Scalable Estimation - Experimental Basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This workbook is an introduction to the basic concepts and designs relating to the paper \n",
    "\n",
    "**Fast estimation of sparse quantum noise** by *Harper, Yu and Flammia*\n",
    "\n",
    "This workbook is going to go through the basic ideas behind experimental design for a trivial 6 qubit system. \n",
    "\n",
    "### Initial things to note about the example\n",
    "\n",
    "This is of marginal utility of only a 6 qubit system! There are only 4096 Paulis to measure in a 6 qubit system. The protocol requires a minimum number of 4n+2 experiments, each measuring (2^6) 64 possible outcomes. 26*64 = 1664 measurements - we can reconstruct all the Paulis for not much more than this! For this type of protocol we are assuming a $\\delta$ of about $0.25$, ie $4^{0.25*6}$, so we are expecting that we will only be seeking to recover the 8-9 highest weight Paulis - obviously as system size increases that is where the algorithm shines. So for instance with the 14 qubit example, in a later workbook - it makes a lot more sense.\n",
    "\n",
    "---\n",
    "<div style=\"border: 3px solid red\"><p style=\"padding:5px 10px 5px 10px;\"><strong>Warning:</strong> As mentioned above this is a long and tedious workbook that is, ulitmately, in some sense disappointing. Because we simulate the entire experiment we can (and do) look at all the intermediate results. Six qubits takes about a minute to simulate a run, and we need to do 4*6+2 of them. At then end we get 8 (well often closer to 12) numbers that are *approximately* correct. I'll try and include a qiskit simulation, which will have a less realistic noise model - but will be more qubits. Then, of course, there is the work book which was used for the paper, it is based off actual 14 qubit experimental data and recovers a lot more information (because it is a bigger system). But if you want the whole gory detail, the system here is small enough to grasp everything that is happening but big enough to be not entirely trivial, although it's a lot of work for very little (because of the small size of the system).</p></div>\n",
    "\n",
    "---\n",
    "\n",
    "### Assumed knowledge \n",
    "\n",
    "The workbook assumes some familiarity with the basic decoder, which is detailed in the workbook Scalabale Estimate - Basic Concepts. Another starter workbook that might be useful is Hadamard Basics and Observations - which also goes through the Hadamard transform (there is some duplication) but then shows how it fits in with the SuperOperator representation, the impact of only being able to measure commuting Paulis (in the one experiment) and how that relates to the circuits we design and the measurements we make. We will be using these concepts in the circuits we simulate here, and I probably won't go through it again here.\n",
    "\n",
    "Because we are simulating the experiments here it is a bit painful - but I wanted to have an exact noise model so we could check we were in fact recovering what we expectes. \n",
    "\n",
    "The other workbook released with the code will show how the algorithm performs in practice with data derived from an IBM Quantum Experience 14 qubit machine.\n",
    "\n",
    "### This is the place to start if you want to understand how the local stabiliser circuits are formed and the various decoding bins collated.\n",
    "\n",
    "I have left volumes and volumes of data in the cells. If you are trying to debug your own decoder - that will be helpful.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Software needed "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this introductory notebook, we need minimal software. All these packages should be available through the Julia package manager. However, we will need some to help with the simulation etc.\n",
    "\n",
    "If you get an error trying to \"use\" them the error message tells you how to load them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "#3 (generic function with 1 method)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Hadamard\n",
    "using PyPlot\n",
    "# convenience (type /otimes<tab>) - <tab> is the \"tab\" key.\n",
    "⊗ = kron\n",
    "# type /oplus<tab>\n",
    "⊕ = (x,y)->mod.(x+y,2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# I love this add on, especially as some of the simulations take a noticeable time. \n",
    "using ProgressMeter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We are going to need some more of my code\n",
    "# You can get it by doing the following, in the main julia repl (hit ']' to get to the package manager)\n",
    "# pkg> add https://github.com/rharper2/Juqst.jl\n",
    "\n",
    "# Currently there is harmless warning re overloading Hadamard.\n",
    "\n",
    "\n",
    "using Juqst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Main.PEEL"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is the code in this github that implements the various peeling algorithms for us.\n",
    "include(\"peel.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Main.PEEL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some preliminary information.\n",
    "\n",
    "## This is replicated from \"Scalable Estimation - Basic Concepts\"\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## Conventions\n",
    "\n",
    "### What's in a name?\n",
    "\n",
    "There are a number of conventions as to where which qubit should be. Here we are going to adopt a least significant digit approach - which is different from the normal 'ket' approach.\n",
    "\n",
    "So for example: IZ means and I 'Pauli' on qubit = 2 and a Z 'Pauli' on qubit = 1 (indexing off 1).\n",
    "\n",
    "### Arrays indexed starting with 1.\n",
    "\n",
    "For those less familiar with Julia, unlike - say - python all arrays and vectors are indexed off 1. Without going into the merits or otherwise of this, we just need to keep it in mind. With our bitstring the bitstring 0000 represents the two qubits II, it has value 0, but it will index the first value in our vector i.e. 1. \n",
    "\n",
    "\n",
    "### Representing Paulis with bitstrings.\n",
    "\n",
    "There are many ways to represent Paulis with bit strings, including for instance the convention used in **Improved Simulation of Stabilizer Circuits**, *Scott Aaronson and Daniel Gottesman*, [arXiv:quant-ph/0406196v5](https://arxiv.org/abs/quant-ph/0406196v5).\n",
    "\n",
    "Here we are going to use one that allows us to naturally translate the Pauli to its position in our vector of Pauli eigenvalues (of course this is arbitrary, we could map them however we like).\n",
    "\n",
    "The mapping I am going to use is this (together with the least significant convention):\n",
    "\n",
    "---\n",
    "\n",
    "- I $\\rightarrow$ 00\n",
    "- X $\\rightarrow$ 01\n",
    "- Y $\\rightarrow$ 10\n",
    "- Z $\\rightarrow$ 11\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "This then naturally translates as below:\n",
    "\n",
    "### SuperOperator  - Pauli basis\n",
    "\n",
    "We have defined our SuperOperator basis to be as below, which means with the julia vector starting at 1 we have : \n",
    "\n",
    "<table class=\"tg\" style=\"font-size:large\">\n",
    "  <tr >\n",
    "    <th style=\"text-align:center\">Pauli</th>\n",
    "    <th style=\"text-align:center\">Vector Index</th>\n",
    "    <th style=\"width:100px;text-align:center\">---</th>\n",
    "    <th style=\"text-align:center\">Binary</th>\n",
    "    <th style=\"text-align:center\">Integer</th>\n",
    "  </tr>\n",
    "  <tr >\n",
    "    <td style=\"text-align:center\">II</td>\n",
    "    <td style=\"text-align:center\">1</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0000</td>\n",
    "    <td style=\"text-align:center\">0</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">IX</td>\n",
    "    <td style=\"text-align:center\">2</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0001</td>\n",
    "    <td style=\"text-align:center\">1</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">IY</td>\n",
    "    <td style=\"text-align:center\">3</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0010</td>\n",
    "    <td style=\"text-align:center\">2</td>\n",
    "  </tr>\n",
    "      <tr>\n",
    "    <td style=\"text-align:center\">IZ</td>\n",
    "    <td style=\"text-align:center\">4</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0011</td>\n",
    "    <td style=\"text-align:center\">3</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">XI</td>\n",
    "    <td style=\"text-align:center\">5</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0100</td>\n",
    "    <td style=\"text-align:center\">4</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">XX</td>\n",
    "    <td style=\"text-align:center\">6</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0101</td>\n",
    "    <td style=\"text-align:center\">5</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">XY</td>\n",
    "    <td style=\"text-align:center\">7</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0110</td>\n",
    "    <td style=\"text-align:center\">6</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">XZ</td>\n",
    "    <td style=\"text-align:center\">8</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">0111</td>\n",
    "    <td style=\"text-align:center\">7</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">YI</td>\n",
    "    <td style=\"text-align:center\">9</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1000</td>\n",
    "    <td style=\"text-align:center\">8</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">YX</td>\n",
    "    <td style=\"text-align:center\">10</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1001</td>\n",
    "    <td style=\"text-align:center\">9</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">YY</td>\n",
    "    <td style=\"text-align:center\">11</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1010</td>\n",
    "    <td style=\"text-align:center\">10</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">YZ</td>\n",
    "    <td style=\"text-align:center\">12</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1011</td>\n",
    "    <td style=\"text-align:center\">11</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">ZI</td>\n",
    "    <td style=\"text-align:center\">13</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1100</td>\n",
    "    <td style=\"text-align:center\">12</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">ZX</td>\n",
    "    <td style=\"text-align:center\">14</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1101</td>\n",
    "    <td style=\"text-align:center\">13</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td style=\"text-align:center\">ZY</td>\n",
    "    <td style=\"text-align:center\">15</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1110</td>\n",
    "    <td style=\"text-align:center\">14</td>\n",
    "  </tr>\n",
    "      <tr>\n",
    "    <td style=\"text-align:center\">ZZ</td>\n",
    "    <td style=\"text-align:center\">16</td>\n",
    "    <td style=\"width:100px;text-align:center\">→</td>\n",
    "    <td style=\"text-align:center\">1111</td>\n",
    "    <td style=\"text-align:center\">15</td>\n",
    "  </tr>\n",
    "\n",
    "\n",
    "</table>\n",
    "\n",
    "I have set this out in painful detail, because its important to understand the mapping for the rest to make sense.\n",
    "\n",
