qPINN_world_domination.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Installing dependencies."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
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            "Note: you may need to restart the kernel to use updated packages.\n"
          ]
        }
      ],
      "source": [
        "%pip install pennylane\n",
        "%pip install qiskit\n",
        "%pip install tensorflow"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Importing libraries."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "e1VhjzsMJtxq"
      },
      "outputs": [],
      "source": [
        "import pennylane as qml\n",
        "\n",
        "import qiskit\n",
        "\n",
        "import numpy as np\n",
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import minimize"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Defining inital differential equation and variables."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "ZrPGvzYOEdy6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0.0\n"
          ]
        }
      ],
      "source": [
        "u0 =1\n",
        "l_const = 8\n",
        "k_const = 0.1\n",
        "\n",
        "max_t = 0.9\n",
        "\n",
        "# Definition of the differential equation (DE)\n",
        "def diff_eq(du, u, t, k, l):\n",
        "  return du + l*u*(k + np.tan(l*t))\n",
        "\n",
        "# Returns the value of the constant c using the initial condition, defining the exact solution to the DE.\n",
        "def initial_condition(u0, t, k, l):\n",
        "  const = u0 - np.exp(-k*l*t)*np.cos(l*t)\n",
        "  return const\n",
        "\n",
        "print(initial_condition(u0, 0, k_const, l_const))\n",
        "\n",
        "# Definition of exact solution to the DE given particular u(0)\n",
        "def particular_sol(t, k = k_const, l = l_const):\n",
        "   c = initial_condition(u0, 0, k_const, l_const)\n",
        "   return np.exp(-k*l*t)*np.cos(l*t) + c\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "now that our DE has a particular solution derived, we can try and solve it using euler's method (first-order runge-kutta method)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 2210.55x1120.39 with 1 Axes>"
            ]
          },
          "execution_count": 66,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from qiskit import QuantumCircuit\n",
        "from qiskit.circuit.library import EfficientSU2\n",
        "\n",
        "# Define amount of qubits used\n",
        "n_qubits = 6\n",
        "# Inititate circuit\n",
        "qc = QuantumCircuit(n_qubits)\n",
        "\n",
        "# Define product feature map (PFM)\n",
        "def product_feature_map(t):\n",
        "    for i in range(n_qubits):\n",
        "        qc.ry(t, i)\n",
        "\n",
        "\n",
        "# Give an arbitrary value to the PFM to check the circuit\n",
        "product_feature_map(0.9)\n",
        "\n",
        "# Implement desired ansatz\n",
        "ansatz = EfficientSU2(n_qubits, reps=5)\n",
        "\n",
        "# Compose circuit with hardware efficient ansatz\n",
        "qc.compose(ansatz, inplace=True)\n",
        "# Decompose circuit to see the gates\n",
        "qc.decompose().draw(output='mpl', style='clifford')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 67,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "72"
            ]
          },
          "execution_count": 67,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Check amount of parameters\n",
        "qc.num_parameters"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "base",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.7"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}