[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit A100 48.22s (5) kkawchak.ipynb

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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 119,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "d3f2b426-ed4b-4aac-886c-fff15b3fbdfb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701141957.1552694\n",
            "Tue Nov 28 03:25:57 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-kokkos\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": 120,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "233ec51c-dd91-42f3-e6ee-4a9bb892f119"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.51 0.4  0.1 ]\n",
            " [0.4  0.68 0.72]\n",
            " [0.1  0.72 0.78]]\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": 121,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "3e550547-4031-405f-e1b9-f0f2489b21ec"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.68 0.72 0.4 ]\n",
            " [0.72 0.78 0.1 ]\n",
            " [0.4  0.1  0.51]]\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": 122,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "f8c853c5-e077-41b0-c5b9-7871bdeca3f5"
      },
      "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": 123,
      "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": 124,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "0b8397d5-b776-4cbb-e02c-68be16a9a1c9"
      },
      "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.kokkos\", 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": 125,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "d7c17a21-909d-45bd-c4f9-fd995d9e5d2f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -1.497004397589927e-06\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": 126,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "fb92d0c5-1d4e-4a7f-8e97-6f4e32173883"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.21150917720003687\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": 127,
      "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": 128,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "f80f8e6c-0d5e-4048-9272-ae89c41fe5b6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  -0.32110732138685627\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": "e8c1b24c-9b4b-4742-c25c-ca10f3feb732"
      },
      "execution_count": 129,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701142005.3732634\n",
            "Tue Nov 28 03:26:45 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
      "provenance": [],
      "gpuType": "A100",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
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