QIBO_basics.ipynb

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  "metadata": {
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      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BKNW2NYD_Q7t",
        "outputId": "8f4a2fff-1aab-4c48-c9f5-76e0de50efc1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: qibo in /usr/local/lib/python3.10/dist-packages (0.2.9)\n",
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          ]
        }
      ],
      "source": [
        "pip install qibo"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pip install qibojit"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XBCC_NYvItkc",
        "outputId": "10eb68cb-6071-4b2c-eea3-de99d66c4b73"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting qibojit\n",
            "  Downloading qibojit-0.1.4-py3-none-any.whl.metadata (2.1 kB)\n",
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            "Downloading qibojit-0.1.4-py3-none-any.whl (35 kB)\n",
            "Installing collected packages: qibojit\n",
            "Successfully installed qibojit-0.1.4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In order to run simulation, we set the qibojit backend as it's more suitable to run simulation and many qubits."
      ],
      "metadata": {
        "id": "wEaunXbRJUYv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import qibo\n",
        "from qibo import Circuit,gates, hamiltonians\n",
        "#setting the backend:\n",
        "qibo.set_backend('qibojit',platform=\"numba\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MsdSZj9bJC_y",
        "outputId": "ae242239-d0d8-426c-c735-1702c4d87e0d"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "[Qibo 0.2.9|INFO|2024-07-30 05:44:15]: Using qibojit (numba) backend on /CPU:0\n",
            "INFO:qibo.config:Using qibojit (numba) backend on /CPU:0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Building first qibo circuit:\n",
        "n=4\n",
        "c=Circuit(nqubits=n)\n",
        "print(c.draw())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_OWMM2vuKNcM",
        "outputId": "59964698-c8e6-4309-d4b6-8933b1e54d5a"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ─\n",
            "q1: ─\n",
            "q2: ─\n",
            "q3: ─\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#adding gates to the circuit:\n",
        "\n",
        "c.add(gates.H(q=0))#applying hadamard to frst qubit\n",
        "c.add(gates.H(q=1))#applying hadamard to second qubit\n",
        "c.add(gates.Z(q=3))#applying Pauli's Z gate to 4th qubit\n",
        "c.add(gates.X(q=0))#applying Pauli's X gate to 3rd qubit\n",
        "c.add(gates.CNOT(q0=0,q1=2))\n",
        "c.add(gates.CZ(q0=2,q1=1))\n",
        "c.add(gates.Y(q=1).controlled_by(2,3,0))\n",
        "print(c.draw())\n",
        "print()\n",
        "print(c.summary())\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "V0FQR8s_MKao",
        "outputId": "fc0b5071-dd0e-43d7-cd8e-d4b4971d97fc"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ─H─H─H─H─X─o─H─X─o───H─X─o───o─H─X─o───o─H─X─o───o─\n",
            "q1: ─H─H─H─H───|─H───|─Z─H───|─Z─Y─H───|─Z─Y─H───|─Z─Y─\n",
            "q2: ─X─────────X─────X─o─────X─o─o─────X─o─o─────X─o─o─\n",
            "q3: ─Z─Z─────────Z───────Z───────o─Z───────o─Z───────o─\n",
            "\n",
            "Circuit depth = 24\n",
            "Total number of gates = 40\n",
            "Number of qubits = 4\n",
            "Most common gates:\n",
            "h: 16\n",
            "z: 6\n",
            "x: 6\n",
            "cx: 5\n",
            "cz: 4\n",
            "y: 3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#executing the circuit:\n",
        "print(c())\n",
        "print()\n",
        "#printing the final state:\n",
        "print(c().state())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pwaV_UHjQzdl",
        "outputId": "d2cc7ff8-8583-4fea-f097-a776c31e2e2a"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(-0.5+0j)|0100> + (-0.5+0j)|0110> + (0.5+0j)|1000> + (-0.5+0j)|1010>\n",
            "\n",
            "[ 0. +0.j -0. +0.j  0. +0.j -0. +0.j -0.5+0.j -0. +0.j -0.5+0.j  0. -0.j\n",
            "  0.5+0.j -0. +0.j -0.5+0.j  0. -0.j  0. +0.j -0. +0.j -0. +0.j -0. +0.j]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#to print the probabilities from the outcome:\n",
        "probs=c().probabilities()\n",
        "print(probs)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WB467PM5Q8ia",
        "outputId": "3af7a4a1-2025-4e58-8974-3c4bb38169c2"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.   0.   0.   0.   0.25 0.   0.25 0.   0.25 0.   0.25 0.   0.   0.\n",
