GroverSearchForMultiState.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "a-Lrj5aof7wx"
      },
      "outputs": [],
      "source": [
        "# !pip install cirq"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import cirq\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from math import sqrt\n",
        "pi= np.pi"
      ],
      "metadata": {
        "id": "0HQLXov5DaAY"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "k=4\n",
        "toBinary= lambda x,size:bin(x)[2:].zfill(size)\n",
        "toDecimal= lambda binary_num: int(binary_num, 2)"
      ],
      "metadata": {
        "id": "VP9dXd_Kg0dz"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "qubits=cirq.NamedQubit.range(k,prefix='q')\n",
        "circuit=cirq.Circuit()\n",
        "sim=cirq.Simulator()\n",
        "auxqubits=cirq.NamedQubit.range(1,prefix=\"aux\")"
      ],
      "metadata": {
        "id": "DAIR5K4Pi3Ff"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def prepareAnicilia():\n",
        "  circuit=cirq.Circuit()\n",
        "  circuit.append(cirq.X(auxqubits[0]))\n",
        "  circuit.append(cirq.H(auxqubits[0]))\n",
        "  return circuit"
      ],
      "metadata": {
        "id": "y12oRhhd2izh"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#inversion and reflection (diffusion) operator\n",
        "def oracle(marked):\n",
        "  circuit=cirq.Circuit()\n",
        "  global qubits\n",
        "  global auxqubits\n",
        "  for mar in marked:\n",
        "    ctrl_state=toBinary(mar,k)\n",
        "    for j,data in enumerate(ctrl_state):\n",
        "        if data=='0':\n",
        "          circuit.append(cirq.X(qubits[j]))\n",
        "    circuit.append(cirq.X(auxqubits[0]).controlled_by(*qubits))\n",
        "\n",
        "    for j,data in enumerate(ctrl_state):\n",
        "      if data=='0':\n",
        "        circuit.append(cirq.X(qubits[j]))\n",
        "  return circuit\n",
        "\n",
        "\n",
        "def reflection(marked):\n",
        "  circuit=cirq.Circuit()\n",
        "  global qubits\n",
        "  global auxqubits\n",
        "\n",
        "  circuit.append(cirq.H.on_each(*qubits))\n",
        "\n",
        "  circuit=circuit+oracle([0])\n",
        "\n",
        "  circuit.append(cirq.H.on_each(*qubits))\n",
        "  return circuit"
      ],
      "metadata": {
        "id": "1kfc7IXEjYC-"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def applyGrover(n,marked):\n",
        "  global circuit\n",
        "  k=len(marked)\n",
        "  theta = np.arcsin(np.sqrt(k/n))%(2*np.pi)\n",
        "  k = np.pi/(4*theta)-0.5\n",
        "  k = int(np.ceil(k))\n",
        "  circuit.append(cirq.H.on_each(qubits))\n",
        "  for _ in range(k):\n",
        "    circuit=circuit+oracle(marked)\n",
        "    circuit=circuit+reflection(marked)\n"
      ],
      "metadata": {
        "id": "u5pDM52_qSmF"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def getlessThan(value,list):\n",
        "  marked=[i for i in list if i < value]\n",
        "  N = 2**4\n",
        "  global circuit\n",
        "  print(marked)\n",
        "  circuit=cirq.Circuit()\n",
        "  circuit=circuit+prepareAnicilia()\n",
        "  applyGrover(N,marked)\n",
        "  print(circuit)"
      ],
      "metadata": {
        "id": "qjGoo7jB0qEF"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a=[1,2,4,5,7,8,9,10,11,12]\n",
        "getlessThan(9,a)\n",
        "\n",
        "print(circuit)\n",
        "circuit.append(cirq.measure(qubits,key='lessThan'))\n",
        "result = sim.run(circuit, repetitions=1000000)\n",
        "custom_histogram = result.histogram(key = 'lessThan')\n",
        "\n",
        "cirq.plot_state_histogram(custom_histogram, plt.subplot(),title=\"lessThan\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 818
        },
        "id": "N9FkbYNEdmTU",
        "outputId": "b306fc69-9f4d-41b4-e17f-3b1c9c678725"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1, 2, 4, 5, 7, 8]\n",
            "aux0: ───X───H───────X───────────X───────────X───────────X───────────X───────X───────────────X───────────\n",
            "                     │           │           │           │           │       │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───X───@───X───X───@───X───X───@───X───@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │       │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───────@───────────@───────────@───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │               │\n",
            "q2: ─────H───────X───@───X───────@───X───────@───X───X───@───X───────@───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │               │\n",
            "q3: ─────H───────────@───X───────@───X───X───@───X───────@───────────@───X───@───X───H───X───@───X───H───\n",
            "aux0: ───X───H───────X───────────X───────────X───────────X───────────X───────X───────────────X───────────\n",
