689 lines (689 with data), 190.6 kB

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "TS6zWfrlNVpz",
        "outputId": "1cc311a6-1cfe-4fab-cda5-94e0cd055c87"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1700379676.1201804\n",
            "Sun Nov 19 07:41:16 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",
        "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": "markdown",
      "metadata": {
        "id": "x7Q73jKsNVp0"
      },
      "source": [
        "An equivariant graph embedding\n",
        "==============================\n",
        "\n",
        "::: {.meta}\n",
        ":property=\\\"og:description\\\": Find out more about how to embedd graphs\n",
        "into quantum states. :property=\\\"og:image\\\":\n",
        "<https://pennylane.ai/qml/_images/thumbnail_tutorial_equivariant_graph_embedding.png>\n",
        ":::\n",
        "\n",
        "::: {.related}\n",
        "tutorial\\_geometric\\_qml Geometric quantum machine learning\n",
        ":::\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7wijfDxKNVp1"
      },
      "source": [
        "A notorious problem when data comes in the form of graphs \\-- think of\n",
        "molecules or social media networks \\-- is that the numerical\n",
        "representation of a graph in a computer is not unique. For example, if\n",
        "we describe a graph via an [adjacency\n",
        "matrix](https://en.wikipedia.org/wiki/Adjacency_matrix) whose entries\n",
        "contain the edge weights as off-diagonals and node weights on the\n",
        "diagonal, any simultaneous permutation of rows and columns of this\n",
        "matrix refer to the same graph.\n",
        "\n",
        "![](../demonstrations/equivariant_graph_embedding/adjacency-matrices.png){.align-center\n",
        "width=\"60.0%\"}\n",
        "\n",
        "For example, the graph in the image above is represented by each of the\n",
        "two equivalent adjacency matrices. The top matrix can be transformed\n",
        "into the bottom matrix by swapping the first row with the third row,\n",
        "then swapping the third column with the third column, then the new first\n",
        "row with the second, and finally the first colum with the second.\n",
        "\n",
        "But the number of such permutations grows factorially with the number of\n",
        "nodes in the graph, which is even worse than an exponential growth!\n",
        "\n",
        "If we want computers to learn from graph data, we usually want our\n",
        "models to \\\"know\\\" that all these permuted adjacency matrices refer to\n",
        "the same object, so we do not waste resources on learning this property.\n",
        "In mathematical terms, this means that the model should be in- or\n",
        "equivariant (more about this distinction below) with respect to\n",
        "permutations. This is the basic motivation of [Geometric Deep\n",
        "Learning](https://geometricdeeplearning.com/), ideas of which have found\n",
        "their way into quantum machine learning.\n",
        "\n",
        "This tutorial shows how to implement an example of a trainable\n",
        "permutation equivariant graph embedding as proposed in [Skolik et al.\n",
        "(2022)](https://arxiv.org/pdf/2205.06109.pdf). The embedding maps the\n",
        "adjacency matrix of an undirected graph with edge and node weights to a\n",
        "quantum state, such that permutations of an adjacency matrix get mapped\n",
        "to the same states *if only we also permute the qubit registers in the\n",
        "same fashion*.\n",
        "\n",
        "::: {.note}\n",
        "::: {.title}\n",
        "Note\n",
        ":::\n",
        "\n",
        "The tutorial is meant for beginners and does not contain the\n",
        "mathematical details of the rich theory of equivariance. Have a look [at\n",
        "this demo](https://pennylane.ai/qml/demos/tutorial_geometric_qml.html)\n",
        "if you want to know more.\n",
        ":::\n",
        "\n",
        "Permuted adjacency matrices describe the same graph\n",
        "===================================================\n",
        "\n",
        "Let us first verify that permuted adjacency matrices really describe one\n",
        "and the same graph. We also gain some useful data generation functions\n",
        "for later.\n",
        "\n",
        "First we create random adjacency matrices. The entry $a_{ij}$ of this\n",
        "matrix corresponds to the weight of the edge between nodes $i$ and $j$\n",
        "in the graph. We assume that graphs have no self-loops; instead, the\n",
        "diagonal elements of the adjacency matrix are interpreted as node\n",
        "weights (or \\\"node attributes\\\").\n",
        "\n",
        "Taking the example of a Twitter user retweet network, the nodes would be\n",
        "users, edge weights indicate how often two users retweet each other and\n",
        "node attributes could indicate the follower count of a user.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "RD3UyP_ONVp2",
        "outputId": "52cada45-2de5-4f63-8957-2036933d1618"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.62 0.51 0.49]\n",
            " [0.51 0.46 0.2 ]\n",
            " [0.49 0.2  0.35]]\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": "cuOQH6WINVp2"
      },
      "source": [
        "Let\\'s also write a function to generate permuted versions of this\n",
        "adjacency matrix.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "i9RRz3GrNVp2",
        "outputId": "fbc624c7-40ea-416b-9a8c-65b007793890"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.46 0.2  0.51]\n",
            " [0.2  0.35 0.49]\n",
            " [0.51 0.49 0.62]]\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": "nD0puQC9NVp2"
      },
      "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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "p5NZCKEfNVp2",
        "outputId": "65b79b22-9329-4823-8959-f8b21bb90fd4"
      },
      "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": "markdown",
      "metadata": {
        "id": "gttt4AcTNVp2"
      },
      "source": [
        "::: {.note}\n",
        "::: {.title}\n",
        "Note\n",
        ":::\n",
        "\n",
