BOBO1997/qaoa_ising_qiskit.ipynb

## qaoa_ising_qiskit.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "80b28a13",
   "metadata": {},
   "source": [
    "# Toy problem: Ground state of the Ising model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3a6869ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bfdc25c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit import Aer, execute\n",
    "from qiskit.circuit import Parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "956d524e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 215.506x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# edited\n",
    "\"\"\"Example of using the ZZ gate.\"\"\"\n",
    "\n",
    "# Pick a value for gamma.\n",
    "gamma = 0.3\n",
    "\n",
    "# Get two qubits.\n",
    "qr = QuantumRegister(2, \"qr\")\n",
    "qc = QuantumCircuit(qr)\n",
    "qc.rzz(gamma * np.pi, qr[0], qr[1])\n",
    "\n",
    "# Display the circuit.\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ff918829",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 142.18x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# edited\n",
    "\"\"\"Example of using the Z gate.\"\"\"\n",
    "# Value of the external magenetic field.\n",
    "h = 1.3 \n",
    "\n",
    "# Display the circuit.\n",
    "qr = QuantumRegister(1, \"qr\")\n",
    "qc = QuantumCircuit(qr)\n",
    "qc.rz(gamma * h * np.pi, qr)\n",
    "qc.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04665232",
   "metadata": {},
   "source": [
    "## Implementing the full circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bd44e28f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# edited\n",
    "\"\"\"Define problem parameters and get a set of GridQubits.\"\"\"\n",
    "# Set the dimensions of the grid.\n",
    "n_cols = 3\n",
    "n_rows = 3\n",
    "\n",
    "# Set the value of the external magnetic field at each site.\n",
    "h = 0.5 * np.ones((n_rows, n_cols))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0b66908f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# edited\n",
    "def gamma_layer(qc, qr, gamma_value, h):\n",
    "    \"\"\"Generator for U(gamma, C) layer of QAOA\n",
    "\n",
    "    Args:\n",
    "        gamma: Float variational parameter for the circuit\n",
    "        h: Array of floats of external magnetic field values\n",
    "    \"\"\"\n",
    "    for i in range(n_rows):\n",
    "        for j in range(n_cols):\n",
    "            if i < n_rows - 1:\n",
    "                qc.rzz(gamma_value * np.pi, qr[i * n_cols + j], qr[(i + 1) * n_cols + j])\n",
    "            if j < n_cols - 1:\n",
    "                qc.rzz(gamma_value * np.pi, qr[i * n_cols + j], qr[i * n_cols + j + 1])\n",
    "            qc.rz(gamma_value * h[i, j] * np.pi, qr[i * n_cols + j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f078071d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# edited\n",
    "def beta_layer(qc, qr, beta_value):\n",
    "    \"\"\"Generator for U(beta, B) layer (mixing layer) of QAOA\"\"\"\n",
    "    qc.rx(beta_value * np.pi, qr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4baadf8d",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600.25x1167.88 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# edited\n",
    "\"\"\"Create the QAOA circuit.\"\"\"\n",
    "# Use sympy.Symbols for the 𝛾 and β parameters.\n",
    "gamma = Parameter(\"gamma\")\n",
    "beta = Parameter(\"beta\")\n",
    "\n",
    "qr = QuantumRegister(n_rows * n_cols, \"qr\")\n",
    "qaoa = QuantumCircuit(qr, name=\"qaoa\")\n",
    "\n",
    "# Start in the H|0> state.\n",
    "qaoa.h(qr)\n",
    "\n",
    "# Implement the U(gamma, C) operator.\n",
    "gamma_layer(qaoa, qr, gamma, h)\n",
    "\n",
    "# Implement the U(beta, B) operator.\n",
    "beta_layer(qaoa, qr, beta)\n",
    "\n",
    "qaoa.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c66dc21",
   "metadata": {},
   "source": [
    "## Computing the energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4001c918",
   "metadata": {},
   "outputs": [],
   "source": [
    "def energy_from_wavefunction(wf, h):\n",
    "    \"\"\"Computes the energy-per-site of the Ising model directly from the\n",
    "    a given wavefunction. \n",
    "\n",
    "    Args:\n",
    "        wf: Array of size 2**(n_rows * n_cols) specifying the wavefunction.\n",
    "        h: Array of shape (n_rows, n_cols) giving the magnetic field values.\n",
