[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit T4 27.53s (4) kkawchak.ipynb

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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "a89beb80-b4d6-49cc-9aa3-363339821c64"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701145942.8514416\n",
            "Tue Nov 28 04:32:22 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "\n",
        "# !pip install pennylane pennylane-lightning-gpu custatevec-cu11 --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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "1c40518d-418d-425b-f7c9-cdf6560f6d4a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.53 0.66 0.37]\n",
            " [0.66 0.81 0.53]\n",
            " [0.37 0.53 0.71]]\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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "1cfbe494-6398-435a-9822-998e27b0c344"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.81 0.53 0.66]\n",
            " [0.53 0.71 0.37]\n",
            " [0.66 0.37 0.53]]\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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "3dd0130c-e552-47aa-be12-3a9829a159ea"
      },
      "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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "8ddfbd93-b74f-41a1-eafe-a9430f55dc83"
      },
      "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": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "eca362b3-800b-40cb-a5fd-2c01b7d1d771"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0003456006271181661\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": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "624fa1cf-20ce-4391-94c3-56c6d65be462"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.37498823051326524\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": 54,
      "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": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "eeb3d1b1-6942-43dd-cd1b-d73c6d8fa951"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4456400709730666\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": "05a68139-8187-46b4-af19-324f8905cd7d"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701145970.3836432\n",
            "Tue Nov 28 04:32:50 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": "T4",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}