    "So for instance in our EIGENVALUE vector (think superoperator diagonal), the PAUL YX has binary representation Y=10 X=01, therefore 1001, has \"binary-value\" 9 and is the 10th (9+1) entry in our eigenvalue vector.\n",
    "\n",
    "## What's in a Walsh Hadamard Transform?\n",
    "\n",
    "The standard Walsh-Hadmard transform is based off tensor (Kronecker) products of the following matrix:\n",
    "\n",
    "$$\\left(\\begin{array}{cc}1 & 1\\\\1 & -1\\end{array}\\right)^{\\otimes n}$$\n",
    "\n",
    "### WHT_natural\n",
    "\n",
    "So for one qubit it would be:\n",
    "\n",
    "$\\begin{array}{cc}\n",
    "& \\begin{array}{cccc} \\quad 00 &  \\quad 01 & \\quad 10  &\\quad 11 \\end{array}\\\\\n",
    "\\begin{array}{c} 00\\\\ 01\\\\ 10\\\\11\\end{array} &\n",
    "  \\left(\\begin{array}{cccc}\n",
    "   \\quad 1&\\quad 1& \\quad 1 &\\quad 1\\\\\n",
    "   \\quad 1 &\\quad -1 & \\quad 1 &\\quad -1\\\\   \\quad 1&\\quad 1 & \\quad -1 &\\quad -1\\\\   \\quad 1 &\\quad -1 & \\quad -1 &\\quad 1\\\\\\end{array}\\right)\n",
    "\\end{array}$\n",
    "\n",
    "where I have included above (and to the left) of the transform matrix the binary representations of the position and the matrix can also be calculated as $(-1)^{\\langle i,j\\rangle}$ where the inner product here is the binary inner product $i,j\\in\\mathbb{F}_2^n$ as $\\langle i,j\\rangle=\\sum^{n-1}_{t=0}i[t]j[t]$ with arithmetic over $\\mathbb{F}_2$ \n",
    "\n",
    "### WHT_Pauli\n",
    "\n",
    "In the paper we use a different form of the Walsh-Hadamard transform. In this case we use the inner product of the Paulis, not the 'binary bitstring' inner product. The matrix is subtly different some rows or, if you prefer, columns are swapped:\n",
    "\n",
    "$\\begin{array}{cc}\n",
    "& \\begin{array}{cccc} I(00) &  X(01) & Y(10)  & Z(11) \\end{array}\\\\\n",
    "\\begin{array}{c} I(00)\\\\ X(01)\\\\ Y(10)\\\\Z(11)\\end{array} &\n",
    "  \\left(\\begin{array}{cccc}\n",
    "   \\quad 1&\\quad 1& \\quad 1 &\\quad 1\\\\\n",
    "   \\quad 1 &\\quad 1 & \\quad -1 &\\quad -1\\\\   \\quad 1&\\quad -1 & \\quad 1 &\\quad -1\\\\   \\quad 1 &\\quad -1 & \\quad -1 &\\quad 1\\\\\\end{array}\\right)\n",
    "\\end{array}$\n",
    "\n",
    "\n",
    "### Which one to use\n",
    "\n",
    "When transforming Pauli eigenvalue to the probability of a particular error occuring, there are distinct advantages in using the WHT_Pauli transform. The order of the Pauli errors and the order of the Pauli eigenvalues remains the same. However, most common packages (including the one we are going to use here in Julia) don't support this type of transform, rather they implement the WHT_natural transform. The WHT_natural transform also makes the peeling algorithm slightly less fiddly. **However** it does mean we need to be very careful about the order of things. If we use the WHT_natural transform then the following relationship holds - *note the indices (labels) of the Paulis in the probability vector*:\n",
    "\n",
    "\n",
    "![Example of Index change](./figures/HadamardNa.jpg)\n",
    "\n",
    "So the natural translation (labelling of Paulis) then becomes as follows:\n",
    "\n",
    "### Eigenvalue vector space ###\n",
    "\n",
    "\n",
    "- I $\\rightarrow$ 00\n",
    "- X $\\rightarrow$ 01\n",
    "- Y $\\rightarrow$ 10\n",
    "- Z $\\rightarrow$ 11\n",
    "\n",
    "### Probability vector space ###\n",
    "\n",
    "\n",
    "- I $\\rightarrow$ 00\n",
    "- X $\\rightarrow$ 10\n",
    "- Y $\\rightarrow$ 01\n",
    "- Z $\\rightarrow$ 11\n",
    "\n",
    "---\n",
    "\n",
    "The numbers above are the numbers we are going used in the \"Basic concepts\" workbook - here we are going to set up some more general errors\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Set up some Pauli Errors to find"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fidelityLabels (generic function with 1 method)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Some functions to give us labels:\n",
    "function probabilityLabels(x;qubits=2)\n",
    "    str = string(x,base=4,pad=qubits)\n",
    "    paulis = ['I','Y','X','Z']\n",
    "    return map(x->paulis[parse(Int,x)+1],str)\n",
    "end\n",
    "\n",
    "function fidelityLabels(x;qubits=2)\n",
    "    str = string(x,base=4,pad=qubits)\n",
    "    paulis = ['I','X','Y','Z']\n",
    "    return map(x->paulis[parse(Int,x)+1],str)\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number greater than 0.0001 = 12\n",
      "Number greater than 1.0e-5 = 19\n",
      "Number greater than 1.0e-6 = 41\n",
      "Number greater than 1.0e-7 = 55\n",
      "\n",
      "The Paulis errors we might hope to recover with this protocol:\n",
      "001 IIIIII 0.9566049496644947\n",
      "002 IIIIIY 0.009742443708564856\n",
      "003 IIIIIX 0.0038969774834259428\n",
      "005 IIIIYI 0.0002882968036207967\n",
      "017 IIIYII 0.00019223633173193815\n",
      "049 IIIZII 0.0002883544975979071\n",
      "129 IIXIII 0.0002882968036207967\n",
      "257 IYIIII 0.003936905531411864\n",
      "513 IXIIII 0.01968452765705932\n",
      "514 IXIIIY 0.0001996402399296077\n",
      "816 IZIXZZ 0.004\n",
      "2049 XIIIII 0.0002882968036207967\n",
      "\n",
      "\n",
      "The actual oracle i.e. the eigenvalues of the Pauli channel we are going to use.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "4096-element Array{Float64,1}:\n",
       " 1.0\n",
       " 0.972\n",
       " 0.984\n",
       " 0.972\n",
       " 0.9914\n",
       " 0.979412\n",
       " 0.9914048\n",
       " 0.9634168\n",
       " 0.9918\n",
       " 0.979804\n",
       " 0.9918016\n",
       " 0.9638056\n",
       " 0.9992\n",
       " ⋮\n",
       " 0.9493371786\n",
       " 0.922350435\n",
       " 0.9337424811\n",
       " 0.9227557376\n",
       " 0.9497171414\n",
       " 0.9227227986\n",
       " 0.9341194043\n",
       " 0.9231250615\n",
       " 0.9411471971\n",
       " 0.9301642532\n",
       " 0.9415540196\n",
       " 0.9145710756"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To demonstrate the peeling decoder we are going to set up a sparse (fake) distribution.\n",
    "# This is going to be a 4 qubit (so 4^6 = 4096 possible probabilities)\n",
    "# Because of the protocol - we are assuming SPARSE errors - so most of the qubits\n",
    "# Will be good, but there will be a few errors for us to find.\n",
    "\n",
    "dist = zeros(4096)\n",
    "cl = zeros(6,4)\n",
    "\n",
    "# Qubit 1\n",
    "cl[1,2] = 0.01 #y1\n",
    "cl[1,3] = 0.004 #x1\n",
    "cl[1,4] = 0 #z1\n",
    "cl[1,1] = 1-sum(cl[1,:])\n",
    "\n",
    "# Qubit 2\n",
    "cl[2,2] = 0.0003\n",
    "cl[2,3] = 0.0001\n",
    "cl[2,4]=  0\n",
    "cl[2,1] = 1-sum(cl[2,:])\n",
    "\n",
    "# Qubit 3\n",
    "cl[3,2]  = 0.0002\n",
    "cl[3,3] = 0.0001\n",
    "cl[3,4] = 0.0003\n",
    "cl[3,1] = 1-sum(cl[3,:])\n",
    "\n",
    "# Qubit 4\n",
    "cl[4,2] = 1e-4\n",
    "cl[4,3] = 3e-4\n",
    "cl[4,4] = 0\n",
    "cl[4,1] = 1-sum(cl[4,:])\n",
    "\n",
    "\n",
    "# Qubit 5\n",
    "cl[5,2] = 0.004 \n",
    "cl[5,3] = 0.02 \n",
    "cl[5,4] = 0 #z1\n",
    "cl[5,1] = 1-sum(cl[5,:])\n",
    "\n",
    "\n",
    "# Qubit 6\n",
    "cl[6,2] = 1e-4\n",
    "cl[6,3] = 3e-4\n",
    "cl[6,4] = 0\n",
    "cl[6,1] = 1-sum(cl[6,:])\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "for q1 in 1:4\n",
    "    for q2 in 1:4\n",
    "        for q3 in 1:4\n",
    "            for q4 in 1:4\n",
    "                for q5 in 1:4\n",
    "                    for q6 in 1:4\n",
    "                        dist[(q6-1)*4^5+(q5-1)*4^4+(q4-1)*4^3+(q3-1)*4^2+(q2-1)*4+q1] = cl[1,q1]*cl[2,q2]*cl[3,q3]*cl[4,q4]*cl[5,q5]*cl[6,q6]\n",
    "                    end\n",
    "                end\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "dist[3*4^4+2*16+3*4+3+1]= 0.004 # <----- Add an unexpected IZIXZZ error!\n",
    "dist[1] = 0\n",
    "dist[1] = 1-sum(dist)\n",
    "for i in [1e-4,1e-5,1e-6,1e-7]\n",
    "    print(\"Number greater than $i = $(count([x>i for x in dist]))\\n\")\n",
    "end\n",
    "\n",
    "print(\"\\nThe Paulis errors we might hope to recover with this protocol:\\n\")\n",
    "for (ix,i) in enumerate(dist)\n",
    "    if i > 0.0001\n",
    "        print(\"$(string(ix,pad=3)) $(probabilityLabels(ix-1,qubits=6)) $i\\n\")\n",
    "    end\n",
    "end\n",
    "title(\"Distribution of Pauli error rates\")\n",
    "yscale(\"log\")\n",
    "ylabel(\"Error Rate\")\n",
    "xlabel(\"Paulis indexed and sorted by error rate\")\n",
    "scatter(2:50,reverse(sort(dist))[2:50])\n",
    "\n",
    "print(\"\\n\\nThe actual oracle i.e. the eigenvalues of the Pauli channel we are going to use.\\n\\n\")\n",
    "actualOracle = round.(ifwht_natural(dist),digits=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our random SPAM channel has fidelity 0.8539479347605721 and unitarity 0.7615487972527085\n"
     ]
    }
   ],
   "source": [
    "# So we can use our actual oracle to simulate an experiment, we can include some so we will\n",
    "# Rather than simulate a whole lot of Pauli circuits, which would serve to diagonlise the noise\n",
    "# I am going to take the simpler state of assuming we have a Pauli channel - the SPAM will\n",
    "# Therefore just get added on to the end.\n",
    "\n",
    "# Here I am just assuming a suitable 6 qubit, independent random noise channel for SPAM\n",
    "rm = foldl(⊗,[randomFidelityNoise() for _ in 1:6])\n",
    "print(\"Our random SPAM channel has fidelity $(fidelity(rm)) and unitarity $(unitarity(rm))\\n\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Our noise channel is a Pauli channel, so just diagonalise our eigenvalue vector\n",
    "\n",
    "using LinearAlgebra\n",
    "noise = diagm(0=>actualOracle);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# So we have everything we need, we have SPAM channels and the 'diagonal' channel we would get if we \n",
    "# averaged over Paulis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# So Let's get started!\n",
    "\n",
    "Remember the point here is that the eigenvalues are dense, the pauli error rates are sparse. However, we can't sample the Pauli error rates in a SPAM (state preperation and measurement) error free way. We CAN however sample the eigenvalues in a SPAM free way. We wan't to sparsely sample the dense eigenvalues in order to reconstruct the sparse error probabilities.\n",
    "\n",
    "This shows how to do this.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choose our sub-sampling matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the main ideas behind the papers is that we can use the protocols in [Efficient learning of quantum channels](https://arxiv.org/abs/1907.12976) and [Efficient learning of quantum noise](https://arxiv.org/abs/1907.13022) to learn the eigenvalues of an entire stabiliser group ($2^n$) entries at once to arbitrary precision. Whilst it might be quite difficult to learn the eigenvalues of an arbitrary group as this will require an arbitrary $n-$qubit Clifford gate (which can be a lot of primitive gates!) even today's noisy devices can quite easily create a 2-local Stabiliser group over $n-$ qubits. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we are simulating the recovery in a 6 qubit system. That means our bitstrings are 12 bits long. \n",
    "\n",
    "Our experiments will need two sub-sampling groups. The first subsampling group will be two of our potential MuBs (set out below) (selected randomly). The second subsampling group will have single MUBs (potentialSingles below) on the first and fourth qubit, and a potential (two qubit) MuB on qubits 2 and 3.\n",
    "\n",