    "\n",
    "    Returns:\n",
    "        energy: Float equal to the expectation value of the energy per site \n",
    "    \"\"\"\n",
    "    n_sites = n_rows * n_cols\n",
    "\n",
    "    # Z is an array of shape (n_sites, 2**n_sites). Each row consists of the \n",
    "    # 2**n_sites non-zero entries in the operator that is the Pauli-Z matrix on\n",
    "    # one of the qubits times the identities on the other qubits. The\n",
    "    # (i*n_cols + j)th row corresponds to qubit (i,j).\n",
    "    Z = np.array([(-1)**(np.arange(2**n_sites) >> i) for i in range(n_sites - 1, -1, -1)])\n",
    "\n",
    "    # Create the operator corresponding to the interaction energy summed over all\n",
    "    # nearest-neighbor pairs of qubits\n",
    "    ZZ_filter = np.zeros_like(wf, dtype=float)\n",
    "    for i in range(n_rows):\n",
    "        for j in range(n_cols):\n",
    "            if i < n_rows - 1:\n",
    "                ZZ_filter += Z[i * n_cols + j] * Z[(i + 1) * n_cols + j]\n",
    "            if j < n_cols - 1:\n",
    "                ZZ_filter += Z[i * n_cols + j] * Z[i * n_cols + (j + 1)]\n",
    "\n",
    "    energy_operator = -ZZ_filter - h.reshape(n_sites).dot(Z)\n",
    "\n",
    "    # Expectation value of the energy divided by the number of sites\n",
    "    return np.sum(np.abs(wf)**2 * energy_operator) / n_sites"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "abacd146",
   "metadata": {},
   "outputs": [],
   "source": [
    "# edited\n",
    "def energy_from_params(gamma_value, beta_value, qc, h):\n",
    "    \"\"\"Returns the energy given values of the parameters.\"\"\"\n",
    "    # backend = Aer.get_backend(\"qasm_simulator\")\n",
    "    backend = Aer.get_backend(\"statevector_simulator\")\n",
    "    \n",
    "    bc = qc.bind_parameters({gamma: gamma_value, beta: beta_value})\n",
    "    bc = bc.reverse_bits() # make statevector a little-endian form\n",
    "    wf = execute(bc, backend=backend, optimization_level=0).result().get_statevector()\n",
    "    return energy_from_wavefunction(wf, h)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb0c7ce4",
   "metadata": {},
   "source": [
    "## Optimizing the parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b81b3d48",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "\"\"\"Do a grid search over values of 𝛄 and β.\"\"\"\n",
    "# Set the grid size and range of parameters.\n",
    "grid_size = 50\n",
    "gamma_max = 2\n",
    "beta_max = 2\n",
    "\n",
    "# Do the grid search.\n",
    "energies = np.zeros((grid_size, grid_size))\n",
    "for i in range(grid_size):\n",
    "    for j in range(grid_size):\n",
    "        energies[i, j] = energy_from_params(\n",
    "            i * gamma_max / grid_size, j * beta_max / grid_size, qaoa, h\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f7328cfb",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"Plot the energy as a function of the parameters 𝛄 and β found in the grid search.\"\"\"\n",
    "plt.ylabel(r\"$\\gamma$\")\n",
    "plt.xlabel(r\"$\\beta$\")\n",
    "plt.title(\"Energy as a function of parameters\")\n",
    "plt.imshow(energies, extent=(0, beta_max, gamma_max, 0))\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "89683487",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_energy(gamma, beta, qc, h):\n",
    "    \"\"\"Uses a symmetric difference to calulate the gradient.\"\"\"\n",
    "    eps = 10**-3 # Try different values of the discretization parameter\n",
    "\n",
    "    # Gamma-component of the gradient\n",
    "    grad_g = energy_from_params(gamma + eps, beta, qc, h)\n",
    "    grad_g -= energy_from_params(gamma - eps, beta, qc, h)\n",
    "    grad_g /= 2*eps\n",
    "\n",
    "    # Beta-compoonent of the gradient\n",
    "    grad_b = energy_from_params(gamma, beta + eps, qc, h)\n",
    "    grad_b -= energy_from_params(gamma, beta - eps, qc, h)\n",
    "    grad_b /= 2*eps  \n",
    "\n",
    "    return grad_g, grad_b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7ff7249a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step: 0 Energy: 0.35551822054110027\n",
      "Step: 25 Energy: -0.6065680507043341\n",
      "Step: 50 Energy: -0.6068781774949847\n",
      "Step: 75 Energy: -0.6068781801676347\n",
      "Step: 100 Energy: -0.6068781801677109\n",
      "Step: 125 Energy: -0.6068781801677107\n",
      "Step: 150 Energy: -0.6068781801677109\n",
      "\n",
