LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/qiskit.aer 25 qubit V100 190.31s (5) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / qiskit.aer 25 qubit V100 190.31s (5) 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": "e9478416-78f9-4f01-e2de-45f2d78c0bfe"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1695139509.1932652\n",
            "Tue Sep 19 16:05:09 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "# !pip install pennylane custatevec-cu11 pennylane-lightning-gpu\n",
        "# !pip install pennylane-qiskit\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": "88c44bfb-414a-46cd-e80f-79a9634141c9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.51 0.46 0.39]\n",
            " [0.46 0.64 0.51]\n",
            " [0.39 0.51 0.69]]\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": "03301ce0-261a-4bde-c9ed-67927492a28e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.64 0.51 0.46]\n",
            " [0.51 0.69 0.39]\n",
            " [0.46 0.39 0.51]]\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": "5e59855d-02d0-40f4-9fdd-8aac8ddc40f9"
      },
      "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": 57
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "35460c17-f226-4495-ee85-ae681672c225"
      },
      "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(\"qiskit.aer\", 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": "67ef32cf-fbdd-46c3-ba69-78310257e1e9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.00390625\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": "3321be36-e345-46b1-e46f-5a788643e287"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.001953125\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": "cdff8032-dba9-45f1-b008-841e6111d4cb"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  -0.02734375\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": "49436aa2-9958-4b84-91d9-2efb63f96434"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1695139699.5007687\n",
            "Tue Sep 19 16:08:19 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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      },
      "file_extension": ".py",
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "gpuType": "V100"
    },
    "accelerator": "GPU"
  },
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}