LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit TPU 127.81s (4) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit TPU 127.81s (4) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 120,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "91909581-4d9f-49d4-c98b-58138d0eab88"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701149237.8106723\n",
            "Tue Nov 28 05:27:17 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\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": 121,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "69006afc-375f-4c3b-ef52-ac2fcb1a8012"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.41 0.36 0.58]\n",
            " [0.36 0.68 0.5 ]\n",
            " [0.58 0.5  0.9 ]]\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": 122,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "cc805765-ce3d-4eae-dada-60fb266a4f50"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.68 0.5  0.36]\n",
            " [0.5  0.9  0.58]\n",
            " [0.36 0.58 0.41]]\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": 123,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "54f84f95-b848-467b-fcc4-de1b83e9b6d8"
      },
      "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": 124,
      "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": 125,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "05626b00-3950-4706-cc70-02af07eb6614"
      },
      "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(\"lightning.qubit\", 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": 126,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "72b62593-8548-48fe-db26-f0773e153c9b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -1.1128287267136105e-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": 127,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "07f6d5da-6c78-4e59-fe1c-3cd611b1a799"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.10941425944865171\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": 128,
      "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": 129,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "24e18d50-d3ca-4fd4-a788-5ecda77f5ca4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.41547802091265423\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": "14838220-fb69-4f3d-aeec-dfcd4cf48c78"
      },
      "execution_count": 130,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701149365.6184585\n",
            "Tue Nov 28 05:29:25 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "machine_shape": "hm"
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    "accelerator": "TPU"
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