        "The issue of non-unique numerical representations of graphs ultimately\n",
        "stems from the fact that the nodes in a graph do not have an intrinsic\n",
        "order, and by labelling them in a numerical data structure like a matrix\n",
        "we therefore impose an arbitrary order.\n",
        ":::\n",
        "\n",
        "Permutation equivariant embeddings\n",
        "==================================\n",
        "\n",
        "When we design a machine learning model that takes graph data, the first\n",
        "step is to encode the adjacency matrix into a quantum state using an\n",
        "embedding or [quantum feature\n",
        "map](https://pennylane.ai/qml/glossary/quantum_feature_map.html) $\\phi$:\n",
        "\n",
        "$$A \\rightarrow |\\phi(A)\\rangle .$$\n",
        "\n",
        "We may want the resulting quantum state to be the same for all adjacency\n",
        "matrices describing the same graph. In mathematical terms, this means\n",
        "that $\\phi$ is an *invariant* embedding with respect to simultaneous row\n",
        "and column permutations $\\pi(A)$ of the adjacency matrix:\n",
        "\n",
        "$$|\\phi(A) \\rangle = |\\phi(\\pi(A))\\rangle \\;\\; \\text{ for all } \\pi .$$\n",
        "\n",
        "However, invariance is often too strong a constraint. Think for example\n",
        "of an encoding that associates each node in the graph with a qubit. We\n",
        "might want permutations of the adjacency matrix to lead to the same\n",
        "state *up to an equivalent permutation of the qubits* $P_{\\pi}$, where\n",
        "\n",
        "$$P_{\\pi} |q_1,...,q_n \\rangle = |q_{\\textit{perm}_{\\pi}(1)}, ... q_{\\textit{perm}_{\\pi}(n)} \\rangle .$$\n",
        "\n",
        "The function $\\text{perm}_{\\pi}$ maps each index to the permuted index\n",
        "according to $\\pi$.\n",
        "\n",
        "::: {.note}\n",
        "::: {.title}\n",
        "Note\n",
        ":::\n",
        "\n",
        "The operator $P_{\\pi}$ is implemented by PennyLane\\'s\n",
        "`~pennylane.Permute`{.interpreted-text role=\"class\"}.\n",
        ":::\n",
        "\n",
        "This results in an *equivariant* embedding with respect to permutations\n",
        "of the adjacency matrix:\n",
        "\n",
        "$$|\\phi(A) \\rangle = P_{\\pi}|\\phi(\\pi(A))\\rangle \\;\\; \\text{ for all } \\pi .$$\n",
        "\n",
        "This is exactly what the following quantum embedding is aiming to do!\n",
        "The mathematical details behind these concepts use group theory and are\n",
        "beautiful, but can be a bit daunting. Have a look at [this\n",
        "paper](https://arxiv.org/abs/2210.08566) if you want to learn more.\n",
        "\n",
        "Implementation in PennyLane\n",
        "===========================\n",
        "\n",
        "Let\\'s get our hands dirty with an example. As mentioned, we will\n",
        "implement the permutation-equivariant embedding suggested in [Skolik et\n",
        "al. (2022)](https://arxiv.org/pdf/2205.06109.pdf) which has this\n",
        "structure:\n",
        "\n",
        "![](../demonstrations/equivariant_graph_embedding/circuit.png){.align-center\n",
        "width=\"70.0%\"}\n",
        "\n",
        "The image can be found in [Skolik et al.\n",
        "(2022)](https://arxiv.org/pdf/2205.06109.pdf) and shows one layer of the\n",
        "circuit. The $\\epsilon$ are our edge weights while $\\alpha$ describe the\n",
        "node weights, and the $\\beta$, $\\gamma$ are variational parameters.\n",
        "\n",
        "In PennyLane this looks as follows:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "id": "TIDSojceNVp3"
      },
      "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": "fBNWZT2LNVp3"
      },
      "source": [
        "We can use this ansatz in a circuit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "wk7UvVY-NVp3",
        "outputId": "ba3a5bad-7ec9-4612-eda2-064ce16ab447"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 2400x600 with 1 Axes>"
            ],
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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 5\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"lightning.gpu\", wires=n_qubits)\n",
        "\n",
        "@qml.qnode(dev, diff_method=\"adjoint\")\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": "ctJwGkJ3NVp3"
      },
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "EDqMgzZ7NVp3",
        "outputId": "4581a739-3644-4402-f659-00b7a68c205c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.4200109706653141\n"
          ]
        }
      ],
      "source": [
        "result_A = eqc(A, observable, betas, gammas)\n",
        "print(\"Model output for A:\", result_A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DEkoYys7NVp3"
      },
      "source": [
        "If we permute the adjacency matrix, this is what we get:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "qWDQi1aRNVp3",
        "outputId": "521ade5e-fee9-4aeb-c3a6-6dd794016d1a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.236328502946865\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": "0MuYtWbFNVp3"
      },
      "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": 31,
      "metadata": {
        "id": "cQLZbuBENVp4"
      },
      "outputs": [],
      "source": [
        "observable_perm = qml.PauliX(perm[0]) @ qml.PauliX(perm[1]) @ qml.PauliX(perm[3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2e8FSH7dNVp4"
      },
      "source": [
        "Now everything should work out!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "fJ6p7TLFNVp4",
        "outputId": "551f1a23-4cab-4c75-8bf6-eeb4bacb4d67"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4200109706653141\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": "g-F-D4kNNVp4"
      },
      "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": "DAMWWXsOTLna",
        "outputId": "1cc7b004-e9db-4668-cfcd-adc5cf487800"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1700379677.3346224\n",
            "Sun Nov 19 07:41:17 2023\n"
          ]
        }
      ]
    }
  ],
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    "colab": {
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