    "This maximises the seperation of Paulis using local stabiliser (two qubit) groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Array{Array{Int64,1},1},1}:\n",
       " [[0, 0, 0, 0], [1, 1, 0, 1], [1, 0, 1, 1], [0, 1, 1, 0]]\n",
       " [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "potentialSingles = [\n",
    "                    [[0,0],[0,1]], # IX\n",
    "                    [[0,0],[1,0]], # IY\n",
    "                    [[0,0],[1,1]], # IZ\n",
    "                    ]\n",
    "\n",
    "\n",
    "all2QlMuBs =  [  [[0,0,0,0],[1,1,0,1],[1,0,1,1],[0,1,1,0]], #II ZX YZ XY\n",
    "                 [[0,0,0,0],[1,1,1,0],[0,1,1,1],[1,0,0,1]], #II ZY XZ YX\n",
    "                 [[0,0,0,0],[0,0,0,1],[0,1,0,0],[0,1,0,1]], #II IX XI XX\n",
    "                 [[0,0,0,0],[0,0,1,0],[1,0,0,0],[1,0,1,0]], #II IY YI YY\n",
    "                 [[0,0,0,0],[0,0,1,1],[1,1,0,0],[1,1,1,1]]] #II IZ ZI ZZ\n",
    "\n",
    "# We only want to choose the first two types for the initial runs\n",
    "potentialMuBs = [all2QlMuBs[1],all2QlMuBs[2]]\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For the offsets we are using the simplest method for Pauli identification eg:\n",
      "Offset 0: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "Offset 1: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "Offset 2: [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "Offset 3: [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "Offset 4: [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]\n",
      "Offset 5: [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]\n",
      "Offset 6: [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]\n",
      "Offset 7: [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n",
      "Offset 8: [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]\n",
      "Offset 9: [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "Offset 10: [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]\n",
      "Offset 11: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]\n",
      "Offset 12: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n",
      "\n",
      "\n",
      "We have selected two sub-sampling groups. \n",
      "\n",
      "The first is two randomly selected 'two quibt' mubs on  the qubits:\n",
      "Qubits 1&2: [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]\n",
      "Qubits 3&4: [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]\n",
      "Qubits 5&6: [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]\n",
      "\n",
      "\n",
      "\n",
      "The second, we want to offset by 1 qubit, so we have single qubit mubs on qubit 1, a two qubit mub on 2&3 and 4&5 and then we need a single qubit mub on qubit 6.\n",
      "Qubit 1   : [[0, 0], [1, 1]]\n",
      "Qubits 2&3: [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]\n",
      "Qubits 2&3: [[0, 0, 0, 0], [1, 1, 0, 1], [1, 0, 1, 1], [0, 1, 1, 0]]\n",
      "Qubit 4.  : [[0, 0], [1, 1]]\n"
     ]
    }
   ],
   "source": [
    "paulisAll=[]\n",
    "mappings=[]\n",
    "experiments = []\n",
    "\n",
    "# For this example I am just going to choose the second type of MUB.\n",
    "# For six qubits we need three \"potentialMuB\"\n",
    "\n",
    "for i = 1:1\n",
    "     push!(mappings,Dict())\n",
    "     choose = rand(1:2,3)\n",
    "     push!(experiments,vcat([(2,choose[1])],[(2,choose[2])],[(2,choose[3])]))\n",
    "     push!(paulisAll,vcat([potentialMuBs[x] for x in choose]))\n",
    "end\n",
    "\n",
    "\n",
    "# For the next subsample group, choose a single, two doubles and a single.\n",
    "for i = 1:1\n",
    "         push!(mappings,Dict())\n",
    "         chooseS = rand(1:3,2)\n",
    "         choose = rand(1:2,2)\n",
    "         push!(experiments,vcat([(1,chooseS[1])],[(2,choose[1])],[(2,choose[2])],[(1,chooseS[2])]))\n",
    "         push!(paulisAll,vcat([potentialSingles[chooseS[1]]],[potentialMuBs[x] for x in choose],[potentialSingles[chooseS[2]]]))\n",
    "end\n",
    "\n",
    "\n",
    "# Create the 'bit' offsets\n",
    "# This is used to work out the Pauli we isolate in a single bin. Here we have 2*(n=2), 4 bits per Pauli\n",
    "ds = vcat(\n",
    "    [[0 for _ = 1:12]],\n",
    "    [map(x->parse(Int,x),collect(reverse(string(i,base=2,pad=12)))) for i in [2^b for b=0:11]]);\n",
    "# e.g.\n",
    "print(\"For the offsets we are using the simplest method for Pauli identification eg:\\n\")\n",
    "for (ix,i) in enumerate(ds)\n",
    "    print(\"Offset $(ix-1): $i\\n\")\n",
    "end\n",
    "\n",
    "print(\"\\n\\nWe have selected two sub-sampling groups. \\n\\nThe first is two randomly selected 'two quibt' mubs on  the qubits:\\n\")\n",
    "print(\"Qubits 1&2: $(paulisAll[1][1])\\n\")\n",
    "print(\"Qubits 3&4: $(paulisAll[1][2])\\n\")\n",
    "print(\"Qubits 5&6: $(paulisAll[1][3])\\n\\n\")\n",
    "\n",
    "print(\"\\n\\nThe second, we want to offset by 1 qubit, so we have single qubit mubs on qubit 1, a two qubit mub on 2&3 and 4&5 and then we need a single qubit mub on qubit 6.\\n\")\n",
    "print(\"Qubit 1   : $(paulisAll[2][1])\\n\")\n",
    "print(\"Qubits 2&3: $(paulisAll[2][2])\\n\")\n",
    "print(\"Qubits 2&3: $(paulisAll[2][3])\\n\")\n",
    "print(\"Qubit 4.  : $(paulisAll[2][4])\\n\")\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Any,1}:\n",
       " [(2, 2), (2, 2), (2, 2)]\n",
       " [(1, 3), (2, 2), (2, 1), (1, 3)]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Here there are two sets of experiments\n",
    "# The tuple for each qubit, is the (number, experiment type), \n",
    "# the numbers for each will add up to 4 (since we have 4 qubits)\n",
    "experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## So what are these experiments?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Let's pull in the figure from the paper which shows all the experimental designs:\n",
    "\n",
    "![diagram showing designs](./figures/PhaseOffset.pdf)\n",
    "\n",
    "Okay that's a bit busy, lets break it down."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 1 was to choose one MUB from the set for each pair of qubits, well that is what we did in PaulisAll, lets look at the first element of that"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Array{Array{Int64,1},1},1}:\n",
       " [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]\n",
       " [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]\n",
       " [[0, 0, 0, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "paulisAll[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So because it was randomly chosen, you will have to look at that and convince yourself that indeed that each of the two elements shown above are one of these four sets of MuBs.\n",
    "\n",
    "So the first experiment (the top row of (2)) is just an experiment to extract those eigenvalues.\n",
    "\n",
    "How do we do that?\n",
    "\n",
    "Well we have the circuits we need in the appendix of the paper - they look like this:\n",
    "\n",
    "![circuits](./figures/circuits.png)\n",
    "\n",
    "Where what we are going to need on each two qubit pair is either (a) or (c), depending on the MUB randomly selected"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up the circuits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the two qubit expermeints, circuit 1 is (a) above and circuit (2) is (c) above.\n",
    "\n",
    "Effectively we take an input state in the computational basis, apply these circuits, do a Pauli twirl of varing gates, reverse the circuit and measure in the computational basis.\n",
    "\n",
    "To simulate this I am just going to set up the circuits as a superoperator. The way rb Pauli twirling works, the noise will be subsumed into the SPAM error - which we will then fit out, but I am getting ahead of myself.\n",
    "\n",
    "Let's create the superoperator that does (a) and (c) on two qubits:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**For a more detailed explanation of what I am doing in the next cell, look at the Hadamard Basics and Observations workbook**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Juqst\n",
    "# Set up the relevant gates\n",
    "cnot21 = [1 0;0 1]⊗[1 0;0 0]+ [0 1;1 0]⊗[0 0;0 1]\n",
    "superCnot21 = makeSuper(cnot21)\n",
    "superPI = makeSuper([1 0;0 im]⊗[1 0;0 1])\n",
    "superIP = makeSuper([1 0;0 1]⊗[1 0;0 im])\n",
    "superHH = makeSuper((1/sqrt(2)*[1 1;1 -1])⊗(1/sqrt(2)*[1 1;1 -1]));\n",
    "superH = makeSuper((1/sqrt(2)*[1 1;1 -1]))\n",
    "superP = makeSuper([1 0;0 im])\n",
    "# The two qubit experiment are (a) and (b) above\n",
    "# Recall circuits are left to right, matrices right to left\n",
    "circuit2q = [superCnot21*superPI*superCnot21*superIP*superHH,\n",
    "             superCnot21*superPI*superCnot21*superPI*superHH]\n",
    "# The single qubit ones are Paulis, X,Y,Z\n",
    "circuit1q = [superH,superP*superH,makeSuper([1 0;0 1])];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the first experiment is as shown in the above diagram ... this bit:\n",
    "\n",
    "![experiment](./figures/experiment.png)\n",
    "\n",
    "where our C's (left hand side of that diagram - which I have just noticed is (irritatingly) right to left (you can tell from the |0> on the right). Each of the circuits 2q calculated above represents one of our two choices of Mubs, we would then twirl with Paulis, average over lots of different twirls (to diagonalise it) and then reverse out and measure.\n",
    "\n",
    "I am NOT going to simulate the Pauli twirl, but rather I am just going to use the (already) diagonal noise matrix we calculated earlier. The noisy circuits2q and state and measurement errors will be simulated by using the measurement (SPAM) noise matrix formed earlier. \n",
    "\n",
    "(I probably will do the whole thing in a qiskit simulation)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Tuple{Int64,Int64},1}:\n",
       " (2, 2)\n",
       " (2, 2)\n",
       " (2, 2)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# So the circuits we want are shown here\n",
    "experiments[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "generateGates (generic function with 1 method)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function generateGates(experiment,circuits)\n",
    "    # We expect the gates as a tuple, i.e. (a,b) where a is number of qubits and b is the experiment number\n",
    "    # circuits is a an array of size upto number of qubits, so circuits[a][b] returns an \"a\" qubit experiment\n",
    "    # we can then use foldl to kron up the circuits\n",
    "    return foldl(⊗, [circuits[x[1]][x[2]] for x in reverse(experiment)])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simplify the code here, we know its two qubits:\n",
    "# Note the order of the \\kron - obviously with an experiment you just set up the actual experiment!\n",
    "\n",
    "# You can think of generateGates, doing the equivalent of the following\n",
    "#initialGates = circuit2q[experiments[1][3][2]]⊗circuit2q[experiments[1][2][2]]⊗circuit2q[experiments[1][1][2]]\n",
    "initialGates = generateGates(experiments[1],[circuit1q,circuit2q])\n",
    "\n",
    "reverseGates = transpose(initialGates); # yay superoperators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# So there is a bit of delay here, mainly its the genZs which isn't the most efficient, but we only do it once.\n",
    "\n",
    "# We can generate the computational basis measurment vectors (again see Hadamard Basics and Observations for details)\n",
    "zs = Juqst.genZs(6);\n",
