514 lines (514 with data), 2.1 MB

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "04ebd741-af9b-45c8-f85d-8516ae4d6c49"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695104609.1491048\n",
            "Tue Sep 19 06:23:29 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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "794d92bf-26bd-4452-b0f2-7c40ace6dea4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.11 0.8  0.67]\n",
            " [0.8  0.51 0.85]\n",
            " [0.67 0.85 0.83]]\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": "a2f6dcca-3d89-4306-bb2c-9ca5b51f9cbf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.51 0.85 0.8 ]\n",
            " [0.85 0.83 0.67]\n",
            " [0.8  0.67 0.11]]\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": "38db6841-f0c8-4beb-fded-0301b8a325b4"
      },
      "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": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "823c825a-5326-4f65-b006-f361eb7886a3"
      },
      "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.qubit\", 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": "c2a43d7c-5675-4208-8495-01d71226ae39"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.3889629427685978\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": "a6fd1444-d4a4-469a-c9e5-386883ba85e6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.899473282305857\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": "b388083b-3ed0-4b93-b2b2-0477155094c0"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.9164428068626415\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": "8054849a-f973-4d8f-81af-9fd6ad7e44c7"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695104748.932202\n",
            "Tue Sep 19 06:25:48 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
}