LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.gpu 25 qubit V100 23.13s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit V100 23.13s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "92c0976e-12bb-4d2d-bb3d-e709c28a0a3d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695104144.9403753\n",
            "Tue Sep 19 06:15:44 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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "3e6d90eb-824b-4a88-ee1f-865d4fe35d47"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.97 0.38 0.62]\n",
            " [0.38 0.34 0.79]\n",
            " [0.62 0.79 0.05]]\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": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "40b0f5a7-8fc3-4746-f357-5fe14d893ea6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.34 0.79 0.38]\n",
            " [0.79 0.05 0.62]\n",
            " [0.38 0.62 0.97]]\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": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "e17074ef-14f1-4574-df81-06e0f508cd41"
      },
      "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": 17,
      "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": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "0d5a79fe-fa1b-4234-bb09-572e6bd1e4ef"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "a546b054-3365-436f-f82e-1ed4c5474c86"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.002865115170276828\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": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "5f6a0b5d-5a98-4851-a1a8-6ecdd5019aee"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.19818726580512708\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": 21,
      "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": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "5da12bea-f557-4d10-f72a-9b42ac377fd7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4205469111848164\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": "7f9dff1c-7f87-43e0-c106-eba627463fa9"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695104168.0675397\n",
            "Tue Sep 19 06:16:08 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
}