    "start = zs[1]; #computational basis all 0 state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Faking (simulating) the experiment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In theory we could put this in qiskit or cirq or something - but here I want to simulate a very\n",
    "specific noise channel to show we can recover it, and these simulators only allow more general noise\n",
    "(at the time of writing this).\n",
    "\n",
    "So the basic concept is: \n",
    "\n",
    "- we start with the computational basis vector, \n",
    "- we apply our SPAM\n",
    "- we apply our basis change circuit (initial Gates)\n",
    "- we apply our diagonal noise $m$ times (this is the noise we want to measure - see below for choice of $m$)\n",
    "- we undo our basis change\n",
    "- we find our final probability vector (for observed errors in this basis) (basically each of the measurment arrays we generates - the zs)\n",
    "- then we face a whole lot of random dice rolls to build up some limited shot statistics.\n",
    "\n",
    "Finally repeat all the above for different values of $m$. Here we are just going to use m = 1,3,5,8,10,15,20,40,60,80\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:01:27\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "experiment1_allProbs = []\n",
    "# These will depend on your system\n",
    "lengths =  [1,3,5,8,10,15,20,40,60,80]\n",
    "@showprogress for m in lengths\n",
    "    wholeCircuit = reverseGates*noise^m*initialGates*rm*start./64 # ./64 = Normalise the measurement/state vectors\n",
    "    probs = [z'*wholeCircuit for z in zs]\n",
    "    push!(experiment1_allProbs,probs)\n",
    "end\n",
    "\n",
    "# SO NOTE that although there are 4096 eigenvalues, we can only measure 64 of them at a time, \n",
    "# so the probability matrices are only 64 long."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "M=1 sum = 1.0\n",
      "M=3 sum = 1.0\n",
      "M=5 sum = 1.0\n",
      "M=8 sum = 1.0\n",
      "M=10 sum = 1.0\n",
      "M=15 sum = 1.0\n",
      "M=20 sum = 1.0\n",
      "M=40 sum = 1.0\n",
      "M=60 sum = 1.0\n",
      "M=80 sum = 1.0\n"
     ]
    }
   ],
   "source": [
    "# Quick Sanity check that all of our probabilityvectors sum to 1\n",
    "for (ix,i) in enumerate(experiment1_allProbs)\n",
    "    print(\"M=$(lengths[ix]) sum = $(round(sum(i),digits=9))\\n\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# So the final step, now that we have the probability matrix for that experiment, is to simulate limited shot statistics.\n",
    "\n",
    "# So if we imagined doing 100 sequences, of 200 measurements per seq thats 20,000 shots.\n",
    "const shotsToDo = 20000\n",
    "\n",
    "# Quick helper function\n",
    "function shotSimulator(size,shots,cumulativeMatrix)\n",
    "    toRet = []\n",
    "    for todo = 1:length(cumulativeMatrix)\n",
    "        counted = zeros(size)\n",
    "        rolls = rand(shots)\n",
    "        for i in rolls\n",
    "            #using the fact that the cululativeMatrix is (effectively) sorted.\n",
    "            counted[searchsortedfirst(cumulativeMatrix[todo],i,)] +=1\n",
    "        end\n",
    "        push!(toRet,counted./shots)\n",
    "    end\n",
    "    return toRet\n",
    "end\n",
    "\n",
    "# We need culmlative probability matrixes\n",
    "cumMatrix = map(cumsum,experiment1_allProbs)\n",
    "experiment1_observed = shotSimulator(64,shotsToDo,cumMatrix);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The next step is to recreate the eigenvalues that we have 'measured' in the experiment. \n",
    "\n",
    "This is just following the protocol in https://arxiv.org/abs/1907.13022, Efficient Learning of Quantum Noise\n",
    "(and https://arxiv.org/abs/1907.12976 Efficient Estimation of Pauli Channels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  We want to Hadamard transform the observed Probabilities \n",
    "\n",
    "if we do that we will see for each eigenvalue (element in the matrix) an exponential decay curve - lets look"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "experiment1_SpamyEigenvalues = map(ifwht_natural,experiment1_observed);\n",
    "# Dont bother with the first element as its all 1.\n",
    "for x = 2:64\n",
    "    toPlot = [d[x] for d in experiment1_SpamyEigenvalues]\n",
    "    plot(lengths,toPlot)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## So fit and extract\n",
    "\n",
    "What we want to do is fit them to and exponential decay curve and extract the decay factor. Juqst has the code for this, and you are welcome to look at the documentation and example notebooks for that!\n",
    "            \n",
    "For those that can't be bothered reading docs! fitTheFidelites returns params that contains both the SPAM component and the fidelity - the second parameter is the number of measurements used in the fit and the last is if any of the fits failed. We just want to extract the eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64-element Array{Float64,1}:\n",
       " 1.0\n",
       " 0.9832608361319543\n",
       " 0.9646570732960278\n",
       " 0.9800387381402719\n",
       " 0.9903753752127014\n",
       " 0.9897432673667202\n",
       " 0.9703648881064589\n",
       " 0.9707983647823297\n",
       " 0.9910993219118764\n",
       " 0.9905212250582103\n",
       " 0.9712593549596166\n",
       " 0.9716276673089288\n",
       " 0.9983868398109271\n",
       " ⋮\n",
       " 0.989878184282456\n",
       " 0.9729367252562507\n",
       " 0.9545101559822675\n",
       " 0.9698695367819199\n",
       " 0.9906399998241464\n",
       " 0.9736318429466285\n",
       " 0.9555478313164661\n",
       " 0.9707389168429829\n",
       " 0.9817336194412914\n",
       " 0.9811482272883943\n",
       " 0.9616005947070917\n",
       " 0.9615911546605903"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(params,l, failed) = fitTheFidelities(lengths,experiment1_observed)\n",
    "experiment1_fidelities = vcat(1,[p[2] for p in params]) # We don't fit the first one, it is always 1 for CPTP maps\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## So what did we actually extract?\n",
    "\n",
    "Note this bit is kind of fidly - to get everything to match up\n",
    "\n",
    "Well we extracted certain fidelities!\n",
    "\n",
    "The four fidelities on the first qubit were:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Array{Int64,1},1}:\n",
       " [0, 0, 0, 0]\n",
       " [1, 1, 1, 0]\n",
       " [0, 1, 1, 1]\n",
       " [1, 0, 0, 1]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "paulisAll[1][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Array{Int64,1},1}:\n",
       " [0, 0, 0, 0]\n",
       " [1, 1, 1, 0]\n",
       " [0, 1, 1, 1]\n",
       " [1, 0, 0, 1]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "paulisAll[1][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Turn those into a number...\n",
    "fidelitiesExtracted = []\n",
    "function binaryArrayToNumber(x)\n",
    "    return foldl((y1,y2)->y1<<1+y2,x)\n",
    "end\n",
    "for x0 in paulisAll[1][3]\n",
    "    p56 = binaryArrayToNumber(x0)\n",
    "    for x1 in paulisAll[1][2]\n",
    "        p34 = binaryArrayToNumber(x1)\n",
    "        for x2 in paulisAll[1][1]\n",
    "            p12= binaryArrayToNumber(x2)\n",
    "            push!(fidelitiesExtracted,p56*4^4+p34*16+p12+1) # + 1 cause we index of 1 in Julia\n",
    "        end\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64-element Array{Any,1}:\n",
       "    1\n",
       "   15\n",
       "    8\n",
       "   10\n",
       "  225\n",
       "  239\n",
       "  232\n",
       "  234\n",
       "  113\n",
       "  127\n",
       "  120\n",
       "  122\n",
       "  145\n",
       "    ⋮\n",
       " 2529\n",
       " 2543\n",
       " 2536\n",
       " 2538\n",
       " 2417\n",
       " 2431\n",
       " 2424\n",
       " 2426\n",
       " 2449\n",
       " 2463\n",
       " 2456\n",
       " 2458"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelitiesExtracted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002 : [1]\n",
      "0.9832064000000004 : [15, 195, 269, 449, 3075, 3329]\n",
      "0.9634168000000002 : [8, 52]\n",
      "0.9798040000000003 : [10]\n",
      "0.9904006400000003 : [45, 225, 3105]\n",
      "0.9896211041000001 : [239, 493, 3119, 3299, 3373, 3553]\n",
      "0.9698631548000001 : [232, 2256, 3112, 3216]\n",
      "0.9702369407000003 : [234, 1230, 3114, 3150]\n",
      "0.9912001200000004 : [69, 113, 137, 1029, 1073, 2057]\n",
      "0.9904135538000003 : [127, 381, 1087, 1187, 1223, 1267, 1341, 1441, 1477, 1521, 2147, 2251, 2401, 2505, 3143, 3187, 3211, 3397, 3441, 3465]\n",
      "0.9706397831000002 : [120, 188, 1080, 1132, 2108]\n",
      "0.9710202744000004 : [122, 1082]\n",
      "0.9984006000000005 : [145, 2065]\n",
      "0.9816210645000005 : [159, 413, 2079, 2259, 2333, 2513, 3219, 3473]\n",
      "0.9618631160000003 : [152, 1244, 2072, 3164]\n",
      "0.9782369015000004 : [86, 154, 1046, 2074]\n",
      "0.9512320000000001 : [525, 705, 3585]\n",
      "0.9507968975000002 : [719, 3599, 3779]\n",
      "0.9318140799000001 : [576, 676, 712, 756, 2596, 3592, 3636]\n",
      "0.9318593505000003 : [610, 714, 1570, 3594]\n",
      "0.9576978427000002 : [749, 3629, 3809]\n",
      "0.9412762310000002 : [3823]\n",
      "0.9223237737000003 : [3816]\n",
      "0.9383561771000004 : [3818]\n",
      "0.9584647295000001 : [637, 1597, 1697, 1733, 1777, 2657, 2761, 3653, 3697, 3721]\n",
      "0.9420363741000003 : [1711, 1791, 2671, 3711]\n",
      "0.9230687405000002 : [1704, 1784, 2664, 2732, 2812, 3704, 3772]\n",
      "0.9391075758000004 : [694, 1638, 1706, 1786, 2614, 2666, 3706]\n",
      "0.9496978043000003 : [669, 2589, 2769, 3729]\n",
      "0.9492761929000003 : [2783, 3743]\n",
      "0.9303237365000002 : [2776, 3736]\n",
      "0.9303561395000003 : [1750, 2778, 3670, 3738]\n",
      "0.9518095999999999 : [833, 1793]\n",
      "0.9354397671 : [811, 847, 1807, 1987, 3907]\n",
      "0.9166038358 : [840, 884, 908, 1800, 1844, 2828]\n",
      "0.9325868533000001 : [842, 1802]\n",
      "0.9422873137999999 : [877, 1837, 2017, 3937, 4041]\n",
      "0.9419308672999999 : [2031, 3951]\n",
      "0.9231250615 : [2024, 3052, 3944, 4012, 4092]\n",
      "0.9230953112000001 : [934, 1014, 2026, 2854, 2958, 3894, 3946]\n",
      "0.9430482664999998 : [1861, 1905, 1929, 2889]\n",
      "0.9426851285 : [1919, 2951, 2995]\n",
      "0.9238642636999999 : [1912, 1980, 2940]\n",
      "0.9238408957 : [1914]\n",
      "0.9502872757 : [1937, 2897]\n",
      "0.9339308295 : [1951, 2911]\n",
      "0.9151250244999999 : [1944, 2904, 2972]\n",
      "0.9310952738999999 : [1878, 1946, 2906]\n",
      "0.9834048 : [131, 385, 2051, 2305]\n",
      "0.9826867828 : [295, 399, 2319, 2499, 3459]\n",
      "0.9630672783 : [392, 436, 1380, 1484, 2312, 2356, 3404]\n",
      "0.9633823887000001 : [326, 370, 394, 1286, 1330, 2314]\n",
      "0.9898191868000001 : [175, 255, 429, 509, 2095, 2275, 2349, 2529, 3135, 3235, 3271, 3315, 3389, 3489, 3525, 3569]\n",
      "0.9731151128000002 : [2543, 3503, 3583]\n",
      "0.9535269870000003 : [2536, 3496, 3576]\n",
      "0.9698287985000003 : [1510, 2538, 3430, 3498, 3578]\n",
      "0.9906117951000001 : [1159, 1203, 1413, 1457, 2119, 2163, 2187, 2373, 2417, 2441]\n",
      "0.9739007512000003 : [1471, 2431]\n",
      "0.9542969401000001 : [1464, 2424, 2492]\n",
      "0.9706053993000002 : [1398, 1466, 2426]\n",
      "0.9818191472000001 : [1119, 1373, 2195, 2449]\n",
      "0.9811150735000002 : [2463]\n",
      "0.9615269485000001 : [2456]\n",