      "Learned gamma: 0.19753237841096172\n",
      "Learned beta: 0.2684381345958432\n"
     ]
    }
   ],
   "source": [
    "\"\"\"Run a simple gradient descent optimizer.\"\"\"\n",
    "gamma_value, beta_value = 0.2, 0.7 # Try different initializations\n",
    "eta = 10**-2 # Try adjusting the learning rate.\n",
    "\n",
    "# Perform gradient descent for a given number of steps.\n",
    "num_steps = 150\n",
    "for i in range(num_steps + 1):\n",
    "    # Compute the gradient.\n",
    "    grad_g, grad_b = gradient_energy(gamma_value, beta_value, qaoa, h)\n",
    "\n",
    "    # Update the parameters.\n",
    "    gamma_value -= eta * grad_g\n",
    "    beta_value -= eta * grad_b\n",
    "\n",
    "    # Status updates.\n",
    "    if not i % 25:\n",
    "        print(\"Step: {} Energy: {}\".format(i, energy_from_params(gamma_value, beta_value, qaoa, h)))\n",
    "\n",
    "print(\"\\nLearned gamma: {}\\nLearned beta: {}\".format(gamma_value, beta_value, qaoa, h))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1361bfc5",
   "metadata": {},
   "source": [
    "## Getting the approximate solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d4fafa22",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1621.88x1288.28 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"Add measurements to the QAOA circuit.\"\"\"\n",
    "qaoa_meas = qaoa.copy()\n",
    "qaoa_meas.measure_all()\n",
    "qaoa_meas.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c9f6e867",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Sample from the QAOA circuit.\"\"\"\n",
    "num_reps = 1000  # Try different numbers of repetitions.\n",
    "gamma_value, beta_value = 0.2, 0.25  # Try different values of the parameters.\n",
    "\n",
    "# Sample from the circuit.\n",
    "backend = Aer.get_backend(\"qasm_simulator\")\n",
    "bc = qaoa_meas.bind_parameters({gamma: gamma_value, beta: beta_value})\n",
    "bc = bc.reverse_bits() # make statevector a little-endian form\n",
    "result = execute(bc, backend=backend, shots=num_reps, optimization_level=0).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "612a30dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_energy(meas):\n",
    "    \"\"\"Returns the energy computed from measurements.\n",
    "\n",
    "    Args:\n",
    "        meas: Measurements/samples.\n",
    "    \"\"\"\n",
    "    Z_vals = 1 - 2 * meas.reshape(n_rows,n_cols)\n",
    "    energy = 0\n",
    "    for i in range(n_rows):\n",
    "        for j in range(n_cols):\n",
    "            if i < n_rows - 1:\n",
    "                energy -= Z_vals[i, j] * Z_vals[i + 1, j]\n",
    "            if j < n_cols - 1:\n",
    "                energy -= Z_vals[i, j] * Z_vals[i, j + 1]\n",
    "            energy -= h[i, j] * Z_vals[i, j]\n",
    "    return energy / (n_rows * n_cols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5a83181c",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"Compute the energies of the most common measurement results.\"\"\"\n",
    "# Get a histogram of the measurement results.\n",
    "hist = result.get_counts()\n",
    "\n",
    "# Consider the top 10 of them.\n",
    "num = 10\n",
    "\n",
    "# Get the most common measurement results and their probabilities.\n",
    "configs = [int(k, 2) for k, v in sorted(hist.items(), key=lambda item: -item[1])[:num]]\n",
    "probs = [v / num_reps for k, v in sorted(hist.items(), key=lambda item: -item[1])[:num]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "5f14bed9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction of outputs displayed: 0.24\n"
     ]
    }
   ],
   "source": [
    "\"\"\"Plot the most common measurement results and their energies.\"\"\"\n",
    "# Plot probabilities of the most common bitstrings.\n",
    "plt.title(\"Probability of {} Most Common Outputs\".format(num))\n",
    "plt.bar([x for x in range(len(probs))],probs)\n",
    "plt.show()\n",
    "meas = [[int(s) for s in \"\".join([str(b) for b in bin(k)[2:]]).zfill(n_rows * n_cols)] for k in configs]\n",
    "costs = [compute_energy(np.array(m)) for m in meas]\n",
    "\n",
    "# Plot energies of the most common bitstrings.\n",
    "plt.title(\"Energy of {} Most Common Outputs\".format(num))\n",
    "plt.bar([x for x in range(len(costs))], costs)\n",
    "plt.show()\n",
    "print(\"Fraction of outputs displayed: {}\".format(np.sum(probs).round(2)))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}