LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit V100 140.56s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit V100 140.56s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "75b301f7-bc34-4914-ff39-bf4e48d0e185"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695104848.881991\n",
            "Tue Sep 19 06:27:28 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": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "7c6860fa-d7f0-4cee-e711-19dc31f2cc78"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.91 0.59 0.79]\n",
            " [0.59 0.65 0.48]\n",
            " [0.79 0.48 0.87]]\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": 59,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "c2e922f8-24ea-4860-8b83-fa8f5b13d408"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.65 0.48 0.59]\n",
            " [0.48 0.87 0.79]\n",
            " [0.59 0.79 0.91]]\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": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "05af20c9-d8e8-4801-d080-852cde3ff7f1"
      },
      "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": 61,
      "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": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "eb77f575-d8d5-4a5a-b367-bf8dda0a57a5"
      },
      "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.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": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "e7baca0f-3646-4568-ed5d-cc02665b0ee4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -3.008889693479943e-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": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "5f1267cb-e0c2-4bd6-ea00-12503a0d0bcf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.05927943733988345\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": 65,
      "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": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "5f5c0420-cf4f-4b0b-f658-a345be00c1b2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  -0.49793426201880275\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": "48d9d999-435f-4839-96ce-e5ac171a8d0c"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695104989.4397397\n",
            "Tue Sep 19 06:29:49 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
}