      "0.9618287597000003 : [1430, 2390, 2458]\n"
     ]
    }
   ],
   "source": [
    "xx = ifwht_natural([z'*reverseGates*noise*initialGates*start for z in zs]/64)\n",
    "for p in xx\n",
    "    print(\"$p : $(findall(x->isapprox(x,p),actualOracle))\\n\")\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IIIIII (0):\tEstimate: 1.0 <-> 1.0 \tPercentage Error: 0.0%\n",
      "IIIIZY (14):\tEstimate: 0.9832608361319543 <-> 0.9832064 \tPercentage Error: 0.0055%\n",
      "IIIIXZ (7):\tEstimate: 0.9646570732960278 <-> 0.9634168 \tPercentage Error: 0.1287%\n",
      "IIIIYX (9):\tEstimate: 0.9800387381402719 <-> 0.979804 \tPercentage Error: 0.024%\n",
      "IIZYII (224):\tEstimate: 0.9903753752127014 <-> 0.99040064 \tPercentage Error: 0.0026%\n",
      "IIZYZY (238):\tEstimate: 0.9897432673667202 <-> 0.9896211041 \tPercentage Error: 0.0123%\n",
      "IIZYXZ (231):\tEstimate: 0.9703648881064589 <-> 0.9698631548 \tPercentage Error: 0.0517%\n",
      "IIZYYX (233):\tEstimate: 0.9707983647823297 <-> 0.9702369407 \tPercentage Error: 0.0579%\n",
      "IIXZII (112):\tEstimate: 0.9910993219118764 <-> 0.99120012 \tPercentage Error: 0.0102%\n",
      "IIXZZY (126):\tEstimate: 0.9905212250582103 <-> 0.9904135538 \tPercentage Error: 0.0109%\n",
      "IIXZXZ (119):\tEstimate: 0.9712593549596166 <-> 0.9706397831 \tPercentage Error: 0.0638%\n",
      "IIXZYX (121):\tEstimate: 0.9716276673089288 <-> 0.9710202744 \tPercentage Error: 0.0626%\n",
      "IIYXII (144):\tEstimate: 0.9983868398109271 <-> 0.9984006 \tPercentage Error: 0.0014%\n",
      "IIYXZY (158):\tEstimate: 0.9816396544088348 <-> 0.9816210645 \tPercentage Error: 0.0019%\n",
      "IIYXXZ (151):\tEstimate: 0.9630306745343353 <-> 0.961863116 \tPercentage Error: 0.1214%\n",
      "IIYXYX (153):\tEstimate: 0.9783072392054106 <-> 0.9782369015 \tPercentage Error: 0.0072%\n",
      "ZYIIII (3584):\tEstimate: 0.9514835150444942 <-> 0.951232 \tPercentage Error: 0.0264%\n",
      "ZYIIZY (3598):\tEstimate: 0.9515309733577308 <-> 0.9507968975 \tPercentage Error: 0.0772%\n",
      "ZYIIXZ (3591):\tEstimate: 0.932643098614912 <-> 0.9318140799 \tPercentage Error: 0.089%\n",
      "ZYIIYX (3593):\tEstimate: 0.9322540498379835 <-> 0.9318593505 \tPercentage Error: 0.0424%\n",
      "ZYZYII (3808):\tEstimate: 0.9579087801820729 <-> 0.9576978427 \tPercentage Error: 0.022%\n",
      "ZYZYZY (3822):\tEstimate: 0.9417971158393882 <-> 0.941276231 \tPercentage Error: 0.0553%\n",
      "ZYZYXZ (3815):\tEstimate: 0.9229103493504338 <-> 0.9223237737 \tPercentage Error: 0.0636%\n",
      "ZYZYYX (3817):\tEstimate: 0.938529492706552 <-> 0.9383561771 \tPercentage Error: 0.0185%\n",
      "ZYXZII (3696):\tEstimate: 0.9586122537568325 <-> 0.9584647295 \tPercentage Error: 0.0154%\n",
      "ZYXZZY (3710):\tEstimate: 0.9425888723713586 <-> 0.9420363741 \tPercentage Error: 0.0586%\n",
      "ZYXZXZ (3703):\tEstimate: 0.9241770495676275 <-> 0.9230687405 \tPercentage Error: 0.1201%\n",
      "ZYXZYX (3705):\tEstimate: 0.9392281393389654 <-> 0.9391075758 \tPercentage Error: 0.0128%\n",
      "ZYYXII (3728):\tEstimate: 0.9499896036110115 <-> 0.9496978043 \tPercentage Error: 0.0307%\n",
      "ZYYXZY (3742):\tEstimate: 0.9500263013509378 <-> 0.9492761929 \tPercentage Error: 0.079%\n",
      "ZYYXXZ (3735):\tEstimate: 0.9310705623964437 <-> 0.9303237365 \tPercentage Error: 0.0803%\n",
      "ZYYXYX (3737):\tEstimate: 0.9304279718914741 <-> 0.9303561395 \tPercentage Error: 0.0077%\n",
      "XZIIII (1792):\tEstimate: 0.9523829811985322 <-> 0.9518096 \tPercentage Error: 0.0602%\n",
      "XZIIZY (1806):\tEstimate: 0.9354014070361333 <-> 0.9354397671 \tPercentage Error: 0.0041%\n",
      "XZIIXZ (1799):\tEstimate: 0.9164784117221473 <-> 0.9166038358 \tPercentage Error: 0.0137%\n",
      "XZIIYX (1801):\tEstimate: 0.9324552055488328 <-> 0.9325868533 \tPercentage Error: 0.0141%\n",
      "XZZYII (2016):\tEstimate: 0.9428764991933171 <-> 0.9422873138 \tPercentage Error: 0.0625%\n",
      "XZZYZY (2030):\tEstimate: 0.9424099413395579 <-> 0.9419308673 \tPercentage Error: 0.0509%\n",
      "XZZYXZ (2023):\tEstimate: 0.9231068616750641 <-> 0.9231250615 \tPercentage Error: 0.002%\n",
      "XZZYYX (2025):\tEstimate: 0.9226096191597515 <-> 0.9230953112 \tPercentage Error: 0.0526%\n",
      "XZXZII (1904):\tEstimate: 0.9433893508802024 <-> 0.9430482665 \tPercentage Error: 0.0362%\n",
      "XZXZZY (1918):\tEstimate: 0.9433295308810477 <-> 0.9426851285 \tPercentage Error: 0.0684%\n",
      "XZXZXZ (1911):\tEstimate: 0.924157841802963 <-> 0.9238642637 \tPercentage Error: 0.0318%\n",
      "XZXZYX (1913):\tEstimate: 0.9233739259911855 <-> 0.9238408957 \tPercentage Error: 0.0505%\n",
      "XZYXII (1936):\tEstimate: 0.9506967945081665 <-> 0.9502872757 \tPercentage Error: 0.0431%\n",
      "XZYXZY (1950):\tEstimate: 0.9337481845917214 <-> 0.9339308295 \tPercentage Error: 0.0196%\n",
      "XZYXXZ (1943):\tEstimate: 0.9153037424583959 <-> 0.9151250245 \tPercentage Error: 0.0195%\n",
      "XZYXYX (1945):\tEstimate: 0.930701917126143 <-> 0.9310952739 \tPercentage Error: 0.0422%\n",
      "YXIIII (2304):\tEstimate: 0.9833897349521105 <-> 0.9834048 \tPercentage Error: 0.0015%\n",
      "YXIIZY (2318):\tEstimate: 0.9828025932436972 <-> 0.9826867828 \tPercentage Error: 0.0118%\n",
      "YXIIXZ (2311):\tEstimate: 0.9632490925574481 <-> 0.9630672783 \tPercentage Error: 0.0189%\n",
      "YXIIYX (2313):\tEstimate: 0.9637617576218745 <-> 0.9633823887 \tPercentage Error: 0.0394%\n",
      "YXZYII (2528):\tEstimate: 0.989878184282456 <-> 0.9898191868 \tPercentage Error: 0.006%\n",
      "YXZYZY (2542):\tEstimate: 0.9729367252562507 <-> 0.9731151128 \tPercentage Error: 0.0183%\n",
      "YXZYXZ (2535):\tEstimate: 0.9545101559822675 <-> 0.953526987 \tPercentage Error: 0.1031%\n",
      "YXZYYX (2537):\tEstimate: 0.9698695367819199 <-> 0.9698287985 \tPercentage Error: 0.0042%\n",
      "YXXZII (2416):\tEstimate: 0.9906399998241464 <-> 0.9906117951 \tPercentage Error: 0.0028%\n",
      "YXXZZY (2430):\tEstimate: 0.9736318429466285 <-> 0.9739007512 \tPercentage Error: 0.0276%\n",
      "YXXZXZ (2423):\tEstimate: 0.9555478313164661 <-> 0.9542969401 \tPercentage Error: 0.1311%\n",
      "YXXZYX (2425):\tEstimate: 0.9707389168429829 <-> 0.9706053993 \tPercentage Error: 0.0138%\n",
      "YXYXII (2448):\tEstimate: 0.9817336194412914 <-> 0.9818191472 \tPercentage Error: 0.0087%\n",
      "YXYXZY (2462):\tEstimate: 0.9811482272883943 <-> 0.9811150735 \tPercentage Error: 0.0034%\n",
      "YXYXXZ (2455):\tEstimate: 0.9616005947070917 <-> 0.9615269485 \tPercentage Error: 0.0077%\n",
      "YXYXYX (2457):\tEstimate: 0.9615911546605903 <-> 0.9618287597 \tPercentage Error: 0.0247%\n"
     ]
    }
   ],
   "source": [
    "# And (just out of interest we can compare the fidelities we extracted, with the actual values)\n",
    "for i in 1:64\n",
    "    print(\"$(fidelityLabels(fidelitiesExtracted[i]-1,qubits=6)) ($(fidelitiesExtracted[i]-1)):\\tEstimate: $(experiment1_fidelities[i]) <-> $(actualOracle[fidelitiesExtracted[i]]) \\tPercentage Error: $(round.(abs(actualOracle[fidelitiesExtracted[i]]-experiment1_fidelities[i])/(actualOracle[fidelitiesExtracted[i]])*100,digits=4))%\\n\")\n",
    "end\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Not bad for 20,000 shots.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building up our eigenvalue Oracle\n",
    "\n",
    "So now we can begin to populate our estimating oracle that we will use to run the peeling decoder.\n",
    "\n",
    "we have 16 values, lets fill them in..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets make it a vector of vectors \n",
    "# - why? Well some of the experiments will have duplicate eigenvalue estimates, and we will want\n",
    "# To end up averaging them.\n",
    "\n",
    "estimateOracle = [[] for _ in 1:4096]\n",
    "\n",
    "for i in 1:64\n",
    "    push!(estimateOracle[fidelitiesExtracted[i]],experiment1_fidelities[i])\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4096-element Array{Array{Any,1},1}:\n",
       " [1.0]\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " [0.9646570732960278]\n",
       " []\n",
       " [0.9800387381402719]\n",
       " []\n",
       " []\n",
       " []\n",
       " ⋮\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []\n",
       " []"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "estimateOracle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mQGroup: 1 Exp: 1100%|███████████████████████████████████| Time: 0:01:25\u001b[39m\n",
      "\u001b[32mQGroup: 2 Exp: 1100%|███████████████████████████████████| Time: 0:01:22\u001b[39m\n",
      "\u001b[32mQubitPairs100%|█████████████████████████████████████████| Time: 0:02:48\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# So I am going to just do all of the above for each of the 5 (other than the one already done) for each of the qubits\n",
    "e1_all_additional_fidelities = []\n",
    "e1_fidelity_extracted = []\n",
    "# Note we don't actually need to save the actual probabilities - but I am going to use them later\n",
    "# To demonstrate some different recovery regimes.\n",
    "e1_all_actualProbabilities = []\n",
    "e1_gatesUsed = []\n",
    "@showprogress 1 \"QubitPairs\" for qubitPairOn = 1:2 # qubit pairs here are 1&2, 3&4 and 5&6\n",
    "    for experimentType = 1:2\n",
    "        if experiments[1][qubitPairOn][2] != experimentType\n",
    "            # Its one we haven't done\n",
    "            expOnFirstPair  = experiments[1][1][2]\n",
    "            expOnSecondPair = experiments[1][2][2]\n",
    "            expOnThirdPair  = experiments[1][3][2]\n",
    "\n",
    "            \n",
    "            if qubitPairOn == 1\n",
    "                expOnFirstPair = experimentType\n",
    "            elseif qubitPairOn == 2\n",
    "                expOnSecondPair = experimentType\n",
    "            else\n",
    "                expOnThirdPair = experimentType\n",
    "            end\n",
    "            initialGates = circuit2q[expOnThirdPair]⊗circuit2q[expOnSecondPair]⊗circuit2q[expOnFirstPair]\n",
    "            push!(e1_gatesUsed,initialGates)\n",
    "            reverseGates = transpose(initialGates) # yay superoperators.\n",
    "            # So at this point we have set up one of the 'new' experiments.\n",
    "            additionalExperiment = []\n",
    "            # Get the actual probabilities.\n",
    "            @showprogress 1 \"QGroup: $qubitPairOn Exp: $experimentType\" for m in lengths\n",
    "                wholeCircuit = rm*reverseGates*noise^m*initialGates*start./64 # Normalising our zs\n",
    "                probs = [z'*wholeCircuit for z in zs]\n",
    "                push!(additionalExperiment,probs)\n",
    "            end\n",
    "            push!(e1_all_actualProbabilities,additionalExperiment)\n",
    "            # Generate the measurement statistics\n",
    "            cumMatrix = map(cumsum,additionalExperiment)\n",
    "            experiment1_additional_observed = shotSimulator(64,shotsToDo,cumMatrix);\n",
    "            # Fit and extract the fidelities\n",
    "            (params,l, failed) = fitTheFidelities(lengths,experiment1_additional_observed)\n",
    "            experiment1_additional_fidelities = vcat(1,[p[2] for p in params])\n",
    "            push!(e1_all_additional_fidelities,experiment1_additional_fidelities)\n",
    "            fidelitiesExtracted=[]\n",
    "            for x0 in all2QlMuBs[expOnThirdPair]\n",
    "                p56 = binaryArrayToNumber(x0)\n",
    "                for x1 in all2QlMuBs[expOnSecondPair]\n",
    "                    p34 = binaryArrayToNumber(x1)\n",
