requests.post(req_str, json=data)\n",
        "  json_obj = json.loads(result.content)\n",
        "  return json_obj['result']\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "paBx8zyRhdz0"
      },
      "source": [
        "## Let's play Tiq-Taq-Toq on TheQ"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VkwgNRKdWhwd"
      },
      "source": [
        "# Run this cell to play the game. \n",
        "\n",
        "# Generate a random pair of qubits to be entangled\n",
        "r1 = np.random.randint(9)\n",
        "r2 = np.random.randint(9)\n",
        "while r1 == r2:\n",
        "  r2 = np.random.randint(9)\n",
        "\n",
        "# Uncomment the line below to see which qubits are entangled. In the real game, this will not be shown to the players.\n",
        "#print(\"Control aubit: {} \\nTarget qubit: {}\".format(r1, r2))\n",
        "\n",
        "# Display the indices of the qubits on the board\n",
        "print(\"\\n Index of the qubits \\n \\n \")\n",
        "sp.pprint(sp.Matrix([['____', 0, '____', 1, '____', 2, '____'], \n",
        "          ['____', 3, '____', 4, '____', 5, '____'], \n",
        "          ['____', 6, '____', 7, '____', 8, '____']]))\n",
        "\n",
        "# Initialize the scores\n",
        "player_scores = [0, 0]\n",
        "\n",
        "# The game runs for only 4 rounds. \n",
        "for round in range(4):\n",
        "\n",
        "  # Initialize the quantum circuit\n",
        "  reg_id = create_circuit(9,0)\n",
        "\n",
        "  # Apply Hadamard gates on all qubits except target qubit to initialize them to the \"+\" state\n",
        "  for i in range(9):\n",
        "    if i != r2:\n",
        "      gate(reg_id, 'hadamard', {'q': i})\n",
        "\n",
        "  # Some more required initializaions \n",
        "  chosen_qubits = []\n",
        "  limit0 = 0\n",
        "  limit1 = 0\n",
        "  print(\"\\n Round: {}\".format(round + 1))\n",
        "  board_values = [1/4] * 9\n",
        "  x = symbols('+')\n",
        "\n",
        "  # Display the initial state of the board\n",
        "  print(\"\\n\\n\\n Initial state of the board \\n \\n\")\n",
        "  sp.pprint(sp.Matrix([['____', divisor(0, board_values[0], chosen_qubits), '____', divisor(1, board_values[1], chosen_qubits), '____', divisor(2, board_values[2], chosen_qubits), '____'], \n",
        "            ['____', divisor(3, board_values[3], chosen_qubits), '____', divisor(4, board_values[4], chosen_qubits), '____', divisor(5, board_values[5], chosen_qubits), '____'], \n",
        "            ['____', divisor(6, board_values[6], chosen_qubits), '____', divisor(7, board_values[7], chosen_qubits), '____', divisor(8, board_values[8], chosen_qubits), '____']]))\n",
        "\n",
        "  rot_graph([1/4] * 9)\n",
        "\n",
        "  # Players input where to apply an X gate\n",
        "  X_gate0 = getpass.getpass(prompt = \"\\n Player {}, Enter qubit for X gate [0-8]\".format(round % 2))\n",
        "  X_gate1 = getpass.getpass(prompt = \"\\n Player {}, Enter qubit for X gate [0-8]\".format((round + 1) % 2))\n",
        "\n",
        "\n",
        "  # Only 9 squares in total. So only 9 moves allowed in each round.\n",
        "  while len(chosen_qubits) <= 9:\n",
        "\n",
        "    # Take the first player's move for rotation target\n",
        "    (player0_qubit, player0_choice) = get_player_input(round % 2, limit0, chosen_qubits)\n",
        "    \n",
        "    # Check for exit\n",
        "    if player0_qubit == 'exit':\n",
        "      break    \n",
        "    \n",
        "    # If rotated then increase the used rotation for the first player\n",
