LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit CPU 173.69s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit CPU 173.69s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "6e7ce6f8-8f7b-4cd0-bd15-7c527d00a6d9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701187857.6687076\n",
            "Tue Nov 28 16:10:57 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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "34556a98-9007-4b65-db28-7d25f40b4b42"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.96 0.57 0.14]\n",
            " [0.57 0.65 0.08]\n",
            " [0.14 0.08 0.62]]\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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "a7261308-d16f-4d29-8bba-73cddc01146c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.65 0.08 0.57]\n",
            " [0.08 0.62 0.14]\n",
            " [0.57 0.14 0.96]]\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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "3e207277-c5a4-4c92-a96b-ad16e8da5174"
      },
      "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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "230a3146-78d4-4745-8940-efbc6dc2dbe0"
      },
      "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": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "918fe204-51cd-4970-8699-1bb24c2170f9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.00014475505166622327\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": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "7b125d61-f97a-45cb-fc24-dcf64c02b3dc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.1784078013151884\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": 54,
      "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": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "576ada50-4f88-4884-b7de-8fcb1e20ed02"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.17768324026837945\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": "6f63c7ab-710b-405b-8c99-64e6f0c052e7"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701188031.3600874\n",
            "Tue Nov 28 16:13:51 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
}