            " 0.   0.  ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#in order to add measurement gates, we copy the initial steps again:\n",
        "\n",
        "n=4\n",
        "c=Circuit(nqubits=n)\n",
        "c.add(gates.H(q=0))#applying hadamard to frst qubit\n",
        "c.add(gates.H(q=1))#applying hadamard to second qubit\n",
        "c.add(gates.Z(q=3))#applying Pauli's Z gate to 4th qubit\n",
        "c.add(gates.X(q=0))#applying Pauli's X gate to 3rd qubit\n",
        "c.add(gates.CNOT(q0=0,q1=2))\n",
        "c.add(gates.CZ(q0=2,q1=1))\n",
        "c.add(gates.Y(q=1).controlled_by(2,3,0))\n",
        "#adding measurement gates now:\n",
        "\n",
        "c.add(gates.M(*range(n)))\n",
        "print(c.draw())\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-T3VlhSxSRpB",
        "outputId": "7577174a-2c07-4294-9445-33800b40fa15"
      },
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ─H─X─o───o─M─\n",
            "q1: ─H───|─Z─Y─M─\n",
            "q2: ─────X─o─o─M─\n",
            "q3: ─Z───────o─M─\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Again we can execute and collect the outcome.\n",
        "#but now we can mention the shots\n",
        "outcome=c(nshots=1000)\n",
        "print(outcome)\n",
        "print()\n",
        "print(outcome.probabilities())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fcf3gx-dS34G",
        "outputId": "b9bec292-4852-4f93-d693-5f516b62427f"
      },
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(0.5+0j)|0000> + (0.5+0j)|0100> + (0.5+0j)|1010> + (-0.5+0j)|1110>\n",
            "\n",
            "[0.25 0.   0.   0.   0.25 0.   0.   0.   0.   0.   0.25 0.   0.   0.\n",
            " 0.25 0.  ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#to collect the frequencies(no.of shots)\n",
        "frequencies=outcome.frequencies()\n",
        "print(frequencies)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PVo6DS8PTksZ",
        "outputId": "333352ae-abf5-40a6-ccf7-6e02806e3684"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Counter({'0000': 273, '0100': 250, '1110': 241, '1010': 236})\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pip install git+https://github.com/qiboteam/qiboedu"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_HD8YookULlD",
        "outputId": "df098ca4-5a51-4c43-b587-e0f22fb46314"
      },
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting git+https://github.com/qiboteam/qiboedu\n",
            "  Cloning https://github.com/qiboteam/qiboedu to /tmp/pip-req-build-828al6d0\n",
            "  Running command git clone --filter=blob:none --quiet https://github.com/qiboteam/qiboedu /tmp/pip-req-build-828al6d0\n",
            "  Resolved https://github.com/qiboteam/qiboedu to commit c05f53215f1e0efff377a0310748b8dc3753dac7\n",
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "Collecting matplotlib<4.0.0,>=3.8.0 (from qiboedu==0.1.0)\n",
            "  Downloading matplotlib-3.9.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (11 kB)\n",
            "Requirement already satisfied: qibo<0.3.0,>=0.2.4 in /usr/local/lib/python3.10/dist-packages (from qiboedu==0.1.0) (0.2.9)\n",
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            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (1.2.1)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (0.12.1)\n",
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            "Requirement already satisfied: kiwisolver>=1.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (1.4.5)\n",
            "Requirement already satisfied: numpy>=1.23 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (1.26.4)\n",
            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (24.1)\n",
            "Requirement already satisfied: pillow>=8 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (9.4.0)\n",
            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (3.1.2)\n",
            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib<4.0.0,>=3.8.0->qiboedu==0.1.0) (2.8.2)\n",
            "Requirement already satisfied: cma<4.0.0,>=3.3.0 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (3.4.0)\n",
            "Requirement already satisfied: hyperopt<0.3.0,>=0.2.7 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (0.2.7)\n",
            "Requirement already satisfied: joblib<2.0.0,>=1.2.0 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (1.4.2)\n",
            "Requirement already satisfied: networkx<4.0.0,>=3.2.1 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (3.3)\n",
