LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/cirq.qsim 25 qubit TPU 182.67s (2) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / cirq.qsim 25 qubit TPU 182.67s (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": "b1d18d3c-6a71-42d9-e684-c7573ea49246"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701152118.0298834\n",
            "Tue Nov 28 06:15:18 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": "d37f7715-cff4-4f7c-8ae5-2fdb40d3ca27"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.29 0.05 0.7 ]\n",
            " [0.05 0.87 0.5 ]\n",
            " [0.7  0.5  0.49]]\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": "643180e6-caea-477e-8eba-7396300f4400"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.87 0.5  0.05]\n",
            " [0.5  0.49 0.7 ]\n",
            " [0.05 0.7  0.29]]\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": "e8a1d9dd-1e8a-4c01-8183-15f38d5575f4"
      },
      "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": 59
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "dc991559-8b91-4ef8-e685-c8467e8a9e76"
      },
      "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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "8ada4149-45ed-41f3-dd39-46f9c5f1f96e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -1.566490808840859e-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": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "e783b01a-8c23-4eba-8948-8bbb2e97e9dc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.23714675195515156\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": "29c33af9-a530-4ece-8225-36221f564a84"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.2707641269080341\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": "7fc46307-127b-4419-bace-3714e6860e56"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701152300.7011817\n",
            "Tue Nov 28 06:18:20 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "file_extension": ".py",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
      "provenance": []
    },
    "accelerator": "TPU"
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}