LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit TPU 126.88s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit TPU 126.88s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 98,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "0cb1e706-9d75-4d18-d009-9cdb652b86e8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701148320.9503872\n",
            "Tue Nov 28 05:12:00 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": 99,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "f1c31789-1c99-4d8a-a880-56bffd9057bf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.95 0.33 0.43]\n",
            " [0.33 0.5  0.36]\n",
            " [0.43 0.36 0.84]]\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": 100,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "304de967-b4aa-4064-baf8-1aff2e399756"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.5  0.36 0.33]\n",
            " [0.36 0.84 0.43]\n",
            " [0.33 0.43 0.95]]\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": 101,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "95aade1f-445b-487c-bb44-d3202926e33b"
      },
      "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": 102,
      "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": 103,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "7ea29035-0e7f-49e7-bf61-748f0360262a"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
            "image/png": 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AAAAAAAAAAAAAAAAAAAAAAAAAAABs8g4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAsMk7AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMCmnVwuKypwb1EAAAAASUVORK5CYII=\n"
          },
          "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": 104,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "c933c326-9c0c-4c3d-a46b-2485df7fb5b8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -1.9669092986127015e-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": 105,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "97209f3d-ee54-4d44-e3a7-6936050ec3da"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.5425705665319529\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": 106,
      "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": 107,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "33b45898-8dad-44e2-ba03-fe18ff8ae026"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.279927225680345\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": "3927093b-f7b5-4489-fa66-1fa6270e0226"
      },
      "execution_count": 108,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701148447.8260462\n",
            "Tue Nov 28 05:14:07 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"
    },
    "accelerator": "TPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}