{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c4e97d94-9f03-4956-bb03-2f1753d8afa5",
   "metadata": {},
   "source": [
    "# Adaptive QPE\n",
    "\n",
    "**Download this notebook - {nb-download}`adaptive-qpe.ipynb`**\n",
    "\n",
    "Implementation of the adaptive random walk phase estimation algorithm from\n",
    "https://arxiv.org/abs/2208.04526.\n",
    "\n",
    "The example Hamiltonian and numbers are taken from https://arxiv.org/abs/2206.12950."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8462b05b-5e24-46c7-9021-0bdaf9e90029",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "from guppylang import guppy\n",
    "from guppylang.std.angles import angle\n",
    "from guppylang.std.builtins import comptime, result\n",
    "from guppylang.std.quantum import discard, measure, qubit, h, rz, x, crz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d77268ee-b737-41cf-86a8-6abfb10b9b89",
   "metadata": {},
   "outputs": [],
   "source": [
    "@guppy\n",
    "def oracle(ctrl: qubit, q: qubit, t: float) -> None:\n",
    "    \"\"\"Applies a controlled e^-iπHt/2 gate for the example Hamiltonian H = 0.5 * Z.\"\"\"\n",
    "    crz(ctrl, q, angle(0.5 * t))\n",
    "\n",
    "\n",
    "@guppy\n",
    "def eigenstate() -> qubit:\n",
    "    \"\"\"Prepares eigenstate of the example Hamiltonian H = 0.5 * Z.\"\"\"\n",
    "    q = qubit()\n",
    "    x(q)\n",
    "    return q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f4b1a3fe-5586-44a4-b891-7af85c28013e",
   "metadata": {},
   "outputs": [],
   "source": [
    "sqrt_e = math.sqrt(math.e)\n",
    "sqrt_e_div = math.sqrt((math.e - 1) / math.e)\n",
    "\n",
    "\n",
    "@guppy\n",
    "def main() -> None:\n",
    "    # Pick initial estimate of phase mean and stdv\n",
    "    # and prepare eigenstate\n",
    "    mu, sigma = comptime(sqrt_e_div), 1 / comptime(sqrt_e)\n",
    "    tgt = eigenstate()\n",
    "    for _ in range(24):\n",
    "        t = 1 / sigma\n",
    "\n",
    "        aux = qubit()\n",
    "        h(aux)\n",
    "        rz(aux, angle((sigma - mu) * t))\n",
    "        oracle(aux, tgt, t)\n",
    "        h(aux)\n",
    "\n",
    "        if measure(aux):\n",
    "            mu += sigma / comptime(sqrt_e)\n",
    "        else:\n",
    "            mu -= sigma / comptime(sqrt_e)\n",
    "        sigma *= comptime(sqrt_e_div)\n",
    "\n",
    "    discard(tgt)\n",
    "    result(\"eigenvalue\", 2 * mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4a51f004-53aa-41d0-884b-cdfd7c6efab5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EmulatorResult(results=[QsysShot(entries=[('eigenvalue', 2.3679925580437398)])])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "emulator = main.emulator(n_qubits=2).with_seed(2)\n",
    "emulator.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "526d9fad-1a5a-4adb-bf11-41729e03c3cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.ticker as ticker\n",
    "\n",
    "# run more shots\n",
    "shots = emulator.with_shots(500).run()\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.hist([shot.as_dict()[\"eigenvalue\"] for shot in shots], bins=100)\n",
    "ax.xaxis.set_major_locator(ticker.MultipleLocator(0.5))\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "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": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}