            "Requirement already satisfied: openqasm3>=0.5.0 in /usr/local/lib/python3.10/dist-packages (from openqasm3[parser]>=0.5.0->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (1.0.0)\n",
            "Requirement already satisfied: scipy<2.0.0,>=1.10.1 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (1.13.1)\n",
            "Requirement already satisfied: setuptools<70.0.0,>=69.1.1 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (69.5.1)\n",
            "Requirement already satisfied: sympy<2.0.0,>=1.11.1 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (1.13.1)\n",
            "Requirement already satisfied: tabulate<0.10.0,>=0.9.0 in /usr/local/lib/python3.10/dist-packages (from qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (0.9.0)\n",
            "Requirement already satisfied: numba>=0.59.0 in /usr/local/lib/python3.10/dist-packages (from qibojit<0.2.0,>=0.1.2->qiboedu==0.1.0) (0.60.0)\n",
            "Requirement already satisfied: psutil<6.0.0,>=5.9.5 in /usr/local/lib/python3.10/dist-packages (from qibojit<0.2.0,>=0.1.2->qiboedu==0.1.0) (5.9.5)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.10/dist-packages (from hyperopt<0.3.0,>=0.2.7->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (1.16.0)\n",
            "Requirement already satisfied: future in /usr/local/lib/python3.10/dist-packages (from hyperopt<0.3.0,>=0.2.7->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (1.0.0)\n",
            "Requirement already satisfied: tqdm in /usr/local/lib/python3.10/dist-packages (from hyperopt<0.3.0,>=0.2.7->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (4.66.4)\n",
            "Requirement already satisfied: cloudpickle in /usr/local/lib/python3.10/dist-packages (from hyperopt<0.3.0,>=0.2.7->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (2.2.1)\n",
            "Requirement already satisfied: py4j in /usr/local/lib/python3.10/dist-packages (from hyperopt<0.3.0,>=0.2.7->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (0.10.9.7)\n",
            "Requirement already satisfied: llvmlite<0.44,>=0.43.0dev0 in /usr/local/lib/python3.10/dist-packages (from numba>=0.59.0->qibojit<0.2.0,>=0.1.2->qiboedu==0.1.0) (0.43.0)\n",
            "Requirement already satisfied: antlr4-python3-runtime<4.14,>=4.7 in /usr/local/lib/python3.10/dist-packages (from openqasm3[parser]>=0.5.0->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (4.13.1)\n",
            "Requirement already satisfied: mpmath<1.4,>=1.1.0 in /usr/local/lib/python3.10/dist-packages (from sympy<2.0.0,>=1.11.1->qibo<0.3.0,>=0.2.4->qiboedu==0.1.0) (1.3.0)\n",
            "Downloading matplotlib-3.9.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (8.3 MB)\n",
            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m8.3/8.3 MB\u001b[0m \u001b[31m66.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hBuilding wheels for collected packages: qiboedu\n",
            "  Building wheel for qiboedu (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for qiboedu: filename=qiboedu-0.1.0-py3-none-any.whl size=17157 sha256=ee8fcb5e69457b334e4b74db5bfaf94ba2eb8685931b5b26bbac065927387e96\n",
            "  Stored in directory: /tmp/pip-ephem-wheel-cache-004cl8_0/wheels/88/3e/b3/56312e57970f2fabccd0b51c358665866db085f22720ced56a\n",
            "Successfully built qiboedu\n",
            "Installing collected packages: matplotlib, qiboedu\n",
            "  Attempting uninstall: matplotlib\n",
            "    Found existing installation: matplotlib 3.7.1\n",
            "    Uninstalling matplotlib-3.7.1:\n",
            "      Successfully uninstalled matplotlib-3.7.1\n",
            "Successfully installed matplotlib-3.9.1 qiboedu-0.1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "STATE VISUALIZATION:\n",
        "\n",
        "We can use the 'scripts.plotscripts.visualize_state' function, which takes as an argument the counter object you get calling circuit(nshots=nshots).frequencies(binary=True).\n",
        "\n"
      ],
      "metadata": {
        "id": "BlO8pcHUUbox"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from qiboedu.scripts.plotscripts import visualize_states"
      ],
      "metadata": {
        "id": "52HRuYCTUTNA"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "visualize_states(frequencies)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "id": "58Pd9pXDVYI_",
        "outputId": "73e95203-9336-4600-ce7d-85fa0527a872"
      },
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x375 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "*Combining circuits*: two or more circuits into one!"
