LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit TPU 128.00s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit TPU 128.00s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 109,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "60a1312c-e821-4db7-802d-04395a4625d6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701148805.738767\n",
            "Tue Nov 28 05:20:05 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": 110,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "835cdd66-bc92-49d7-d5c5-0e4e899b1e9c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.24 0.63 0.89]\n",
            " [0.63 0.36 0.35]\n",
            " [0.89 0.35 0.09]]\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": 111,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "01772b5c-1f8c-474e-e44f-af3473b6a0c8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.36 0.35 0.63]\n",
            " [0.35 0.09 0.89]\n",
            " [0.63 0.89 0.24]]\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": 112,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "8628c94d-fb17-4475-ef30-08bed3eb25b6"
      },
      "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": 113,
      "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": 114,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "0801e802-edfa-4fdf-98f1-e85295e3e4b4"
      },
      "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": 115,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "a2cac07f-be7f-41b8-f3b0-eb802937bbc4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -8.23957133789736e-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": 116,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "fc5b5679-36ce-4d7b-a477-b2ada28c3c0a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.05324341629960435\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": 117,
      "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": 118,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "f4e0998e-4a1c-460b-a9be-603d531414bf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.12742190180073423\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": "12caaf45-4f7a-4258-9dfc-e1e9420c29d4"
      },
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701148933.7366037\n",
            "Tue Nov 28 05:22:13 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
}