LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit TPU 178.81s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit TPU 178.81s (5) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "14398a09-faa5-4656-b8ca-c168659d9830"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701153267.4710774\n",
            "Tue Nov 28 06:34:27 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": 58,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "020cbcf1-291b-4048-ab1d-c9a458f92f39"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.22 0.67 0.45]\n",
            " [0.67 0.67 0.33]\n",
            " [0.45 0.33 0.12]]\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": 59,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "d7fa502b-db42-40df-a9ce-91cd3cb4229a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.67 0.33 0.67]\n",
            " [0.33 0.12 0.45]\n",
            " [0.67 0.45 0.22]]\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": 60,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "e92e7800-de7b-4f97-a535-4e8762d79985"
      },
      "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": 61,
      "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": 62,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 59
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "d4ea2828-52f0-4f9c-ce02-7d197cc8c111"
      },
      "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": 63,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "28d5178f-0a67-48ef-b9cf-2358d5303cda"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0003764328064344291\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": 64,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "2bfd679e-c1ff-4543-cdbe-492e6156c0e7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.34422474820166826\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": 65,
      "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": 66,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "6fa9f2d0-9173-457a-fd7a-203deb5becfe"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.3601335329003632\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": "61f673a2-f9ac-4673-abde-4d3e57e84366"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701153446.2810938\n",
            "Tue Nov 28 06:37:26 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": []
    },
    "accelerator": "TPU"
  },
  "nbformat": 4,
  "nbformat_minor": 0
}