LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit CPU 97.71s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit CPU 97.71s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "f10ef1d3-ec4f-4439-c4ab-1200bacde8be"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701185529.2919455\n",
            "Tue Nov 28 15:32:09 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": 47,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "ac51e761-d369-4bd2-e015-bf2fe1a8195f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.49 0.5  0.46]\n",
            " [0.5  0.1  0.35]\n",
            " [0.46 0.35 0.07]]\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": 48,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "91011b51-59a4-4c6e-be43-150535a26c72"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.1  0.35 0.5 ]\n",
            " [0.35 0.07 0.46]\n",
            " [0.5  0.46 0.49]]\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": 49,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "b75c305a-a108-4c0c-cb10-391cd35f2324"
      },
      "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": 50,
      "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": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 76
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "b9d95e80-71d3-43af-aec6-675d5970a5aa"
      },
      "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": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "5bc6d4e1-fb30-4d42-b8f6-e4650355661a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0007605278619006121\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": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "12c4e95b-4ff8-475f-b529-18c79f322ff2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.015659716536846918\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": 54,
      "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": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "54da0f03-0414-45d8-ce63-328ed5172602"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.06314755726903626\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": "871c2b98-4645-4726-baae-9a48bee2d9e3"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701185627.0023003\n",
            "Tue Nov 28 15:33:47 2023\n"
          ]
        }
      ]
    }
  ],
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