LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit TPU 178.45s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit TPU 178.45s (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": "c206654a-b6e7-43ca-826a-66d3a650947f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701151655.1616263\n",
            "Tue Nov 28 06:07:35 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": "41484743-b2f2-492c-9d3e-26df8e1236ea"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.73 0.47 0.88]\n",
            " [0.47 0.18 0.44]\n",
            " [0.88 0.44 0.84]]\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": "1c69cc47-ea79-452e-ffdb-22e93a6092d9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.18 0.44 0.47]\n",
            " [0.44 0.84 0.88]\n",
            " [0.47 0.88 0.73]]\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": "96e9f638-6b64-44e6-d3ab-fd1bec5bdcf8"
      },
      "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": 59
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "05dbf352-caaf-4a14-b09b-8d715d5b6442"
      },
      "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": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "b5f12894-45ac-4a04-da39-de52a8716763"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -9.63789199981413e-06\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": "4e6a9a99-b070-4cab-ca81-e47dbbc6fb58"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.00440061092376709\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": "7495836e-c00d-4078-ff3e-8511d7de7b4e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.20047103893011808\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": "beb54956-aff7-43c0-d57b-45eff4bd8809"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701151833.6165862\n",
            "Tue Nov 28 06:10:33 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
}