    "                    for x2 in all2QlMuBs[expOnFirstPair]\n",
    "                        p12= binaryArrayToNumber(x2)\n",
    "                        push!(fidelitiesExtracted,p56*4^4+p34*16+p12+1) # + 1 cause we index of 1 in Julia\n",
    "                    end\n",
    "                end\n",
    "            end\n",
    "            push!(e1_fidelity_extracted,fidelitiesExtracted)\n",
    "        end\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "222"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:01:22\u001b[39m\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IIIIII (0):\tEstimate: 1.0 <-> 1.0 \tPercentage Error: 0.0%\n",
      "IIIIZY (14):\tEstimate: 0.9836187322885085 <-> 0.9832064 \tPercentage Error: 0.0419%\n",
      "IIIIXZ (7):\tEstimate: 0.9639149560621026 <-> 0.9634168 \tPercentage Error: 0.0517%\n",
      "IIIIYX (9):\tEstimate: 0.97991687180008 <-> 0.979804 \tPercentage Error: 0.0115%\n",
      "IIZYII (224):\tEstimate: 0.9904880047810369 <-> 0.99040064 \tPercentage Error: 0.0088%\n",
      "IIZYZY (238):\tEstimate: 0.9897596835861429 <-> 0.9896211041 \tPercentage Error: 0.014%\n",
      "IIZYXZ (231):\tEstimate: 0.970063280711357 <-> 0.9698631548 \tPercentage Error: 0.0206%\n",
      "IIZYYX (233):\tEstimate: 0.9704973944327957 <-> 0.9702369407 \tPercentage Error: 0.0268%\n",
      "IIXZII (112):\tEstimate: 0.9913602144274899 <-> 0.99120012 \tPercentage Error: 0.0162%\n",
      "IIXZZY (126):\tEstimate: 0.9905850799039289 <-> 0.9904135538 \tPercentage Error: 0.0173%\n",
      "IIXZXZ (119):\tEstimate: 0.9710270405876867 <-> 0.9706397831 \tPercentage Error: 0.0399%\n",
      "IIXZYX (121):\tEstimate: 0.9713669111696482 <-> 0.9710202744 \tPercentage Error: 0.0357%\n",
      "IIYXII (144):\tEstimate: 0.9985077456470959 <-> 0.9984006 \tPercentage Error: 0.0107%\n",
      "IIYXZY (158):\tEstimate: 0.9820389965856001 <-> 0.9816210645 \tPercentage Error: 0.0426%\n",
      "IIYXXZ (151):\tEstimate: 0.9627793127924436 <-> 0.961863116 \tPercentage Error: 0.0953%\n",
      "IIYXYX (153):\tEstimate: 0.9785209950264261 <-> 0.9782369015 \tPercentage Error: 0.029%\n",
      "ZYIIII (3584):\tEstimate: 0.9512704184526202 <-> 0.951232 \tPercentage Error: 0.004%\n",
      "ZYIIZY (3598):\tEstimate: 0.9507057490779569 <-> 0.9507968975 \tPercentage Error: 0.0096%\n",
      "ZYIIXZ (3591):\tEstimate: 0.9318305497849405 <-> 0.9318140799 \tPercentage Error: 0.0018%\n",
      "ZYIIYX (3593):\tEstimate: 0.9320273704855208 <-> 0.9318593505 \tPercentage Error: 0.018%\n",
      "ZYZYII (3808):\tEstimate: 0.9576946852145771 <-> 0.9576978427 \tPercentage Error: 0.0003%\n",
      "ZYZYZY (3822):\tEstimate: 0.9412133254382572 <-> 0.941276231 \tPercentage Error: 0.0067%\n",
      "ZYZYXZ (3815):\tEstimate: 0.922295169711348 <-> 0.9223237737 \tPercentage Error: 0.0031%\n",
      "ZYZYYX (3817):\tEstimate: 0.9383138005903416 <-> 0.9383561771 \tPercentage Error: 0.0045%\n",
      "ZYXZII (3696):\tEstimate: 0.9587926560545154 <-> 0.9584647295 \tPercentage Error: 0.0342%\n",
      "ZYXZZY (3710):\tEstimate: 0.9425654934879208 <-> 0.9420363741 \tPercentage Error: 0.0562%\n",
      "ZYXZXZ (3703):\tEstimate: 0.92339141164174 <-> 0.9230687405 \tPercentage Error: 0.035%\n",
      "ZYXZYX (3705):\tEstimate: 0.939465275233001 <-> 0.9391075758 \tPercentage Error: 0.0381%\n",
      "ZYYXII (3728):\tEstimate: 0.9505758184090124 <-> 0.9496978043 \tPercentage Error: 0.0925%\n",
      "ZYYXZY (3742):\tEstimate: 0.9499205478803402 <-> 0.9492761929 \tPercentage Error: 0.0679%\n",
      "ZYYXXZ (3735):\tEstimate: 0.9306643121087222 <-> 0.9303237365 \tPercentage Error: 0.0366%\n",
      "ZYYXYX (3737):\tEstimate: 0.9312744179958689 <-> 0.9303561395 \tPercentage Error: 0.0987%\n",
      "XZIIII (1792):\tEstimate: 0.9513329862753058 <-> 0.9518096 \tPercentage Error: 0.0501%\n",
      "XZIIZY (1806):\tEstimate: 0.9353769438978451 <-> 0.9354397671 \tPercentage Error: 0.0067%\n",
      "XZIIXZ (1799):\tEstimate: 0.9165118424555322 <-> 0.9166038358 \tPercentage Error: 0.01%\n",
      "XZIIYX (1801):\tEstimate: 0.9319194365558223 <-> 0.9325868533 \tPercentage Error: 0.0716%\n",
      "XZZYII (2016):\tEstimate: 0.9421912516986911 <-> 0.9422873138 \tPercentage Error: 0.0102%\n",
      "XZZYZY (2030):\tEstimate: 0.9414158013240314 <-> 0.9419308673 \tPercentage Error: 0.0547%\n",
      "XZZYXZ (2023):\tEstimate: 0.9225669804339347 <-> 0.9231250615 \tPercentage Error: 0.0605%\n",
      "XZZYYX (2025):\tEstimate: 0.9226527128231293 <-> 0.9230953112 \tPercentage Error: 0.0479%\n",
      "XZXZII (1904):\tEstimate: 0.9434457325925045 <-> 0.9430482665 \tPercentage Error: 0.0421%\n",
      "XZXZZY (1918):\tEstimate: 0.942653009971232 <-> 0.9426851285 \tPercentage Error: 0.0034%\n",
      "XZXZXZ (1911):\tEstimate: 0.9238292567898823 <-> 0.9238642637 \tPercentage Error: 0.0038%\n",
      "XZXZYX (1913):\tEstimate: 0.9234554719666535 <-> 0.9238408957 \tPercentage Error: 0.0417%\n",
      "XZYXII (1936):\tEstimate: 0.9504061076561945 <-> 0.9502872757 \tPercentage Error: 0.0125%\n",
      "XZYXZY (1950):\tEstimate: 0.9344223468149836 <-> 0.9339308295 \tPercentage Error: 0.0526%\n",
      "XZYXXZ (1943):\tEstimate: 0.9150527789048778 <-> 0.9151250245 \tPercentage Error: 0.0079%\n",
      "XZYXYX (1945):\tEstimate: 0.9307148653758337 <-> 0.9310952739 \tPercentage Error: 0.0409%\n",
      "YXIIII (2304):\tEstimate: 0.9836592542669564 <-> 0.9834048 \tPercentage Error: 0.0259%\n",
      "YXIIZY (2318):\tEstimate: 0.9829948836613357 <-> 0.9826867828 \tPercentage Error: 0.0314%\n",
      "YXIIXZ (2311):\tEstimate: 0.9629371510619611 <-> 0.9630672783 \tPercentage Error: 0.0135%\n",
      "YXIIYX (2313):\tEstimate: 0.9632530202802688 <-> 0.9633823887 \tPercentage Error: 0.0134%\n",
      "YXZYII (2528):\tEstimate: 0.9899561201666218 <-> 0.9898191868 \tPercentage Error: 0.0138%\n",
      "YXZYZY (2542):\tEstimate: 0.9734135813520179 <-> 0.9731151128 \tPercentage Error: 0.0307%\n",
      "YXZYXZ (2535):\tEstimate: 0.9534757475781179 <-> 0.953526987 \tPercentage Error: 0.0054%\n",
      "YXZYYX (2537):\tEstimate: 0.9693840433966625 <-> 0.9698287985 \tPercentage Error: 0.0459%\n",
      "YXXZII (2416):\tEstimate: 0.9908507151068997 <-> 0.9906117951 \tPercentage Error: 0.0241%\n",
      "YXXZZY (2430):\tEstimate: 0.9743807320915888 <-> 0.9739007512 \tPercentage Error: 0.0493%\n",
      "YXXZXZ (2423):\tEstimate: 0.9545487729278829 <-> 0.9542969401 \tPercentage Error: 0.0264%\n",
      "YXXZYX (2425):\tEstimate: 0.9704739272266707 <-> 0.9706053993 \tPercentage Error: 0.0135%\n",
      "YXYXII (2448):\tEstimate: 0.9822206102326522 <-> 0.9818191472 \tPercentage Error: 0.0409%\n",
      "YXYXZY (2462):\tEstimate: 0.9814222407864774 <-> 0.9811150735 \tPercentage Error: 0.0313%\n",
      "YXYXXZ (2455):\tEstimate: 0.9615603517693696 <-> 0.9615269485 \tPercentage Error: 0.0035%\n",
      "YXYXYX (2457):\tEstimate: 0.9620298364703991 <-> 0.9618287597 \tPercentage Error: 0.0209%\n"
     ]
    }
   ],
   "source": [
    "#initialGates = generateGates(experiments[1],[circuit1q,circuit2q])\n",
    "expOnFirstPair  = experiments[1][1][2]\n",
    "expOnSecondPair = experiments[1][2][2]\n",
    "expOnThirdPair  = experiments[1][3][2]\n",
    "print(expOnFirstPair,expOnSecondPair,expOnThirdPair)\n",
    "            \n",
    "initialGates = circuit2q[expOnThirdPair]⊗circuit2q[expOnSecondPair]⊗circuit2q[expOnFirstPair]\n",
    "\n",
    "\n",
    "\n",
    "reverseGates = transpose(initialGates); # yay superoperators.\n",
    "experiment1_allProbs = []\n",
    "# These will depend on your system\n",
    "lengths =  [1,3,5,8,10,15,20,40,60,80]\n",
    "@showprogress for m in lengths\n",
    "    wholeCircuit = reverseGates*noise^m*initialGates*rm*start./64 # ./64 = Normalise the measurement/state vectors\n",
    "    probs = [z'*wholeCircuit for z in zs]\n",
    "    push!(experiment1_allProbs,probs)\n",
    "end\n",
    "\n",
    "\n",
    "# We need culmlative probability matrixes\n",
    "cumMatrix = map(cumsum,experiment1_allProbs)\n",
    "experiment1_observed = shotSimulator(64,shotsToDo,cumMatrix);\n",
    "(params,l, failed) = fitTheFidelities(lengths,experiment1_observed)\n",
    "experiment1_fidelities = vcat(1,[p[2] for p in params]) # We don't fit the first one, it is always 1 for CPTP maps\n",
    "\n",
    "fidelitiesExtracted = []\n",
    "function binaryArrayToNumber(x)\n",
    "    return foldl((y1,y2)->y1<<1+y2,x)\n",
    "end\n",
    "\n",
    "           for x0 in all2QlMuBs[expOnThirdPair]\n",
    "                p56 = binaryArrayToNumber(x0)\n",
    "                for x1 in all2QlMuBs[expOnSecondPair]\n",
    "                    p34 = binaryArrayToNumber(x1)\n",
    "                    for x2 in all2QlMuBs[expOnFirstPair]\n",
    "                        p12= binaryArrayToNumber(x2)\n",
    "                        push!(fidelitiesExtracted,p56*4^4+p34*16+p12+1) # + 1 cause we index of 1 in Julia\n",
    "                    end\n",
    "                end\n",
    "            end\n",
    "\n",
    "\n",
    "# for x0 in paulisAll[1][3]\n",
    "#     p56 = binaryArrayToNumber(x0)\n",
    "#     for x1 in paulisAll[1][2]\n",
    "#         p34 = binaryArrayToNumber(x1)\n",
    "#         for x2 in paulisAll[1][1]\n",
    "#             p12= binaryArrayToNumber(x2)\n",
    "#             push!(fidelitiesExtracted,p56*4^4+p34*16+p12+1) # + 1 cause we index of 1 in Julia\n",
    "#         end\n",
    "#     end\n",
    "# end\n",
    "# And (just out of interest we can compare the fidelities we extracted, with the actual values)\n",
    "for i in 1:64\n",
    "    print(\"$(fidelityLabels(fidelitiesExtracted[i]-1,qubits=6)) ($(fidelitiesExtracted[i]-1)):\\tEstimate: $(experiment1_fidelities[i]) <-> $(actualOracle[fidelitiesExtracted[i]]) \\tPercentage Error: $(round.(abs(actualOracle[fidelitiesExtracted[i]]-experiment1_fidelities[i])/(actualOracle[fidelitiesExtracted[i]])*100,digits=4))%\\n\")\n",
    "end\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### So now we need to put into the oracle the offsets for this experiment we will need.\n",
    "\n",
    "This is step 2 in the diagram from the paper (a long way back up there $\\uparrow$.\n",
    "\n",
    "Basically for each pair of qubits, we have to cycle through four of the two qubit mubs (there are five but we have done one already). That means we have another 8 experiments, i.e. 2n where n is the number of qubits. For each sub-sampling group we need to do 2n+1 experiments. Let's create the initial and reverse gates for each of the 3 Mubs we haven't already got ([II,IX,XI,XX], [II,IY,YI,YY], [II,IZ,ZI,ZZ]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Array{Float64,2},1}:\n",
       " [1.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [1.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [1.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [1.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]\n",
       " [1.0 0.0 … 0.0 0.0; 0.0 1.0 … 0.0 0.0; … ; 0.0 0.0 … 1.0 0.0; 0.0 0.0 … 0.0 1.0]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We already had the first bit, repeating just to make the cell self-contained.\n",
    "circuit2q = [superCnot21*superPI*superCnot21*superIP*superHH,\n",
    "             superCnot21*superPI*superCnot21*superPI*superHH]\n",
    "\n",
    "push!(circuit2q,superHH) # The XX one\n",
    "push!(circuit2q,superIP*superPI*superHH) # the YY one\n",
    "push!(circuit2q,makeSuper([1 0;0 1]⊗[1 0;0 1])) # The ZZ one i.e. nothing.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mQGroup: 1 Exp: 1100%|███████████████████████████████████| Time: 0:01:23\u001b[39m\n",
