LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qiskit.aer 25 qubit V100 187.19s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qiskit.aer 25 qubit V100 187.19s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "5a89ce3a-1c7e-45c7-a2e5-ac317f5062d4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695114135.131743\n",
            "Tue Sep 19 09:02:15 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",
        "# !pip install pennylane-qiskit\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": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "282899d6-740f-455b-c92c-39984ab4d491"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.15 0.72 0.24]\n",
            " [0.72 0.67 0.57]\n",
            " [0.24 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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "e6373490-7f11-4dbb-c342-c27cb18cc844"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.67 0.57 0.72]\n",
            " [0.57 0.83 0.24]\n",
            " [0.72 0.24 0.15]]\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": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "dec8bab6-735c-4ab8-a521-24407af4e219"
      },
      "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": 35,
      "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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "d7be578b-6845-4346-cf63-da8dbe7f7b3a"
      },
      "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(\"qiskit.aer\", 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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "7d6a0d77-2ea2-4de4-a139-c2c36c043d26"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.734375\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "8d0e294c-a7c2-44ee-8b41-01c317d2ab64"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.951171875\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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "7db5e7af-89ba-47d3-9c14-c0f77eea1928"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.943359375\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": "331638f1-65e7-4291-80e5-3c54c237a2f8"
      },
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695114322.3190691\n",
            "Tue Sep 19 09:05:22 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
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        "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
}