        "    if player0_choice in [0,4,8,16]:\n",
        "      if player0_choice != 0:\n",
        "        limit0 += 1/player0_choice\n",
        "        board_values[player0_qubit] = (board_values[player0_qubit] + (((-1) ** (round + 1)) * (1/player0_choice)))\n",
        "    \n",
        "    # Record which square was played\n",
        "    chosen_qubits.append(player0_qubit)\n",
        "    \n",
        "    sp.pprint(sp.Matrix([['____', divisor(0, board_values[0], chosen_qubits), '____', divisor(1, board_values[1], chosen_qubits), '____', divisor(2, board_values[2], chosen_qubits), '____'], \n",
        "                      ['____', divisor(3, board_values[3], chosen_qubits), '____', divisor(4, board_values[4], chosen_qubits), '____', divisor(5, board_values[5], chosen_qubits), '____'], \n",
        "                      ['____', divisor(6, board_values[6], chosen_qubits), '____', divisor(7, board_values[7], chosen_qubits), '____', divisor(8, board_values[8], chosen_qubits), '____']]))\n",
        "    rot_graph(board_values)\n",
        "\n",
        "    # Display remaining angle usage \n",
        "    sp.pprint(\"\\n Player {} remaining angle usage: \".format(round % 2))\n",
        "    if 0.5 - limit0 == 0:\n",
        "      sp.pprint(0)\n",
        "    else:\n",
        "      sp.pprint((0.5 - limit0).as_integer_ratio()[0] * pi/(0.5 - limit0).as_integer_ratio()[1])\n",
        "\n",
        "    # Apply rotation\n",
        "    if player0_qubit != r2 and player0_choice!=0:\n",
        "      gate(reg_id, 'yrot', {'q': player0_qubit, 'theta': ((-1) ** (round)) * 2 * math.pi/player0_choice})\n",
        "    \n",
        "    if len(chosen_qubits) == 9:\n",
        "      break\n",
        "\n",
        "    # Take second player's move for rotation target\n",
        "    (player1_qubit, player1_choice) = get_player_input((round + 1) % 2, limit1, chosen_qubits)\n",
        "\n",
        "    # Check for exit\n",
        "    if player1_qubit == 'exit':\n",
        "      break    \n",
        "    \n",
        "    # If rotated then increase the used roatation\n",
        "    if player1_choice in [0,4,8,16]:\n",
        "      if player1_choice != 0:\n",
        "        limit1 += 1/player1_choice\n",
        "        board_values[player1_qubit] = (board_values[player1_qubit] + (((-1) ** (round)) * (1/player1_choice)))\n",
        "\n",
        "    # Record which square was played\n",
        "    chosen_qubits.append(player1_qubit)\n",
        "    \n",
        "    sp.pprint(sp.Matrix([['____', divisor(0, board_values[0], chosen_qubits), '____', divisor(1, board_values[1], chosen_qubits), '____', divisor(2, board_values[2], chosen_qubits), '____'], \n",
        "                      ['____', divisor(3, board_values[3], chosen_qubits), '____', divisor(4, board_values[4], chosen_qubits), '____', divisor(5, board_values[5], chosen_qubits), '____'], \n",
        "                      ['____', divisor(6, board_values[6], chosen_qubits), '____', divisor(7, board_values[7], chosen_qubits), '____', divisor(8, board_values[8], chosen_qubits), '____']]))\n",
        "    rot_graph(board_values)\n",
        "\n",
        "    # Display remaining angle usage \n",
        "    print(\"\\n Player {} remaining angle usage:\".format((round + 1) % 2))\n",
        "    if 0.5 - limit1 == 0:\n",
        "      sp.pprint(0)\n",
        "    else:\n",
        "      sp.pprint((0.5 - limit1).as_integer_ratio()[0] * pi/(0.5 - limit1).as_integer_ratio()[1])\n",
        "    \n",
        "    # Apply rotation\n",
        "    if player1_qubit != r2 and player1_choice!=0:\n",