      "\u001b[32mQGroup: 1 Exp: 3100%|███████████████████████████████████| Time: 0:01:24\u001b[39m\n",
      "\u001b[32mQGroup: 1 Exp: 4100%|███████████████████████████████████| Time: 0:01:22\u001b[39m\n",
      "\u001b[32mQGroup: 1 Exp: 5100%|███████████████████████████████████| Time: 0:01:23\u001b[39m\n",
      "\u001b[32mQGroup: 2 Exp: 1100%|███████████████████████████████████| Time: 0:01:26\u001b[39m\n",
      "\u001b[32mQGroup: 2 Exp: 3100%|███████████████████████████████████| Time: 0:01:22\u001b[39m\n",
      "\u001b[32mQGroup: 2 Exp: 4100%|███████████████████████████████████| Time: 0:01:24\u001b[39m\n",
      "\u001b[32mQGroup: 2 Exp: 5100%|███████████████████████████████████| Time: 0:01:24\u001b[39m\n",
      "\u001b[32mQGroup: 3 Exp: 1100%|███████████████████████████████████| Time: 0:01:23\u001b[39m\n",
      "\u001b[32mQGroup: 3 Exp: 3100%|███████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup: 3 Exp: 4100%|███████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup: 3 Exp: 5100%|███████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQubitPairs100%|█████████████████████████████████████████| Time: 0:16:27\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# So I am going to just do all of the above for each of the 5 (other than the one already done) for each of the qubits\n",
    "e1_all_additional_fidelities = []\n",
    "e1_fidelity_extracted = []\n",
    "# Note we don't actually need to save the actual probabilities - but I am going to use them later\n",
    "# To demonstrate some different recovery regimes.\n",
    "e1_all_actualProbabilities = []\n",
    "@showprogress 1 \"QubitPairs\" for qubitPairOn = 1:3 # qubit pairs here are 1&2, 3&4 and 5&6\n",
    "    for experimentType = 1:5\n",
    "        if experiments[1][qubitPairOn][2] != experimentType\n",
    "            # Its one we haven't done\n",
    "            expOnFirstPair  = experiments[1][1][2]\n",
    "            expOnSecondPair = experiments[1][2][2]\n",
    "            expOnThirdPair  = experiments[1][3][2]\n",
    "\n",
    "            \n",
    "            if qubitPairOn == 1\n",
    "                expOnFirstPair = experimentType\n",
    "            elseif qubitPairOn == 2\n",
    "                expOnSecondPair = experimentType\n",
    "            else\n",
    "                expOnThirdPair = experimentType\n",
    "            end\n",
    "            initialGates = circuit2q[expOnThirdPair]⊗circuit2q[expOnSecondPair]⊗circuit2q[expOnFirstPair]\n",
    "\n",
    "            reverseGates = transpose(initialGates) # yay superoperators.\n",
    "            # So at this point we have set up one of the 'new' experiments.\n",
    "            additionalExperiment = []\n",
    "            # Get the actual probabilities.\n",
    "            @showprogress 1 \"QGroup: $qubitPairOn Exp: $experimentType\" for m in lengths\n",
    "                wholeCircuit = reverseGates*noise^m*initialGates*rm*start./64 # Normalising our zs\n",
    "                probs = [z'*wholeCircuit for z in zs]\n",
    "                push!(additionalExperiment,probs)\n",
    "            end\n",
    "            push!(e1_all_actualProbabilities,additionalExperiment)\n",
    "            # Generate the measurement statistics\n",
    "            cumMatrix = map(cumsum,additionalExperiment)\n",
    "            experiment1_additional_observed = shotSimulator(64,shotsToDo,cumMatrix);\n",
    "            # Fit and extract the fidelities\n",
    "            (params,l, failed) = fitTheFidelities(lengths,experiment1_additional_observed)\n",
    "            experiment1_additional_fidelities = vcat(1,[p[2] for p in params])\n",
    "            push!(e1_all_additional_fidelities,experiment1_additional_fidelities)\n",
    "            fidelitiesExtracted=[]\n",
    "            for x0 in all2QlMuBs[expOnThirdPair]\n",
    "                p56 = binaryArrayToNumber(x0)\n",
    "                for x1 in all2QlMuBs[expOnSecondPair]\n",
    "                    p34 = binaryArrayToNumber(x1)\n",
    "                    for x2 in all2QlMuBs[expOnFirstPair]\n",
    "                        p12= binaryArrayToNumber(x2)\n",
    "                        push!(fidelitiesExtracted,p56*4^4+p34*16+p12+1) # + 1 cause we index of 1 in Julia\n",
    "                    end\n",
    "                end\n",
    "            end\n",
    "            push!(e1_fidelity_extracted,fidelitiesExtracted)\n",
    "        end\n",
    "    end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IIIIII (1): \tEstimate: 1.0 <-> 1.0 \tPercentage Error: 0.0%\n",
      "IIIIZY (15): \tEstimate: 0.98344 <-> 0.98321 \tPercentage Error: 0.0237%\n",
      "IIIIXZ (8): \tEstimate: 0.96326 <-> 0.96342 \tPercentage Error: 0.016%\n",
      "IIIIYX (10): \tEstimate: 0.98009 <-> 0.9798 \tPercentage Error: 0.0288%\n",
      "IIZYII (225): \tEstimate: 0.99057 <-> 0.9904 \tPercentage Error: 0.0168%\n",
      "IIZYZY (239): \tEstimate: 0.98959 <-> 0.98962 \tPercentage Error: 0.0029%\n",
      "IIZYXZ (232): \tEstimate: 0.96985 <-> 0.96986 \tPercentage Error: 0.0018%\n",
      "IIZYYX (234): \tEstimate: 0.97078 <-> 0.97024 \tPercentage Error: 0.0556%\n",
      "IIXZII (113): \tEstimate: 0.99144 <-> 0.9912 \tPercentage Error: 0.0241%\n",
      "IIXZZY (127): \tEstimate: 0.99054 <-> 0.99041 \tPercentage Error: 0.0127%\n",
      "IIXZXZ (120): \tEstimate: 0.97058 <-> 0.97064 \tPercentage Error: 0.006%\n",
      "IIXZYX (122): \tEstimate: 0.97178 <-> 0.97102 \tPercentage Error: 0.0786%\n",
      "IIYXII (145): \tEstimate: 0.99838 <-> 0.9984 \tPercentage Error: 0.0019%\n",
      "IIYXZY (159): \tEstimate: 0.98207 <-> 0.98162 \tPercentage Error: 0.0457%\n",
      "IIYXXZ (152): \tEstimate: 0.96182 <-> 0.96186 \tPercentage Error: 0.0047%\n",
      "IIYXYX (154): \tEstimate: 0.9784 <-> 0.97824 \tPercentage Error: 0.0164%\n",
      "IZIIII (769): \tEstimate: 0.95314 <-> 0.952 \tPercentage Error: 0.1194%\n",
      "IZIIZY (783): \tEstimate: 0.93591 <-> 0.93563 \tPercentage Error: 0.0298%\n",
      "IZIIXZ (776): \tEstimate: 0.91672 <-> 0.91679 \tPercentage Error: 0.0071%\n",
      "IZIIYX (778): \tEstimate: 0.9337 <-> 0.93277 \tPercentage Error: 0.0995%\n",
      "IZZYII (993): \tEstimate: 0.94322 <-> 0.94248 \tPercentage Error: 0.0788%\n",
      "IZZYZY (1007): \tEstimate: 0.943 <-> 0.94212 \tPercentage Error: 0.0935%\n",
      "IZZYXZ (1000): \tEstimate: 0.92388 <-> 0.92331 \tPercentage Error: 0.0621%\n",
      "IZZYYX (1002): \tEstimate: 0.92456 <-> 0.92328 \tPercentage Error: 0.1388%\n",
      "IZXZII (881): \tEstimate: 0.94355 <-> 0.94324 \tPercentage Error: 0.0328%\n",
      "IZXZZY (895): \tEstimate: 0.94297 <-> 0.94287 \tPercentage Error: 0.0099%\n",
      "IZXZXZ (888): \tEstimate: 0.9236 <-> 0.92405 \tPercentage Error: 0.0485%\n",
      "IZXZYX (890): \tEstimate: 0.92427 <-> 0.92403 \tPercentage Error: 0.0262%\n",
      "IZYXII (913): \tEstimate: 0.95116 <-> 0.95048 \tPercentage Error: 0.0716%\n",
      "IZYXZY (927): \tEstimate: 0.93411 <-> 0.93412 \tPercentage Error: 0.0008%\n",
      "IZYXXZ (920): \tEstimate: 0.91568 <-> 0.91531 \tPercentage Error: 0.0402%\n",
      "IZYXYX (922): \tEstimate: 0.9319 <-> 0.93128 \tPercentage Error: 0.0665%\n",
      "ZIIIII (3073): \tEstimate: 0.99922 <-> 0.9992 \tPercentage Error: 0.0024%\n",
      "ZIIIZY (3087): \tEstimate: 0.98264 <-> 0.98241 \tPercentage Error: 0.0236%\n",
      "ZIIIXZ (3080): \tEstimate: 0.96244 <-> 0.96264 \tPercentage Error: 0.0206%\n",
      "ZIIIYX (3082): \tEstimate: 0.97929 <-> 0.97902 \tPercentage Error: 0.0275%\n",
      "ZIZYII (3297): \tEstimate: 0.98974 <-> 0.9896 \tPercentage Error: 0.0142%\n",
      "ZIZYZY (3311): \tEstimate: 0.98882 <-> 0.98883 \tPercentage Error: 0.0013%\n",
      "ZIZYXZ (3304): \tEstimate: 0.96902 <-> 0.96909 \tPercentage Error: 0.007%\n",
      "ZIZYYX (3306): \tEstimate: 0.96998 <-> 0.96945 \tPercentage Error: 0.0541%\n",
      "ZIXZII (3185): \tEstimate: 0.99059 <-> 0.9904 \tPercentage Error: 0.0193%\n",
      "ZIXZZY (3199): \tEstimate: 0.98978 <-> 0.98962 \tPercentage Error: 0.0165%\n",
      "ZIXZXZ (3192): \tEstimate: 0.96985 <-> 0.96986 \tPercentage Error: 0.0012%\n",
      "ZIXZYX (3194): \tEstimate: 0.971 <-> 0.97024 \tPercentage Error: 0.0786%\n",
      "ZIYXII (3217): \tEstimate: 0.99761 <-> 0.9976 \tPercentage Error: 0.0006%\n",
      "ZIYXZY (3231): \tEstimate: 0.98131 <-> 0.98083 \tPercentage Error: 0.0492%\n",
      "ZIYXXZ (3224): \tEstimate: 0.96122 <-> 0.96109 \tPercentage Error: 0.0136%\n",
      "ZIYXYX (3226): \tEstimate: 0.97779 <-> 0.97745 \tPercentage Error: 0.0339%\n",
      "ZZIIII (3841): \tEstimate: 0.95228 <-> 0.95124 \tPercentage Error: 0.1091%\n",
      "ZZIIZY (3855): \tEstimate: 0.9351 <-> 0.93487 \tPercentage Error: 0.0241%\n",
      "ZZIIXZ (3848): \tEstimate: 0.91584 <-> 0.91605 \tPercentage Error: 0.0232%\n",
      "ZZIIYX (3850): \tEstimate: 0.93288 <-> 0.93203 \tPercentage Error: 0.091%\n",
      "ZZZYII (4065): \tEstimate: 0.94233 <-> 0.94172 \tPercentage Error: 0.0648%\n",
      "ZZZYZY (4079): \tEstimate: 0.94211 <-> 0.94137 \tPercentage Error: 0.079%\n",
      "ZZZYXZ (4072): \tEstimate: 0.92296 <-> 0.92257 \tPercentage Error: 0.0423%\n",
      "ZZZYYX (4074): \tEstimate: 0.92375 <-> 0.92254 \tPercentage Error: 0.1311%\n",
      "ZZXZII (3953): \tEstimate: 0.94266 <-> 0.94248 \tPercentage Error: 0.0196%\n",
      "ZZXZZY (3967): \tEstimate: 0.94212 <-> 0.94212 \tPercentage Error: 0.0001%\n",
      "ZZXZXZ (3960): \tEstimate: 0.92275 <-> 0.92331 \tPercentage Error: 0.0608%\n",
      "ZZXZYX (3962): \tEstimate: 0.92347 <-> 0.92328 \tPercentage Error: 0.0205%\n",
      "ZZYXII (3985): \tEstimate: 0.95038 <-> 0.94972 \tPercentage Error: 0.0695%\n",
      "ZZYXZY (3999): \tEstimate: 0.93337 <-> 0.93337 \tPercentage Error: 0.0009%\n",
      "ZZYXXZ (3992): \tEstimate: 0.91486 <-> 0.91457 \tPercentage Error: 0.0317%\n",
      "ZZYXYX (3994): \tEstimate: 0.93119 <-> 0.93054 \tPercentage Error: 0.0703%\n"
     ]
    }
   ],
   "source": [
    "# So for example, if we look at some of these additional 12 experiments, we see\n",
    "# The following - look at the changing eigevalues we sample (left hand side).\n",
    "# E.g. exerimpent 12 as qubits 5&6 with the the II IZ ZI ZZ stabiliser.\n",
    "\n",
    "toExtract = 12\n",
    "\n",
    "# And (just out of interest we can compare the fidelities we extracted, with the actual values)\n",
    "for i in 1:64\n",
    "    print(\"$(fidelityLabels(e1_fidelity_extracted[toExtract][i]-1,qubits=6)) \",\n",
    "          \"($(e1_fidelity_extracted[toExtract][i])): \",\n",
    "          \"\\tEstimate: $(round(e1_all_additional_fidelities[toExtract][i],digits=5))\",\n",
    "          \" <-> $(round(actualOracle[e1_fidelity_extracted[toExtract][i]],digits=5)) \",\n",
    "          \"\\tPercentage Error: $(round.(abs(actualOracle[e1_fidelity_extracted[toExtract][i]]-e1_all_additional_fidelities[toExtract][i])/(actualOracle[e1_fidelity_extracted[toExtract][i]])*100,digits=4))%\\n\")\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# So we just need to fill in the oracle\n",
    "\n",
    "for (expNo,x) in enumerate(e1_fidelity_extracted)\n",
    "    for (fidelityIndex,fidelity)  in enumerate(x)\n",
    "        push!(estimateOracle[fidelity],e1_all_additional_fidelities[expNo][fidelityIndex])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "001 1.0 \t[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
      "002 0.972 \t[0.97245]\n",
      "003 0.984 \t[0.98379]\n",
      "004 0.972 \t[0.97222]\n",
      "005 0.9914 \t[0.99144]\n",
      "006 0.97941 \t[0.97957]\n",
      "007 0.9914 \t[0.99154]\n",
