LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/default.qubit 25 qubit V100 733.88s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / default.qubit 25 qubit V100 733.88s (1) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "4a17f6c5-22c3-45a2-ce3f-cd07a87b7da2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695106577.1399357\n",
            "Tue Sep 19 06:56:17 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": 91,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "6810986d-ad73-494d-8bce-c1405d8507ba"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.19 0.26 0.2 ]\n",
            " [0.26 0.08 0.56]\n",
            " [0.2  0.56 0.47]]\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": 92,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "06465cf5-45da-4ff1-ffcc-ade92ef78f45"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.08 0.56 0.26]\n",
            " [0.56 0.47 0.2 ]\n",
            " [0.26 0.2  0.19]]\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": 93,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "a154b6d7-d744-4a42-b27f-8e97ca5b885a"
      },
      "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": 94,
      "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": 95,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "eef06c1a-3b5f-48cc-9211-39379b7ffd01"
      },
      "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(\"default.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": 96,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "2648ca53-fec8-4821-d493-27075085c9ad"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0013308723434476838\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": 97,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "33475f42-b652-4c1e-a3c3-1f4a1c289320"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.021309164486142146\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": 98,
      "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": 99,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "4fa790cc-cd55-4a84-ef08-f5c18b1450fc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3629983275417163\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": "2a526f0e-b636-40ac-9686-4b73634bbbd6"
      },
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695107311.0243957\n",
            "Tue Sep 19 07:08:31 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
}