LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit CPU 97.69s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit CPU 97.69s (4) 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": "98815d5c-a018-41e8-d2ca-721ae88a3843"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701185715.7468147\n",
            "Tue Nov 28 15:35:15 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "\n",
        "# !pip install pennylane\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": "f3161730-5c5b-463d-d7af-189bb61280db"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.42 0.6  0.64]\n",
            " [0.6  0.92 0.57]\n",
            " [0.64 0.57 0.83]]\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": "d1c6fe50-aa11-4e82-8fb1-ed2b41059935"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.92 0.57 0.6 ]\n",
            " [0.57 0.83 0.64]\n",
            " [0.6  0.64 0.42]]\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": "394127bd-e957-4815-ef70-3f1910af9935"
      },
      "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": 76
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "93480f36-13fb-448f-a6c1-43eaae489fcc"
      },
      "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": "865917c8-308c-474b-8d99-fcac702efa5e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.00024862776373466483\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": "69a29e45-6709-45a3-94ac-50a83a9c8d56"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.05186186408247438\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": "ee36a86c-2825-48ea-cbd6-9f36260f74cb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.13374304233721385\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": "07bc675b-d60f-4853-f27d-f06ba6458bad"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701185813.434064\n",
            "Tue Nov 28 15:36:53 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": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}