{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "logical-diving",
   "metadata": {},
   "source": [
    "This notebook is used to define a noise model for benchmarking purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "understanding-business",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import qutip as qt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fallen-office",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Preparing Q# environment...\n"
     ]
    }
   ],
   "source": [
    "import qsharp\n",
    "from qsharp.experimental import enable_noisy_simulation, get_noise_model, set_noise_model\n",
    "enable_noisy_simulation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "pursuant-plenty",
   "metadata": {},
   "outputs": [],
   "source": [
    "I, X, Y, Z = qt.qeye(2), qt.sigmax(), qt.sigmay(), qt.sigmaz()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "labeled-strike",
   "metadata": {},
   "outputs": [],
   "source": [
    "sI, sX, sY, sZ = map(qt.to_super, [I, X, Y, Z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "answering-europe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def total_dephasing_channel():\n",
    "    return (1 / 2) * sI + (1 / 2) * sZ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "attached-juice",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dephasing_channel(p):\n",
    "    return (1 - p) * sI + p * total_dephasing_channel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "serious-warner",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.900 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.900 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = (4, 4), type = super, isherm = True\n",
       "Qobj data =\n",
       "[[1.  0.  0.  0. ]\n",
       " [0.  0.9 0.  0. ]\n",
       " [0.  0.  0.9 0. ]\n",
       " [0.  0.  0.  1. ]]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dephasing_channel(0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "requested-instruction",
   "metadata": {},
   "outputs": [],
   "source": [
    "def total_depolarizing_channel():\n",
    "    return (sI + sX + sY + sZ) / 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "exact-argument",
   "metadata": {},
   "outputs": [],
   "source": [
    "def depolarizing_channel(p):\n",
    "    return (1 - p) * sI + p * total_depolarizing_channel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "academic-focus",
   "metadata": {},
   "outputs": [],
   "source": [
    "def finite_visibility_meas(visibility):\n",
    "    return [\n",
    "        qt.to_super(visibility * (I + sign * Z) / 2 + (1 - visibility) * I / 2)\n",
    "        for sign in (+1, -1)\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "inclusive-active",
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model = get_noise_model()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "instructional-mortality",
   "metadata": {},
   "outputs": [],
   "source": [
    "noise_model['x'] = depolarizing_channel(0.1) * sX\n",
    "noise_model['z'] = dephasing_channel(0.1) * sZ\n",
    "noise_model['z_meas']['effects'] = finite_visibility_meas(0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "voluntary-parallel",
   "metadata": {},
   "outputs": [],
   "source": [
    "set_noise_model(noise_model)\n",
    "qsharp.client._execute('%experimental.noise_model --save benchmark-noise-model.json')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "functional-concentrate",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}