LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit CPU 175.10s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit CPU 175.10s (1) 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": "8d3174c1-c2b4-419a-b9c6-97a561e9a98e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701186944.1813025\n",
            "Tue Nov 28 15:55:44 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-Cirq\n",
        "# !pip install qsimcirq\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": "e5d6d859-5ff6-4d94-a011-b96ccdbaf683"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.39 0.49 0.67]\n",
            " [0.49 0.67 0.24]\n",
            " [0.67 0.24 0.1 ]]\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": "c91554ea-d11c-4528-d404-71bd5eeb38ff"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.67 0.24 0.49]\n",
            " [0.24 0.1  0.67]\n",
            " [0.49 0.67 0.39]]\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": "20a4ed20-6f87-4741-d11a-068504dc09a8"
      },
      "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": 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": 75
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "70867352-1930-4e09-c57b-d1fb65d4dc56"
      },
      "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(\"cirq.qsim\", 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": "fc6072f6-ff78-4158-f590-51ccba6d0949"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.00014683287532604727\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": "302c92de-4016-431b-a177-12f62a0efb9b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.41122672287747264\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": "b4aec4c4-d03b-44b4-b7dd-463aebb194b2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.40879438526462764\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": "b4453a34-f34c-4fc4-c74a-8819c6861ab6"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701187119.2818453\n",
            "Tue Nov 28 15:58:39 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": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}