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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Robust Phase Estimation (RPE) Tutorial\n",
    "This notebook demonstrates how to use Robust Phase Estimation (RPE) to estimate certain parameters of a standard single-qubit gate set.  The RPE protocol is contained within the `extras` package of pyGSTi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fully specified RPE configuration.\n"
     ]
    }
   ],
   "source": [
    "#Import relevant namespaces.\n",
    "from __future__ import print_function\n",
    "\n",
    "import pygsti\n",
    "import pygsti.construction.std1Q_XY as Std1Q_XY\n",
    "from pygsti.extras import rpe\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Declare the particular RPE instance we are interested in\n",
    "#(X and Y pi/2 rotations)\n",
    "rpeconfig_inst = rpe.rpeconfig_GxPi2_GyPi2_UpDn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Declare a variety of relevant parameters\n",
    "\n",
    "gs_target = Std1Q_XY.gs_target\n",
    "gs_target.set_all_parameterizations('TP')\n",
    "maxLengths_1024 = [0,1,2,4,8,16,32,64,128,256,512,1024]\n",
    "\n",
    "stringListsRPE = rpe.rpeconstruction.make_rpe_angle_string_list_dict(10,rpeconfig_inst)\n",
    "\n",
    "angleList = ['alpha','epsilon','theta']\n",
    "\n",
    "numStrsD = {}\n",
    "numStrsD['RPE'] = [6*i for i in np.arange(1,12)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Create noisy gateset\n",
    "gs_real = gs_target.randomize_with_unitary(.01,seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Extract noisy gateset angles\n",
    "true_alpha = rpe.extract_alpha(gs_real,rpeconfig_inst)\n",
    "true_epsilon = rpe.extract_epsilon(gs_real,rpeconfig_inst)\n",
    "true_theta = rpe.extract_theta(gs_real,rpeconfig_inst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Simulate dataset\n",
    "N=100\n",
    "DS = pygsti.construction.generate_fake_data(gs_real,stringListsRPE['totalStrList'],N,sampleError='binomial',seed=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Analyze dataset\n",
    "resultsRPE = rpe.analyze_rpe_data(DS,gs_real,stringListsRPE,rpeconfig_inst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha_true - pi/2 = 0.0279649415513\n",
      "epsilon_true - pi/2 = 0.00671591123378\n",
      "theta_true = 0.0233041210479\n",
      "\n",
      "alpha_true - alpha_est_final = 1.83008894992e-05\n",
      "epsilon_true - epsilon_est_final = 6.16866596674e-05\n",
      "theta_true - theta_est_final = 0.0120789343601\n"
     ]
    }
   ],
   "source": [
    "#Print results\n",
    "print('alpha_true - pi/2 =',true_alpha-np.pi/2)\n",
    "print('epsilon_true - pi/2 =',true_epsilon-np.pi/2)\n",
    "print('theta_true =',true_theta)\n",
    "print()\n",
    "print('alpha_true - alpha_est_final =',resultsRPE['alphaErrorList'][-1])\n",
    "print('epsilon_true - epsilon_est_final =',resultsRPE['epsilonErrorList'][-1])\n",
    "print('theta_true - theta_est_final =',resultsRPE['thetaErrorList'][-1])"
   ]
  }
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