LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit CPU 174.35s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit CPU 174.35s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "617af71a-7c79-44d0-8a7a-ecc6e246e9da"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701187284.5510435\n",
            "Tue Nov 28 16:01:24 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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "5b848180-fbc2-4e7e-acbd-fb61ca28d519"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.93 0.61 0.67]\n",
            " [0.61 0.15 0.41]\n",
            " [0.67 0.41 0.96]]\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": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "87795825-6173-4e9b-8796-dc4ebabd5c66"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.15 0.41 0.61]\n",
            " [0.41 0.96 0.67]\n",
            " [0.61 0.67 0.93]]\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": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "44987e8a-ff8d-49aa-a8a9-02f11146e807"
      },
      "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": 28,
      "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": 29,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 75
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "8105d00c-8334-4f99-9322-d57acb61fcc2"
      },
      "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(\"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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "c1b7cc7e-c999-4dc4-d959-7b90bf57fb63"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0020061025804741645\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": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "b74119b7-3347-40bf-9856-a3db2838acdb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.3030944449128583\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": 32,
      "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": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "d6a1580c-4d63-492f-f258-6cef0054bfae"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.5672022766666487\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": "1a154ade-6d33-4dfa-fe30-7360abae4b53"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701187458.8969262\n",
            "Tue Nov 28 16:04:18 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
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      "codemirror_mode": {
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      },
      "file_extension": ".py",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.17"
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    "colab": {
      "provenance": []
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