LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qiskit.aer 25 qubit V100 188.26s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qiskit.aer 25 qubit V100 188.26s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "d032c9ad-4031-4416-b8eb-fc75ae2538f7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695114420.9574628\n",
            "Tue Sep 19 09:07:00 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": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "fbcefd22-a947-4f8b-fe7e-fc55cf046faf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.2  0.4  0.79]\n",
            " [0.4  0.02 0.48]\n",
            " [0.79 0.48 0.46]]\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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "56c72012-c15d-4645-dffa-63019966c5a5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.02 0.48 0.4 ]\n",
            " [0.48 0.46 0.79]\n",
            " [0.4  0.79 0.2 ]]\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": 45,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "99922c85-35e8-45b2-f70d-24efc7b6f0a1"
      },
      "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": 46,
      "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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "94f6869c-ee67-4124-d497-21cb6a8d3159"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
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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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "9716e510-5d87-4b9f-ee89-259dc7ea4a52"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.005859375\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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "a968aabd-8ea9-4a8b-e256-1eeb5e8d75a2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.521484375\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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "122db58d-2fcf-42d3-c1e3-0712c48f1e13"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.388671875\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": "8c967192-ed97-485f-d32f-b7db8a045f3f"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695114609.221615\n",
            "Tue Sep 19 09:10:09 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
}