LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/qulacs.simulator 25 qubit (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / qulacs.simulator 25 qubit (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "2610533f-dc4f-4873-b441-8e986a08f774"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695140808.7791903\n",
            "Tue Sep 19 16:26:48 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "# !pip install pennylane custatevec-cu11 pennylane-lightning-gpu\n",
        "# !pip install qulacs\n",
        "# !pip install pennylane pennylane-qulacs --upgrade\n",
        "\n",
        "import time\n",
        "seconds = time.time()\n",
        "print(\"Time in seconds since beginning of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "12e063dd-1bc1-4800-d40c-94e2dcae356d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.35 0.91 0.42]\n",
            " [0.91 0.38 0.54]\n",
            " [0.42 0.54 0.45]]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def create_data_point(n):\n",
        "    \"\"\"\n",
        "    Returns a random undirected adjacency matrix of dimension (n,n).\n",
        "    The diagonal elements are interpreted as node attributes.\n",
        "    \"\"\"\n",
        "    mat = np.random.rand(n, n)\n",
        "    A = (mat + np.transpose(mat))/2\n",
        "    return np.round(A, decimals=2)\n",
        "\n",
        "A = create_data_point(3)\n",
        "print(A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fZNWu6j_jAmh"
      },
      "source": [
        "Let\\'s also write a function to generate permuted versions of this\n",
        "adjacency matrix.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "38d5f854-57e7-4361-a567-8efec0389259"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.38 0.54 0.91]\n",
            " [0.54 0.45 0.42]\n",
            " [0.91 0.42 0.35]]\n"
          ]
        }
      ],
      "source": [
        "def permute(A, permutation):\n",
        "    \"\"\"\n",
        "    Returns a copy of A with rows and columns swapped according to permutation.\n",
        "    For example, the permutation [1, 2, 0] swaps 0->1, 1->2, 2->0.\n",
        "    \"\"\"\n",
        "\n",
        "    P = np.zeros((len(A), len(A)))\n",
        "    for i,j in enumerate(permutation):\n",
        "        P[i,j] = 1\n",
        "\n",
        "    return P @ A @ np.transpose(P)\n",
        "\n",
        "A_perm = permute(A, [1, 2, 0])\n",
        "print(A_perm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Js9CqRTZjAmi"
      },
      "source": [
        "If we create [networkx]{.title-ref} graphs from both adjacency matrices\n",
        "and plot them, we see that they are identical as claimed.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "d5dc738e-6b92-455e-e88c-667eeca984f8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
        "\n",
        "# interpret diagonal of matrix as node attributes\n",
        "node_labels = {n: A[n,n] for n in range(len(A))}\n",
        "np.fill_diagonal(A, np.zeros(len(A)))\n",
        "\n",
        "G1 = nx.Graph(A)\n",
        "pos1=nx.spring_layout(G1)\n",
        "nx.draw(G1, pos1, labels=node_labels, ax=ax1, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G1,'weight')\n",
        "nx.draw_networkx_edge_labels(G1,pos1,edge_labels=edge_labels, ax=ax1)\n",
        "\n",
        "# interpret diagonal of permuted matrix as node attributes\n",
        "node_labels = {n: A_perm[n,n] for n in range(len(A_perm))}\n",
        "np.fill_diagonal(A_perm, np.zeros(len(A)))\n",
        "\n",
        "G2 = nx.Graph(A_perm)\n",
        "pos2=nx.spring_layout(G2)\n",
        "nx.draw(G2, pos2, labels=node_labels, ax=ax2, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G2,'weight')\n",
        "nx.draw_networkx_edge_labels(G2,pos2,edge_labels=edge_labels, ax=ax2)\n",
        "\n",
        "ax1.set_xlim([1.2*x for x in ax1.get_xlim()])\n",
        "ax2.set_xlim([1.2*x for x in ax2.get_xlim()])\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "eUhWZ9_3jAmi"
      },
      "outputs": [],
      "source": [
        "import pennylane as qml\n",
        "\n",
        "def perm_equivariant_embedding(A, betas, gammas):\n",
        "    \"\"\"\n",
        "    Ansatz to embedd a graph with node and edge weights into a quantum state.\n",
        "\n",
        "    The adjacency matrix A contains the edge weights on the off-diagonal,\n",
        "    as well as the node attributes on the diagonal.\n",
        "\n",
        "    The embedding contains trainable weights 'betas' and 'gammas'.\n",
        "    \"\"\"\n",
        "    n_nodes = len(A)\n",
        "    n_layers = len(betas) # infer the number of layers from the parameters\n",
        "\n",
        "    # initialise in the plus state\n",
        "    for i in range(n_nodes):\n",
        "        qml.Hadamard(i)\n",
        "\n",
        "    for l in range(n_layers):\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            for j in range(i):\n",
        "            \t# factor of 2 due to definition of gate\n",
        "                qml.IsingZZ(2*gammas[l]*A[i,j], wires=[i,j])\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            qml.RX(A[i,i]*betas[l], wires=i)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "glOVsqRvjAmi"
      },
      "source": [
        "We can use this ansatz in a circuit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "6fa4a646-8dff-4851-f68f-5ab30da4fcf5"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAJu8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAJu8AwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABs8g4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAsMk7AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMCmNTnBxU72WH0AAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"qulacs.simulator\", wires=n_qubits)\n",
