LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit V100 147.73s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit V100 147.73s (2) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 190,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "9751cde4-5ef2-4802-8f6a-ecaf6cd2d2ec"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695111216.5633414\n",
            "Tue Sep 19 08:13:36 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-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": 191,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "88d90b03-0739-440c-f73c-e138f29ae587"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.54 0.41 0.66]\n",
            " [0.41 0.02 0.41]\n",
            " [0.66 0.41 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": 192,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "19d2cace-ae57-42e4-c45f-bc3e8d4dafc9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.02 0.41 0.41]\n",
            " [0.41 0.62 0.66]\n",
            " [0.41 0.66 0.54]]\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": 193,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "37397c6e-a5f7-4a82-caad-e4fd14569b25"
      },
      "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": 194,
      "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": 195,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "dc6f8dbc-d420-43a7-ec6f-5dadf539ce18"
      },
      "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": 196,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "5f6c5edf-c94e-4d5c-9217-e0aa19dc8607"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 2.7793731396608123e-05\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": 197,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "c7961b7d-435f-4e3e-e61c-68a29c27e766"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.42730442760512233\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": 198,
      "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": 199,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "45a7f4e0-a27a-4033-bfce-3a33e2ab9da4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.44380633044056594\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": "a5d690d0-2a3d-4a16-da00-eca5cf881e4e"
      },
      "execution_count": 200,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695111364.288063\n",
            "Tue Sep 19 08:16:04 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
}