LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.kokkos 25 qubit CPU 67.83s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.kokkos 25 qubit CPU 67.83s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "16891afc-7aff-45f2-943f-ad162ef8f84e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701142795.502954\n",
            "Tue Nov 28 03:39:55 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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "9b173325-0040-49f1-a38e-3b30975e0e88"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.54 0.18 0.29]\n",
            " [0.18 0.95 0.2 ]\n",
            " [0.29 0.2  0.07]]\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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "0e47d1e4-128c-47db-9d9f-da3a3ee85245"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.95 0.2  0.18]\n",
            " [0.2  0.07 0.29]\n",
            " [0.18 0.29 0.54]]\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "c8b3b930-b71f-4fd2-c487-18ece20f43af"
      },
      "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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "ca87842f-ef4f-4e31-e6e9-9f60fcfd3bc8"
      },
      "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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "c7a52764-f205-469d-f81d-1a6934beb4a2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.0010103583828619265\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": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "3c4ed5c5-20eb-42b7-c15d-7610ef3e3bf1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3950800256482168\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": 43,
      "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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "e6b0fbae-1699-43a0-8324-ef282eaa91e4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3155157218418846\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": "8a8e5f1d-5510-489c-a2b6-19ec0629a691"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701142863.328091\n",
            "Tue Nov 28 03:41:03 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": [],
      "machine_shape": "hm"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}