[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit V100 24.70s (3) kkawchak.ipynb

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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "301cbba0-f7fd-4ade-f9bc-e4ac516b0fe8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695104259.9146144\n",
            "Tue Sep 19 06:17:39 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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "5a7f8b78-1cb9-4a98-d9b3-30c76b776a1b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.21 0.65 0.54]\n",
            " [0.65 0.87 0.08]\n",
            " [0.54 0.08 0.06]]\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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "07a9c5a4-fdda-4262-9f99-328f3f77aaae"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.87 0.08 0.65]\n",
            " [0.08 0.06 0.54]\n",
            " [0.65 0.54 0.21]]\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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "04ec1252-eb4c-4349-9ba4-6a06b7e82b72"
      },
      "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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "4e0a2ad0-ab69-4f0b-9ade-0bf333fb2f4e"
      },
      "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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "16d2e374-bcee-48cc-ff93-0ef774fd9afa"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 2.282806340299056e-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": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "e25442a9-cfc7-41aa-b4df-8425bf51b596"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3008289424457497\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": 32,
      "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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "d1c60814-a7d0-49cb-f31f-e0ffb8bd2979"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.37372272325397315\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": "1dc2dd77-5366-43c7-b299-b4580cb59ea7"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695104284.6111548\n",
            "Tue Sep 19 06:18:04 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
}