            "                     │           │           │           │           │       │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───X───@───X───X───@───X───X───@───X───@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │       │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───────@───────────@───────────@───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │               │\n",
            "q2: ─────H───────X───@───X───────@───X───────@───X───X───@───X───────@───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │               │\n",
            "q3: ─────H───────────@───X───────@───X───X───@───X───────@───────────@───X───@───X───H───X───@───X───H───\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a=[1,2,4,5,7,8,9,10,11,12]\n",
        "getlessThan(8,a)\n",
        "\n",
        "print(circuit)\n",
        "circuit.append(cirq.measure(qubits,key='lessThan'))\n",
        "result = sim.run(circuit, repetitions=1000000)\n",
        "custom_histogram = result.histogram(key = 'lessThan')\n",
        "\n",
        "cirq.plot_state_histogram(custom_histogram, plt.subplot(),title=\"lessThan\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 818
        },
        "id": "JQ_dkkklewss",
        "outputId": "89291721-a69c-4662-8c69-b2b49c09bc19"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1, 2, 4, 5, 7]\n",
            "aux0: ───X───H───────X───────────X───────────X───────────X───────────X───────────────X───────────\n",
            "                     │           │           │           │           │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───X───@───X───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───────@───────────@───────────@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │               │\n",
            "q2: ─────H───────X───@───X───────@───X───────@───X───X───@───X───────@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │               │\n",
            "q3: ─────H───────────@───X───────@───X───X───@───X───────@───────────@───────H───X───@───X───H───\n",
            "aux0: ───X───H───────X───────────X───────────X───────────X───────────X───────────────X───────────\n",
            "                     │           │           │           │           │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───X───@───X───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───────@───────────@───────────@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │               │\n",
            "q2: ─────H───────X───@───X───────@───X───────@───X───X───@───X───────@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │               │\n",
            "q3: ─────H───────────@───X───────@───X───X───@───X───────@───────────@───────H───X───@───X───H───\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a=[1,2,4,5,7,8,9,10,11,12]\n",
        "getlessThan(10,a)\n",
        "\n",
        "print(circuit)\n",
        "circuit.append(cirq.measure(qubits,key='lessThan'))\n",
        "result = sim.run(circuit, repetitions=1000000)\n",
        "custom_histogram = result.histogram(key = 'lessThan')\n",
        "\n",
        "cirq.plot_state_histogram(custom_histogram, plt.subplot(),title=\"lessThan\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 818
        },
        "id": "hVfm4KmPe3YH",
        "outputId": "604b9cc3-37b0-4c9d-bb8f-0acb732bede8"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1, 2, 4, 5, 7, 8, 9]\n",
            "aux0: ───X───H───────X───────────X───────────X───────────X───────────X───────X───────────X───────────────X───────────\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───X───@───X───X───@───X───X───@───X───@───────────@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───────@───────────@───────────@───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q2: ─────H───────X───@───X───────@───X───────@───X───X───@───X───────@───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q3: ─────H───────────@───X───────@───X───X───@───X───────@───────────@───X───@───X───────@───────H───X───@───X───H───\n",
            "aux0: ───X───H───────X───────────X───────────X───────────X───────────X───────X───────────X───────────────X───────────\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───X───@───X───X───@───X───X───@───X───@───────────@───────H───X───@───X───H───\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───────@───────────@───────────@───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q2: ─────H───────X───@───X───────@───X───────@───X───X───@───X───────@───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │           │           │           │       │           │               │\n",
            "q3: ─────H───────────@───X───────@───X───X───@───X───────@───────────@───X───@───X───────@───────H───X───@───X───H───\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a=[1,2,4,5,7,8,9,10,11,12]\n",
        "getlessThan(2,a)\n",
        "\n",
        "print(circuit)\n",
        "circuit.append(cirq.measure(qubits,key='lessThan'))\n",
        "result = sim.run(circuit, repetitions=1000000)\n",
        "custom_histogram = result.histogram(key = 'lessThan')\n",