      ],
      "metadata": {
        "id": "E5K5A6MhV60l"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# initialize c1:\n",
        "c1 = Circuit(3)\n",
        "c1.add(gates.H(0))\n",
        "c1.add(gates.CNOT(1,0))\n",
        "c1.add(gates.Z(1))\n",
        "print(c1.draw())\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O5suk6IMVja3",
        "outputId": "748e07be-712c-4400-9c2b-71d8f3c8d3eb"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ─H─X───\n",
            "q1: ───o─Z─\n",
            "q2: ───────\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#initialize c2:\n",
        "c2 = Circuit(3)\n",
        "c2.add(gates.H(2))\n",
        "c2.add(gates.Z(1))\n",
        "c2.add(gates.Y(1))\n",
        "c2.add(gates.CZ(2,1))\n",
        "print(c2.draw())\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "glivmJeuZTPv",
        "outputId": "f8e1b981-a1ba-473e-ddf6-2ec2ad1e93d4"
      },
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ───────\n",
            "q1: ─Z─Y─Z─\n",
            "q2: ─H───o─\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#combining these two circuits:\n",
        "c=c2+c1\n",
        "print(c.draw())\n",
        "print()\n",
        "c=c1+c2\n",
        "print(c.draw())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZcKdZYZPZiaC",
        "outputId": "f4a1aedd-2e8d-4195-d3e7-821dd5a446f9"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ───────H─X───\n",
            "q1: ─Z─Y─Z───o─Z─\n",
            "q2: ─H───o───────\n",
            "\n",
            "q0: ─H─X─────────\n",
            "q1: ───o─Z─Z─Y─Z─\n",
            "q2: ─────H─────o─\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Simulating Bell's state: create a two-qubit circuit, lead one of the two qubits to a superposed state using an Hadamard gate and then apply a controlled-NOT gate to the second qubit using the superposed one as control."
      ],
      "metadata": {
        "id": "zj2PWnD0aY5U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "c = Circuit(2)\n",
        "c.add(gates.H(0))\n",
        "c.add(gates.CNOT(q0=0, q1=1))\n",
        "print(c.add(gates.M(*range(2)))) #measurement part\n",
        "print()\n",
        "print(c(nshots=2000)) #outcome"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uMWkm5uEZz48",
        "outputId": "2af575c0-c509-40d9-d5f4-5f0d74de88f1"
      },
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MeasurementResult(qubits=(0, 1), nshots=0)\n",
            "\n",
            "(0.70711+0j)|00> + (0.70711+0j)|11>\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "frequencies=c().frequencies()\n",
        "print(frequencies)\n",
        "visualize_states(frequencies)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "id": "xDNbN1t-b4Ac",
        "outputId": "fd4b0ffd-d89a-403a-ff37-667ab2a2ae26"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Counter({'11': 541, '00': 459})\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x375 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Parameterized gates : are those gates which are used to manipulate the quantum states."
      ],
      "metadata": {
        "id": "WUVnCVdqcsjO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "nqubits=2\n",
        "nlayers=2 #the loop goes twice\n",
        "c = Circuit(nqubits=nqubits)\n",
        "for l in range(nlayers):\n",
        "  for q in range(nqubits):\n",
        "    c.add(gates.RY(q=q, theta=0))\n",
        "    c.add(gates.RZ(q=q, theta=0))\n",
        "\n",
        "c.add(gates.M(*range(nqubits)))\n",
        "\n",
        "print(c.draw())\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F1IOR7GtcB_l",
        "outputId": "336c0e67-7ad3-4e31-863a-3268494004c0"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ─RY─RZ─RY─RZ─M─\n",
            "q1: ─RY─RZ─RY─RZ─M─\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#modified code\n",
        "nqubits=2\n",
        "nlayers=2 #the loop goes twice\n",
        "c = Circuit(nqubits=nqubits)\n",
        "for l in range(nlayers):\n",
        "  for q in range(nqubits):\n",
        "    c.add(gates.RY(q=q, theta=0))\n",
        "    c.add(gates.RZ(q=q, theta=0)) #theeta is set to 0\n",
        "  c.add(gates.CNOT(q0=0,q1=nqubits-1))\n",
        "c.add(gates.M(*range(nqubits)))\n",
        "\n",
        "print(c.draw())\n",
        "#All the rotational angles are now set to zero, and the final state is equal to the initial state\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QeU5OlzXfox6",
        "outputId": "aaccec5e-98c0-47f8-e565-5a3308c8ec40"
      },
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ─RY─RZ─o─RY─RZ─o─M─\n",
            "q1: ─RY─RZ─X─RY─RZ─X─M─\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# execute the circuit and collect frequencies\n",
        "outcome = c(nshots=1000)\n",
        "freq = outcome.frequencies()\n",
        "\n",
        "print(outcome)\n",
        "\n",