        "      gate(reg_id, 'yrot', {'q': player1_qubit, 'theta': ((-1) ** (round + 1)) * 2 * math.pi/player1_choice})\n",
        "\n",
        "  # Apply X gates\n",
        "  if X_gate0 != r2:\n",
        "    gate(reg_id, 'X', {'q': int(X_gate0)})\n",
        "\n",
        "  if X_gate1 != r2:\n",
        "    gate(reg_id, 'X', {'q': int(X_gate1)})\n",
        "\n",
        "\n",
        "  # Apply CNOT gate\n",
        "  gate(reg_id, 'cnot', {'q_control': r1, 'q_target': r2})\n",
        "  \n",
        "  # Measure the qubits\n",
        "  results = np.zeros(9)\n",
        "  for resu in range(9):\n",
        "    results[resu] = measure_qubit(reg_id,{'lq2m': [resu]})\n",
        "\n",
        "  # Display results of measured board (1's and 0's)\n",
        "  sp.pprint(sp.Matrix([['____', results[0], '____', results[1], '____', results[2], '____'], \n",
        "                      ['____', results[3], '____', results[4], '____', results[5], '____'], \n",
        "                      ['____', results[6], '____', results[7], '____', results[8], '____']]))\n",
        "  \n",
        "  # Update scores from measured board\n",
        "  print (\"Results:\")\n",
        "  res = []\n",
        "  for rex_x in results:\n",
        "    res.append(int(rex_x))\n",
        "  results = res\n",
        "  res_mat = np.reshape(np.array(results), (3, 3))\n",
        "  player0_score_temp = 0\n",
        "  player1_score_temp = 0\n",
        "  for i in range(3):\n",
        "    if len(set(res_mat[i,:])) == 1:\n",
        "      if res_mat[i,0] == (round % 2):\n",
        "        player0_score_temp += 1\n",
        "      else:\n",
        "        player1_score_temp += 1\n",
        "  for i in range(3):\n",
        "    if len(set(res_mat[:,i])) == 1:\n",
        "      if res_mat[0, i] == (round % 2):\n",
        "        player0_score_temp += 1\n",
        "      else:\n",
        "        player1_score_temp += 1\n",
        "  if len(set([res_mat[0, 0], res_mat[1, 1], res_mat[2, 2]])) == 1:\n",
        "    if res_mat[0, 0] == (round % 2):\n",
        "      player0_score_temp += 1\n",
        "    else:\n",
        "      player1_score_temp += 1\n",
        "  if len(set([res_mat[0, 2], res_mat[1, 1], res_mat[2, 0]])) == 1:\n",
        "    if res_mat[1, 1] == (round % 2):\n",
        "      player0_score_temp += 1\n",
        "    else:\n",
        "      player1_score_temp += 1\n",
        "  \n",
        "  # Print score updates\n",
        "  print(\"\\n Player {} gains {} points\\n\".format(round % 2, player0_score_temp))\n",
        "  print(\"\\n Player {} gains {} points\\n\".format((round + 1)% 2, player1_score_temp))\n",
        "  player_scores[round % 2] += player0_score_temp\n",
        "  player_scores[(round + 1) % 2] += player1_score_temp\n",
        "  print(\"\\n Player 0's current score is {} points\\n\".format(player_scores[0]))\n",
        "  print(\"\\n Player 1's current score is {} points\\n\".format(player_scores[1]))\n",
        "\n",
        "  # Destroy circuit after one round\n",
        "  destroy_circuit(reg_id)\n",
        "\n",
        "#End of all rounds display. Printing final scores and deciding the winner\n",
        "if player_scores[0] > player_scores[1]:\n",
        "  print(\"\\n Player 0 wins. \\n\")\n",
        "elif player_scores[0] < player_scores[1]:\n",
        "  print(\"\\n Player 1 wins. \\n\")\n",
        "else:\n",
        "  print(\"\\n Draw \\n\")\n",
        "print(\"\\n Player 0's score {} \\n\".format(player_scores[0]))\n",
        "print(\"\\n Player 1's score {} \\n\".format(player_scores[1]))"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}