[404218]: / Code / PennyLane / Benchmarking Devices / default.qubit 25 qubit (2) kkawchak.ipynb

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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 101,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "cedc28b3-a56d-467a-ab25-99b5f986eb51"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695107709.5078914\n",
            "Tue Sep 19 07:15:09 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": 102,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "a53782c4-1aec-402b-b492-9be4389d6885"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.98 0.53 0.63]\n",
            " [0.53 0.18 0.74]\n",
            " [0.63 0.74 0.12]]\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": 103,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "20f2559b-ff91-4fc5-a613-c18bd5d621ae"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.18 0.74 0.53]\n",
            " [0.74 0.12 0.63]\n",
            " [0.53 0.63 0.98]]\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": 104,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "916adcbb-e3da-4bfc-f4f0-ebaedc81eb8c"
      },
      "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": 105,
      "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": 106,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "8437c0bf-813e-4855-abe7-887abfb872f3"
      },
      "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(\"default.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": 107,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "fd761ce8-8ae1-49f1-d3cc-4a34b2efc514"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 2.486260679046559e-05\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": 108,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "09116035-b8e5-4981-c072-799fb89e7952"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.24170775712967282\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": 109,
      "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": 110,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "a06a6387-9d47-4bf2-e199-3e825e2b7b85"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.4222917641389316\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": "6a69f52a-8a85-4ce6-bc64-17899ff7e510"
      },
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695108434.1627924\n",
            "Tue Sep 19 07:27:14 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
}