        "\n",
        "cirq.plot_state_histogram(custom_histogram, plt.subplot(),title=\"lessThan\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 818
        },
        "id": "SjRuN44BfK01",
        "outputId": "8b5dc29f-9cb6-46bd-910c-6fe04fbe8d01"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1]\n",
            "aux0: ───X───H───────X───────────────X───────────────X───────────────X───────────────X───────────────X───────────\n",
            "                     │               │               │               │               │               │\n",
            "q0: ─────H───────X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───\n",
            "                     │               │               │               │               │               │\n",
            "q1: ─────H───────X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───\n",
            "                     │               │               │               │               │               │\n",
            "q2: ─────H───────X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───\n",
            "                     │               │               │               │               │               │\n",
            "q3: ─────H───────────@───────H───X───@───X───H───────@───────H───X───@───X───H───────@───────H───X───@───X───H───\n",
            "aux0: ───X───H───────X───────────────X───────────────X───────────────X───────────────X───────────────X───────────\n",
            "                     │               │               │               │               │               │\n",
            "q0: ─────H───────X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───\n",
            "                     │               │               │               │               │               │\n",
            "q1: ─────H───────X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───\n",
            "                     │               │               │               │               │               │\n",
            "q2: ─────H───────X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───X───@───X───H───\n",
            "                     │               │               │               │               │               │\n",
            "q3: ─────H───────────@───────H───X───@───X───H───────@───────H───X───@───X───H───────@───────H───X───@───X───H───\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a=[1,2,4,5,7,8,9,10,11,12]\n",
        "getlessThan(3,a)\n",
        "\n",
        "print(circuit)\n",
        "circuit.append(cirq.measure(qubits,key='lessThan'))\n",
        "result = sim.run(circuit, repetitions=1000000)\n",
        "custom_histogram = result.histogram(key = 'lessThan')\n",
        "\n",
        "cirq.plot_state_histogram(custom_histogram, plt.subplot(),title=\"lessThan\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 818
        },
        "id": "lVpDW3_2f7V6",
        "outputId": "625f3e0e-cd1a-47b1-f141-4d46b09d60f5"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1, 2]\n",
            "aux0: ───X───H───────X───────────X───────────────X───────────────X───────────X───────────────X───────────\n",
            "                     │           │               │               │           │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───H───X───@───X───H───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │               │               │           │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───H───X───@───X───H───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │               │               │           │               │\n",
            "q2: ─────H───────X───@───X───────@───────H───X───@───X───H───X───@───X───────@───────H───X───@───X───H───\n",
            "                     │           │               │               │           │               │\n",
            "q3: ─────H───────────@───X───────@───X───H───X───@───X───H───────@───X───────@───X───H───X───@───X───H───\n",
            "aux0: ───X───H───────X───────────X───────────────X───────────────X───────────X───────────────X───────────\n",
            "                     │           │               │               │           │               │\n",
            "q0: ─────H───────X───@───X───X───@───X───H───X───@───X───H───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │               │               │           │               │\n",
            "q1: ─────H───────X───@───X───X───@───X───H───X───@───X───H───X───@───X───X───@───X───H───X───@───X───H───\n",
            "                     │           │               │               │           │               │\n",
            "q2: ─────H───────X───@───X───────@───────H───X───@───X───H───X───@───X───────@───────H───X───@───X───H───\n",
            "                     │           │               │               │           │               │\n",
            "q3: ─────H───────────@───X───────@───X───H───X───@───X───H───────@───X───────@───X───H───X───@───X───H───\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}