{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "from pygsti.extras.errorgenpropagation.propagatableerrorgen import *\n",
    "from pygsti.extras.errorgenpropagation.errorpropagator import *\n",
    "from pygsti.circuits import Circuit\n",
    "import numpy as np\n",
    "import pygsti.processors\n",
    "import pygsti\n",
    "import pygsti.tools.lindbladtools as _lt\n",
    "import scipy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to the Propagatable Error Generators Code"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining a circuit and error generators"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Currently Error Propgagation works for any model that meets three criteria\n",
    "\n",
    "    1.  The circuit is clifford\n",
    "    2.  The errors on each gate can be defined at a time t of interest in the small markovian errors basis\n",
    "    3.  The error error model is defined such that a gate G has some linear combination of error generators following it\n",
    "\n",
    "We can therefore, start a code by defining a circuit and an error model by simply following the common pyGSTi notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "errorModel={\n",
    "    'Gxpi2' : {('H','Y'):.01}\n",
    "\n",
    "}\n",
    "c=Circuit(10*[('Gxpi2',0)])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can take the above definitions and plug them into the errorpropagator function, to get out a list of post-circuit error generators out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n",
      "[[[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]], [[('H', ('Y',), 0.01)]]]\n"
     ]
    }
   ],
   "source": [
    "errors=ErrorPropagator(c,errorModel,BCHOrder=1,BCHLayerwise=False,NonMarkovian=False)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here BCH order determines the to what order the BCH order will be taken to (if applicable). BCHLayerwise will if false, propagatate all errors to the end before taking the BCH expansion, otherwise it will push the errorgens through a layer and combine with the the error generators for that layer by the rules given by the BCHOrder.  Non-markovian prevents any simplification or BCH expansions being taken, instead allowing the output to be a list a lists, where the each sublist denotes the errorgenerators that were occuring at time t in the circuit."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additionally, if you want to describe a gate with multiple associated error definitions you can define it as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('H', ('X',), (0.09999999999999999+0j))]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MultiGateDict={'Gxpi22' : 'Gxpi2'}\n",
    "errorModel={\n",
    "    'Gxpi2' : {('H','Y'):.01},\n",
    "    'Gxpi22' : {('H','X'):.01}\n",
    "\n",
    "}\n",
    "c=Circuit(10*[('Gxpi2',0),('Gxpi22',0)])\n",
    "\n",
    "ErrorPropagator(c,errorModel,MultiGateDict=MultiGateDict, MultiGate=True)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the errors are propagated to the process matrix given by the end of circuit error generators is given by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "expMat=np.zeros([4**len(c.line_labels),4**len(c.line_labels)],dtype=np.complex128)\n",
    "for error in errors:\n",
    "    expMat +=error.toWeightedErrorBasisMatrix()\n",
    "processMatrix = scipy.linalg.expm(expMat)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-Markovianity"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to use the non markovianity function you need to define an n x n correlation where n is the number of layers.  Currently, we are capable of describing each layer to be governed by some stochastic process, that is correlated to the other layers.  To using the code is relatively simple, see the below example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'White noise dephasing')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_coherence = []\n",
    "Ls = range(2,100,5)\n",
    "for L in Ls:\n",
    "    c=Circuit((L)*[('Gi' ,0)])\n",
    "    ErrorDict={'Gi' : {('H','Z'): 1}}\n",
    "    EndErrors = ErrorPropagator(c,ErrorDict,NonMarkovian=True)\n",
    "\n",
    "    corr=np.eye(len(c))*.01\n",
    "    error = averaged_evolution(corr,EndErrors,1)\n",
    "\n",
    "    x_coherence += [np.real(error[1,1])]\n",
    "plt.plot(Ls,x_coherence, color='blue')\n",
    "plt.ylim(0,1.1)\n",
    "plt.xlabel('Circuit Length')\n",
    "plt.ylabel('X Coherence Decay')\n",
    "plt.title('White noise dephasing')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]], [[('H', ('X',), (1+0j))]]]\n"
     ]
    }
   ],
   "source": [
    "list=[propagatableerrorgen('H',['X'],1)]\n",
    "errors=ErrorPropagator(c,list,NonMarkovian=True,ErrorLayerDef=True)\n",
    "print(errors)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "PyGSTi_EOC",
   "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": "3.11.4"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}