LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/lightning.gpu 25 qubit A100 (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / lightning.gpu 25 qubit A100 (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "24373769-83da-4ebb-8f09-3142f969386c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695165484.7891946\n",
            "Tue Sep 19 23:18:04 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",
        "\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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "e28694ea-3ae9-4b1b-eaef-1bb6f7bcecd0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.93 0.5  0.45]\n",
            " [0.5  0.38 0.54]\n",
            " [0.45 0.54 0.23]]\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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "cafa1783-97fd-4385-9db3-53f541647aee"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.38 0.54 0.5 ]\n",
            " [0.54 0.23 0.45]\n",
            " [0.5  0.45 0.93]]\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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "7fabcbce-0ce5-4c34-e6c0-9a8cc256d67e"
      },
      "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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "061bf547-6e2b-4d17-c954-b244776fdb41"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"lightning.gpu\", 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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "6bf0a5b2-1782-49a1-c20f-c49ba7f27482"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -1.4681137572879687e-05\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": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "50a14749-a908-4411-8ad4-233ee8f7cde1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.46773338191124153\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": 32,
      "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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "74494dbd-25c5-4e2d-b8f1-597c7f51ce59"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3473364920399305\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": "f3276fc1-eb5b-4c3b-b1cc-f95830d11e79"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695165504.6497087\n",
            "Tue Sep 19 23:18:24 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": "A100",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}