        "visualize_states(freq)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 411
        },
        "id": "XFVy0U2_f-sG",
        "outputId": "3abf91c3-9688-4550-8db6-7a4b4fa149b2"
      },
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(1+0j)|00>\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x375 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "params=c.get_parameters()\n",
        "c.get_parameters()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UKhZIzRMhI1q",
        "outputId": "fb9e187e-a761-4a48-83a3-cd884f4b4a27"
      },
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(0,), (0,), (0,), (0,), (0,), (0,), (0,), (0,)]"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#generating a new random list of parameters:\n",
        "np.random.seed(42)\n",
        "angles=np.random.random(len(params))\n",
        "print(angles)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "k1iVAPaLha2y",
        "outputId": "c39f5867-a27f-48a7-f5ec-a33286dd5f0b"
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.37454012 0.95071431 0.73199394 0.59865848 0.15601864 0.15599452\n",
            " 0.05808361 0.86617615]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#adding these new set of angles as parameters\n",
        "c.set_parameters(angles)\n",
        "print(c.draw())\n",
        "print()\n",
        "c.get_parameters()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WBbClh1hiUAi",
        "outputId": "73da31d6-5315-4ac0-b38a-b19bf9a5cd2c"
      },
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "q0: ─RY─RZ─o─RY─RZ─o─M─\n",
            "q1: ─RY─RZ─X─RY─RZ─X─M─\n",
            "\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(0.3745401188473625,),\n",
              " (0.9507143064099162,),\n",
              " (0.7319939418114051,),\n",
              " (0.5986584841970366,),\n",
              " (0.15601864044243652,),\n",
              " (0.15599452033620265,),\n",
              " (0.05808361216819946,),\n",
              " (0.8661761457749352,)]"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "outcome = c(nshots=1000)\n",
        "freq = outcome.frequencies()\n",
        "\n",
        "print(outcome)\n",
        "visualize_states(freq)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "id": "5CKl5pncilCR",
        "outputId": "bba02dcc-aacc-45f2-83aa-eb2c6a88502f"
      },
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(0.24457-0.8724j)|00> + (0.35732+0.04459j)|01> + (0.16235+0.12021j)|10> + (0.08551-0.03628j)|11>\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x375 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Hamiltonians:\n",
        " Qibo stores a set of precomputed hamiltonians, which can be called and used to compute expectation values on the states we manipulate using circuits. One of it is the TFIM- transverse field ising model."
      ],
      "metadata": {
        "id": "2Y3mMRsfjBN2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#defining hamiltonian:\n",
        "h=hamiltonians.TFIM(2)\n",
        "matrix=h.matrix\n",
        "print(matrix)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "myFei3R7nTEa",
        "outputId": "62c76061-29d7-4090-effe-f85bfd5373dc"
      },
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-2.-0.j -0.-0.j -0.-0.j -0.-0.j]\n",
            " [-0.-0.j  2.-0.j -0.-0.j -0.-0.j]\n",
            " [-0.-0.j -0.-0.j  2.-0.j -0.-0.j]\n",
            " [-0.-0.j -0.-0.j -0.-0.j -2.-0.j]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#finding the eigenstates,eigenvalues and ground state\n",
        "print(h.eigenvectors())\n",
        "print()\n",
        "print(h.eigenvalues())\n",
        "print()\n",
        "print(h.ground_state())\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eGv8HA6jnmH4",
        "outputId": "86fb5227-4968-4fdb-baa9-4a87aee7d321"
      },
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n",
            " [0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n",
            " [0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n",
            " [0.+0.j 1.+0.j 0.+0.j 0.+0.j]]\n",
            "\n",
            "[-2. -2.  2.  2.]\n",
            "\n",
            "[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#the expectation value of an hamiltonian over a target state\n",
        "# compute the expectation < psi | H | psi > : the circuit we obtained above by a series of rotations\n",
        "print(c().state()) #final state\n",
        "h.expectation(c().state())\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z8sFpy-2oFiC",
        "outputId": "ff935a1c-ddd6-44be-b55f-baf00dfb45f6"
      },
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.24456537-0.8724044j  0.35731797+0.04459447j 0.16234611+0.12020721j\n",
            " 0.08550659-0.03627859j]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-1.3181166854990443"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ]
    }
  ]
}