        "\n",
        "@qml.qnode(dev)\n",
        "def eqc(adjacency_matrix, observable, trainable_betas, trainable_gammas):\n",
        "    \"\"\"Circuit that uses the permutation equivariant embedding\"\"\"\n",
        "\n",
        "    perm_equivariant_embedding(adjacency_matrix, trainable_betas, trainable_gammas)\n",
        "    return qml.expval(observable)\n",
        "\n",
        "\n",
        "A = create_data_point(n_qubits)\n",
        "betas = np.random.rand(n_layers)\n",
        "gammas = np.random.rand(n_layers)\n",
        "observable = qml.PauliX(0) @ qml.PauliX(1) @ qml.PauliX(3)\n",
        "\n",
        "qml.draw_mpl(eqc, decimals=2)(A, observable, betas, gammas)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TIHRQVnDjAmi"
      },
      "source": [
        "Validating the equivariance\n",
        "===========================\n",
        "\n",
        "Let\\'s now check if the circuit is really equivariant!\n",
        "\n",
        "This is the expectation value we get using the original adjacency matrix\n",
        "as an input:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "6f3503b9-5005-4122-cc24-b6ac86391753"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0005767497522288211\n"
          ]
        }
      ],
      "source": [
        "result_A = eqc(A, observable, betas, gammas)\n",
        "print(\"Model output for A:\", result_A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ncmkAwH-jAmj"
      },
      "source": [
        "If we permute the adjacency matrix, this is what we get:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "5e1963ab-f26d-42f9-9db4-49bd2e4b3a1a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.21229861616565854\n"
          ]
        }
      ],
      "source": [
        "perm = [2, 3, 0, 1, 4]\n",
        "A_perm = permute(A, perm)\n",
        "result_Aperm = eqc(A_perm, observable, betas, gammas)\n",
        "print(\"Model output for permutation of A: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZOIqQmysjAmj"
      },
      "source": [
        "Why are the two values different? Well, we constructed an *equivariant*\n",
        "ansatz, not an *invariant* one! Remember, an *invariant* ansatz means\n",
        "that embedding a permutation of the adjacency matrix leads to the same\n",
        "state as an embedding of the original matrix. An *equivariant* ansatz\n",
        "embeds the permuted adjacency matrix into a state where the qubits are\n",
        "permuted as well.\n",
        "\n",
        "As a result, the final state before measurement is only the same if we\n",
        "permute the qubits in the same manner that we permute the input\n",
        "adjacency matrix. We could insert a permutation operator\n",
        "`qml.Permute(perm)` to achieve this, or we simply permute the wires of\n",
        "the observables!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "MgYVIMP6jAmj"
      },
      "outputs": [],
      "source": [
        "observable_perm = qml.PauliX(perm[0]) @ qml.PauliX(perm[1]) @ qml.PauliX(perm[3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pb21hBrLjAmj"
      },
      "source": [
        "Now everything should work out!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "516b6ecc-9a6c-4caa-a5e3-af17c7bd244a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.02484134379232444\n"
          ]
        }
      ],
      "source": [
        "result_Aperm = eqc(A_perm, observable_perm, betas, gammas)\n",
        "print(\"Model output for permutation of A, and with permuted observable: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0wblJk9mjAmj"
      },
      "source": [
        "Et voilà!\n",
        "\n",
        "Conclusion\n",
        "==========\n",
        "\n",
        "Equivariant graph embeddings can be combined with other equivariant\n",
        "parts of a quantum machine learning pipeline (like measurements and the\n",
        "cost function). [Skolik et al.\n",
        "(2022)](https://arxiv.org/pdf/2205.06109.pdf), for example, use such a\n",
        "pipeline as part of a reinforcement learning scheme that finds heuristic\n",
        "solutions for the traveling salesman problem. Their simulations compare\n",
        "a fully equivariant model to circuits that break permutation\n",
        "equivariance and show that it performs better, confirming that if we\n",
        "know about structure in our data, we should try to use this knowledge in\n",
        "machine learning.\n",
        "\n",
        "References\n",
        "==========\n",
        "\n",
        "1.  Andrea Skolik, Michele Cattelan, Sheir Yarkoni,Thomas Baeck and\n",
        "    Vedran Dunjko (2022). Equivariant quantum circuits for learning on\n",
        "    weighted graphs.\n",
        "    [arXiv:2205.06109](https://arxiv.org/abs/2205.06109)\n",
        "2.  Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone,\n",
        "    Patrick J. Coles, Frédéric Sauvage, Martín Larocca and Marco Cerezo\n",
        "    (2022). Theory for Equivariant Quantum Neural Networks.\n",
        "    [arXiv:2210.08566](https://arxiv.org/abs/2210.08566)\n",
        "\n",
        "About the author\n",
        "================\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "seconds = time.time()\n",
        "print(\"Time in seconds since end of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "HFTIJBPqph2f",
        "outputId": "bf6d82be-4058-4231-f186-f5038ebaf4f0"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695141143.1464021\n",
            "Tue Sep 19 16:32:23 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}