LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit CPU 98.97s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit CPU 98.97s (1) 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": "42207ba8-4df4-440b-ea11-80ee1166f385"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701185077.5356395\n",
            "Tue Nov 28 15:24:37 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": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "68df5036-ff3e-4973-e2e1-ed44e403e769"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.07 0.79 0.35]\n",
            " [0.79 0.37 0.8 ]\n",
            " [0.35 0.8  0.17]]\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": "dff40934-12be-4922-ff88-93ae4975b6a8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.37 0.8  0.79]\n",
            " [0.8  0.17 0.35]\n",
            " [0.79 0.35 0.07]]\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": "81d913fd-9ca0-4bee-ca45-b9a2d58d5864"
      },
      "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": 76
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "c187f825-b9c4-4df8-a07e-aeffab1d601f"
      },
      "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": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "87d19f51-b785-462c-f9f1-c1e55f38282e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.00010212573964228739\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": "6cb9fed4-54b1-4081-8a5b-5eb54481f324"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.19877860588889668\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": "26f04c66-4e9d-4619-997f-2d327e0032f1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.03129814430855291\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": "db1c29e2-ae53-41d2-c719-2cf7dda4be90"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701185176.5038161\n",
            "Tue Nov 28 15:26:16 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
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      },
      "file_extension": ".py",
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    "colab": {
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