LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices/lightning.qubit 25 qubit (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices / lightning.qubit 25 qubit (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "5003c422-93ca-4bfa-e173-fb9feec11d87"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695117638.439643\n",
            "Tue Sep 19 10:00:38 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": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "5e96a165-9ac6-4996-a329-aa5d38460ebf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.21 0.81 0.93]\n",
            " [0.81 0.22 0.53]\n",
            " [0.93 0.53 0.67]]\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": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "2cffa5f1-8ba3-443b-b7da-8f4c90a7aa09"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.22 0.53 0.81]\n",
            " [0.53 0.67 0.93]\n",
            " [0.81 0.93 0.21]]\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": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "8991e53b-61ed-4582-c12b-2e82d1652e7f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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          },
          "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": 17,
      "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": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "4d1486ad-e66d-4d09-b04c-439bb78b1112"
      },
      "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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "858d587b-8959-4bb2-f47b-c035679da95f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.002860747767307664\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": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "03b25eaa-1a71-4ef3-9177-d8656e51eb12"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.302819284549631\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": 21,
      "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": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "b555b2b2-b323-4cfd-a456-1a41d5cc3829"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.2610028650210709\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": "8a4593ba-d9b2-44a6-cd50-b173f4f713f0"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695117775.4528546\n",
            "Tue Sep 19 10:02:55 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
}