LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.gpu 25 qubit T4 27.44s (3) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.gpu 25 qubit T4 27.44s (3) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "00800c9a-b41e-4086-ee27-e4c642c0c0c4"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701145821.8597682\n",
            "Tue Nov 28 04:30:21 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 pennylane-lightning-gpu custatevec-cu11 --upgrade\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": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "f576ae15-b677-4457-9a9a-b82334ff6c6c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.94 0.97 0.45]\n",
            " [0.97 0.74 0.62]\n",
            " [0.45 0.62 0.83]]\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": 37,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "bbc01b98-3083-4922-f22f-13a9d38f4725"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.74 0.62 0.97]\n",
            " [0.62 0.83 0.45]\n",
            " [0.97 0.45 0.94]]\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": 38,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "d7dfcba6-c2e0-4d99-aff8-a54978c4fde9"
      },
      "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": 39,
      "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": 40,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "96eec682-0023-42f5-807b-12236d3e8853"
      },
      "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(\"lightning.gpu\", 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": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "58d1193c-38e9-4c44-dc3f-fd25843e0fc3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: -0.0013755505718685297\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": 42,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "37831641-59fd-4605-e872-887367b0cd79"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  0.29287062583727946\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": 43,
      "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": 44,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "06ac6e63-931b-4189-ae0a-8b1d27d70110"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  0.19945302593050696\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": "4a226f11-d4b9-42fc-cccd-0757fa4dc80a"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701145849.3010397\n",
            "Tue Nov 28 04:30:49 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "gpuType": "T4",
      "machine_shape": "hm"
    },
    "accelerator": "GPU"
  },
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  "nbformat_minor": 0
}