[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit V100 29.08s (5) 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": "e9e8284e-a6ac-44ff-ad4a-3073ef1d0961"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695116477.0143328\n",
            "Tue Sep 19 09:41:17 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": "0553dc31-0371-4a24-fbc6-9a9d445a8877"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.47 0.32 0.88]\n",
            " [0.32 0.57 0.44]\n",
            " [0.88 0.44 0.08]]\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": "9c79008b-37d0-4835-8c5d-86b797a87866"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.57 0.44 0.32]\n",
            " [0.44 0.08 0.88]\n",
            " [0.32 0.88 0.47]]\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": "d2c70b75-7baa-4fec-a6df-6b2169250f78"
      },
      "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": "b1594fa6-d341-4214-c6c3-7898a33a72c4"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
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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": "a28e74b3-b446-4a2e-bbe6-2e487df4b276"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.00012355491689196695\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": "885c95d8-8836-457d-f46b-7d5c8cf5171c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.10475816930227183\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": "f6960286-9c91-4088-fd42-890eb16d4e60"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  -0.09288252932202892\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": "7b59fa59-91b7-4102-8b78-f4f1e5296828"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695116506.097747\n",
            "Tue Sep 19 09:41:46 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
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        "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"
  },
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  "nbformat_minor": 0
}