[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit TPU 127.58s (5) kkawchak.ipynb

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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 131,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "ccb27c51-4e21-4254-f7c5-1914ed9aff57"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701149526.4135654\n",
            "Tue Nov 28 05:32:06 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\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": 132,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "f985b11c-b5ab-4f69-f991-96dc50e883db"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.01 0.14 0.75]\n",
            " [0.14 0.29 0.74]\n",
            " [0.75 0.74 0.79]]\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": 133,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "acf67322-0338-4f12-e786-c704735c3636"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.29 0.74 0.14]\n",
            " [0.74 0.79 0.75]\n",
            " [0.14 0.75 0.01]]\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": 134,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "a0ce144e-2f86-460c-d730-a61d519eb38f"
      },
      "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": 135,
      "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": 136,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "8a975103-ff31-4e01-ce63-df5591752b4e"
      },
      "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": 137,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "f925fcbb-d53f-499e-e7ae-88c9086aab09"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.002512195969668442\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": 138,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "851457da-5ab1-4899-bc91-beb1e5129f8b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3690025464626867\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": 139,
      "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": 140,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "b2eb2e4e-c887-46a4-ad99-c6356c8d7e6f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.34973985833247573\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": "68260829-bced-46f9-d3bd-ef10043eef50"
      },
      "execution_count": 141,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701149653.9946897\n",
            "Tue Nov 28 05:34:13 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
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      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
    },
    "colab": {
      "provenance": [],
      "machine_shape": "hm"
    },
    "accelerator": "TPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}