      "008 0.96342 \t[0.96466, 0.96398, 0.96294, 0.96325, 0.9632, 0.96397, 0.96343, 0.96334, 0.96326]\n",
      "009 0.9918 \t[0.99173]\n",
      "010 0.9798 \t[0.98004, 0.98015, 0.97996, 0.97959, 0.97987, 0.9798, 0.97983, 0.97964, 0.98009]\n",
      "011 0.9918 \t[0.99173]\n",
      "012 0.96381 \t[0.96422]\n",
      "013 0.9992 \t[0.99924]\n",
      "014 0.97122 \t[0.97099]\n",
      "015 0.98321 \t[0.98326, 0.98301, 0.98303, 0.98328, 0.98312, 0.98329, 0.98322, 0.98338, 0.98344]\n",
      "016 0.97122 \t[0.97164]\n",
      "017 0.999 \t[0.99905]\n",
      "024 0.96245 \t[0.9621]\n",
      "026 0.97882 \t[0.97902]\n",
      "031 0.98222 \t[0.98198]\n",
      "033 0.9912 \t[0.99122]\n",
      "040 0.97064 \t[0.96982]\n",
      "042 0.97102 \t[0.97078]\n",
      "047 0.99041 \t[0.99034]\n",
      "049 0.9914 \t[0.99143]\n",
      "056 0.97083 \t[0.97072]\n",
      "058 0.97122 \t[0.97188]\n",
      "063 0.99061 \t[0.99061]\n",
      "065 0.9998 \t[0.99983]\n",
      "072 0.96322 \t[0.96257]\n",
      "074 0.97961 \t[0.97967]\n",
      "079 0.98301 \t[0.98293]\n",
      "081 0.9988 \t[0.99889]\n",
      "088 0.96225 \t[0.96175]\n",
      "090 0.97863 \t[0.97867]\n",
      "095 0.98202 \t[0.9819]\n",
      "097 0.991 \t[0.99091]\n",
      "104 0.97045 \t[0.97043]\n",
      "106 0.97082 \t[0.97099]\n",
      "111 0.99022 \t[0.99018]\n",
      "113 0.9912 \t[0.9911, 0.99132, 0.99138, 0.99103, 0.99118, 0.99143, 0.99122, 0.99126, 0.99144]\n",
      "114 0.97922 \t[0.97945]\n",
      "115 0.99121 \t[0.99099]\n",
      "116 0.96322 \t[0.96393]\n",
      "117 0.9986 \t[0.99861]\n",
      "118 0.97063 \t[0.97115]\n",
      "119 0.98261 \t[0.98272]\n",
      "120 0.97064 \t[0.97126, 0.9713, 0.97094, 0.97077, 0.97058]\n",
      "121 0.999 \t[0.99898]\n",
      "122 0.97102 \t[0.97163, 0.97103, 0.97088, 0.97107, 0.97178]\n",
      "123 0.98301 \t[0.98273]\n",
      "124 0.97103 \t[0.97133]\n",
      "125 0.9904 \t[0.99044]\n",
      "126 0.97843 \t[0.97817]\n",
      "127 0.99041 \t[0.99052, 0.99049, 0.99049, 0.9904, 0.99054]\n",
      "128 0.96245 \t[0.96317]\n",
      "129 0.9994 \t[0.99942]\n",
      "136 0.96283 \t[0.96246]\n",
      "138 0.97922 \t[0.9786]\n",
      "143 0.98261 \t[0.98276]\n",
      "145 0.9984 \t[0.99839, 0.99843, 0.99843, 0.99828, 0.99835, 0.99856, 0.99835, 0.9983, 0.99838]\n",
      "146 0.97043 \t[0.97101]\n",
      "147 0.98241 \t[0.98191]\n",
      "148 0.97045 \t[0.97054]\n",
      "149 0.9898 \t[0.98999]\n",
      "150 0.97785 \t[0.9781]\n",
      "151 0.98982 \t[0.98993]\n",
      "152 0.96186 \t[0.96303, 0.96228, 0.96186, 0.9618, 0.96182]\n",
      "153 0.9902 \t[0.99001]\n",
      "154 0.97824 \t[0.97831, 0.97833, 0.97787, 0.97816, 0.9784]\n",
      "155 0.99022 \t[0.98994]\n",
      "156 0.96225 \t[0.96273]\n",
      "157 0.9976 \t[0.99757]\n",
      "158 0.96965 \t[0.96954]\n",
      "159 0.98162 \t[0.98164, 0.98198, 0.98148, 0.98163, 0.98207]\n",
      "160 0.96967 \t[0.97002]\n",
      "161 0.9906 \t[0.99076]\n",
      "168 0.97006 \t[0.96884]\n",
      "170 0.97043 \t[0.96998]\n",
      "175 0.98982 \t[0.98971]\n",
      "177 0.9908 \t[0.99058]\n",
      "184 0.97025 \t[0.97032]\n",
      "186 0.97063 \t[0.97082]\n",
      "191 0.99002 \t[0.98983]\n",
      "193 0.9992 \t[0.99919]\n",
      "200 0.96264 \t[0.96275]\n",
      "202 0.97902 \t[0.97906]\n",
      "207 0.98241 \t[0.98238]\n",
      "209 0.9982 \t[0.99823]\n",
      "216 0.96167 \t[0.96222]\n",
      "218 0.97804 \t[0.9784]\n",
      "223 0.98142 \t[0.98127]\n",
      "225 0.9904 \t[0.99038, 0.99055, 0.99058, 0.99016, 0.99042, 0.99059, 0.99034, 0.99046, 0.99057]\n",
      "226 0.97843 \t[0.97859]\n",
      "227 0.99041 \t[0.99021]\n",
      "228 0.96245 \t[0.96336]\n",
      "229 0.9978 \t[0.99777]\n",
      "230 0.96985 \t[0.97035]\n",
      "231 0.98182 \t[0.98204]\n",
      "232 0.96986 \t[0.97036, 0.97029, 0.96985, 0.97001, 0.96985]\n",
      "233 0.9982 \t[0.99811]\n",
      "234 0.97024 \t[0.9708, 0.97016, 0.97003, 0.96999, 0.97078]\n",
      "235 0.98222 \t[0.9818]\n",
      "236 0.97025 \t[0.97049]\n",
      "237 0.9896 \t[0.98967]\n",
      "238 0.97765 \t[0.97746]\n",
      "239 0.98962 \t[0.98974, 0.98969, 0.9898, 0.98967, 0.98959]\n",
      "240 0.96167 \t[0.96259]\n",
      "241 0.9906 \t[0.99058]\n",
      "248 0.97006 \t[0.97013]\n",
      "250 0.97043 \t[0.97112]\n",
      "255 0.98982 \t[0.98974]\n",
      "257 0.984 \t[0.98416]\n",
      "264 0.96365 \t[0.96451]\n",
      "266 0.96397 \t[0.96369]\n",
      "271 0.98328 \t[0.98343]\n",
      "369 0.99121 \t[0.99107]\n",
      "376 0.95487 \t[0.95525]\n",
      "378 0.97119 \t[0.97133]\n",
      "383 0.97449 \t[0.97444]\n",
      "401 0.98241 \t[0.98228]\n",
      "408 0.9621 \t[0.96265]\n",
      "410 0.96241 \t[0.96167]\n",
      "415 0.9817 \t[0.98183]\n",
      "481 0.99041 \t[0.9903]\n",
      "488 0.9541 \t[0.95443]\n",
      "490 0.97041 \t[0.97051]\n",
      "495 0.9737 \t[0.97375]\n",
      "513 0.952 \t[0.95181]\n",
      "520 0.93256 \t[0.93235]\n",
      "522 0.93261 \t[0.93229]\n",
      "527 0.95156 \t[0.95112]\n",
      "625 0.95923 \t[0.95877]\n",
      "632 0.92381 \t[0.92436]\n",
      "634 0.93986 \t[0.93907]\n",
      "639 0.9428 \t[0.94314]\n",
      "657 0.95046 \t[0.95032]\n",
      "664 0.93107 \t[0.93085]\n",
      "666 0.93111 \t[0.93106]\n",
      "671 0.95004 \t[0.94956]\n",
      "737 0.95846 \t[0.95808]\n",
      "744 0.92307 \t[0.92348]\n",
      "746 0.93911 \t[0.93804]\n",
      "751 0.94204 \t[0.94229]\n",
      "769 0.952 \t[0.95314]\n",
      "776 0.91679 \t[0.91672]\n",
      "778 0.93277 \t[0.9337]\n",
      "783 0.93563 \t[0.93591]\n",
      "881 0.94324 \t[0.94355]\n",
      "888 0.92405 \t[0.9236]\n",
      "890 0.92403 \t[0.92427]\n",
      "895 0.94287 \t[0.94297]\n",
      "913 0.95048 \t[0.95116]\n",
      "920 0.91531 \t[0.91568]\n",
      "922 0.93128 \t[0.9319]\n",
      "927 0.93412 \t[0.93411]\n",
      "993 0.94248 \t[0.94322]\n",
      "1000 0.92331 \t[0.92388]\n",
      "1002 0.92328 \t[0.92456]\n",
      "1007 0.94212 \t[0.943]\n",
      "1025 0.9998 \t[0.99981]\n",
      "1032 0.96322 \t[0.96318]\n",
      "1034 0.97961 \t[0.97964]\n",
      "1039 0.98301 \t[0.98303]\n",
      "1137 0.991 \t[0.99103]\n",
      "1144 0.97045 \t[0.97076]\n",
      "1146 0.97082 \t[0.97067]\n",
      "1151 0.99022 \t[0.99032]\n",
      "1169 0.9982 \t[0.99815]\n",
      "1176 0.96167 \t[0.96161]\n",
      "1178 0.97804 \t[0.97769]\n",
      "1183 0.98142 \t[0.98127]\n",
      "1249 0.9902 \t[0.99013]\n",
      "1256 0.96967 \t[0.96964]\n",
      "1258 0.97004 \t[0.96975]\n",
      "1263 0.98942 \t[0.98961]\n",
      "1281 0.9838 \t[0.98392]\n",
      "1288 0.96345 \t[0.96429]\n",
      "1290 0.96377 \t[0.96347]\n",
      "1295 0.98308 \t[0.98325]\n",
      "1393 0.99101 \t[0.99088]\n",
      "1400 0.95468 \t[0.95503]\n",
      "1402 0.97099 \t[0.97113]\n",
      "1407 0.97429 \t[0.97416]\n",
      "1425 0.98222 \t[0.98206]\n",
      "1432 0.96191 \t[0.96242]\n",
      "1434 0.96222 \t[0.96148]\n",
      "1439 0.98151 \t[0.98164]\n",
      "1505 0.99022 \t[0.99009]\n",
      "1512 0.95391 \t[0.95415]\n",
      "1514 0.97022 \t[0.97026]\n",
      "1519 0.97351 \t[0.97342]\n",
      "1537 0.95181 \t[0.95153]\n",
      "1544 0.93237 \t[0.93249]\n",
      "1546 0.93242 \t[0.93138]\n",
      "1551 0.95137 \t[0.9516]\n",
      "1649 0.95904 \t[0.95917]\n",
      "1656 0.92363 \t[0.92448]\n",
      "1658 0.93967 \t[0.93918]\n",
      "1663 0.94261 \t[0.94289]\n",
      "1681 0.95027 \t[0.94976]\n",
      "1688 0.93088 \t[0.93198]\n",
      "1690 0.93092 \t[0.93027]\n",
      "1695 0.94985 \t[0.9503]\n",
      "1761 0.95827 \t[0.95832]\n",
      "1768 0.92288 \t[0.92245]\n",
      "1770 0.93892 \t[0.93812]\n",
      "1775 0.94185 \t[0.94178]\n",
      "1793 0.95181 \t[0.95238, 0.95156, 0.95179, 0.95135, 0.95203, 0.9521, 0.9519, 0.95136, 0.95258]\n",
      "1794 0.92477 \t[0.92446]\n",
      "1795 0.9362 \t[0.93528]\n",
      "1796 0.92516 \t[0.92545]\n",
      "1797 0.94324 \t[0.94294]\n",
      "1798 0.93221 \t[0.93232]\n",
      "1799 0.94363 \t[0.94354]\n",
      "1800 0.9166 \t[0.91648, 0.91646, 0.91656, 0.91784, 0.9183]\n",
      "1801 0.94362 \t[0.94319]\n",
      "1802 0.93259 \t[0.93246, 0.93224, 0.93296, 0.93349, 0.93417]\n",
      "1803 0.94401 \t[0.94303]\n",
      "1804 0.91697 \t[0.91792]\n",
      "1805 0.95105 \t[0.95141]\n",
      "1806 0.92403 \t[0.92447]\n",
      "1807 0.93544 \t[0.9354, 0.93484, 0.93514, 0.93512, 0.93569]\n",
      "1808 0.92442 \t[0.9247]\n",
      "1809 0.95086 \t[0.951]\n",
      "1816 0.91568 \t[0.91548]\n",
      "1818 0.93165 \t[0.93214]\n",
      "1823 0.9345 \t[0.93388]\n",
      "1825 0.94305 \t[0.94298]\n",
      "1832 0.92386 \t[0.92431]\n",
      "1834 0.92384 \t[0.92486]\n",
      "1839 0.94269 \t[0.94205]\n",
      "1841 0.94324 \t[0.94415]\n",
      "1848 0.92405 \t[0.92538]\n",
      "1850 0.92403 \t[0.92629]\n",
      "1855 0.94287 \t[0.94276]\n",
      "1857 0.95162 \t[0.9515]\n",
      "1864 0.91642 \t[0.91693]\n",
      "1866 0.9324 \t[0.93311]\n",
      "1871 0.93525 \t[0.93491]\n",
      "1873 0.95067 \t[0.95053]\n",
      "1880 0.91549 \t[0.91576]\n",
      "1882 0.93147 \t[0.93215]\n",
      "1887 0.93431 \t[0.9336]\n",
      "1889 0.94286 \t[0.94235]\n",
      "1896 0.92368 \t[0.92356]\n",
      "1898 0.92365 \t[0.92281]\n",
      "1903 0.9425 \t[0.94212]\n",
      "1905 0.94305 \t[0.94339, 0.94273, 0.9423, 0.9423, 0.94314]\n",
      "1906 0.93203 \t[0.93152]\n",
      "1907 0.94344 \t[0.94238]\n",
      "1908 0.91642 \t[0.91613]\n",
      "1909 0.95048 \t[0.95032]\n",
      "1910 0.92347 \t[0.92295]\n",
      "1911 0.93487 \t[0.93504]\n",
      "1912 0.92386 \t[0.92416]\n",
      "1913 0.95086 \t[0.95001]\n",
      "1914 0.92384 \t[0.92337]\n",
      "1915 0.93525 \t[0.93367]\n",
      "1916 0.92423 \t[0.92525]\n",
      "1917 0.94229 \t[0.9425]\n",
      "1918 0.93128 \t[0.93184]\n",
      "1919 0.94269 \t[0.94333]\n",
      "1920 0.91568 \t[0.91546]\n",
      "1921 0.95124 \t[0.95061]\n",
      "1928 0.91605 \t[0.91689]\n",
      "1930 0.93203 \t[0.93251]\n",
      "1935 0.93487 \t[0.93434]\n",
      "1937 0.95029 \t[0.9507, 0.95027, 0.94995, 0.94922, 0.94962]\n",
      "1938 0.92328 \t[0.92244]\n",
      "1939 0.93468 \t[0.93311]\n",
      "1940 0.92368 \t[0.92291]\n",
      "1941 0.94172 \t[0.94114]\n",
      "1942 0.93072 \t[0.93039]\n",
      "1943 0.94212 \t[0.94191]\n",
      "1944 0.91513 \t[0.9153]\n",
      "1945 0.9421 \t[0.94118]\n",
      "1946 0.9311 \t[0.9307]\n",
      "1947 0.9425 \t[0.94089]\n",
      "1948 0.91549 \t[0.91673]\n",
      "1949 0.94953 \t[0.94918]\n",
      "1950 0.92254 \t[0.92334]\n",
      "1951 0.93393 \t[0.93375]\n",
      "1952 0.92294 \t[0.92233]\n",
      "1953 0.94248 \t[0.94202]\n",
      "1960 0.92331 \t[0.92313]\n",
      "1962 0.92328 \t[0.92369]\n",
      "1967 0.94212 \t[0.94103]\n",
      "1969 0.94267 \t[0.94262]\n",
      "1976 0.92349 \t[0.92362]\n",
      "1978 0.92347 \t[0.92327]\n",
      "1983 0.94231 \t[0.94203]\n",
      "1985 0.95105 \t[0.95136]\n",
      "1992 0.91586 \t[0.9177]\n",
      "1994 0.93184 \t[0.93347]\n",
      "1999 0.93469 \t[0.93516]\n",
      "2001 0.9501 \t[0.95018]\n",
      "2008 0.91494 \t[0.91412]\n",
      "2010 0.93091 \t[0.93001]\n",
      "2015 0.93374 \t[0.93245]\n",
      "2017 0.94229 \t[0.94288, 0.94269, 0.94172, 0.94149, 0.94266]\n",
      "2018 0.93128 \t[0.93103]\n",
      "2019 0.94269 \t[0.94167]\n",
      "2020 0.91568 \t[0.91585]\n",
      "2021 0.94972 \t[0.94985]\n",
      "2022 0.92272 \t[0.92263]\n",
      "2023 0.93412 \t[0.93443]\n",
      "2024 0.92313 \t[0.92311]\n",
      "2025 0.9501 \t[0.94919]\n",
      "2026 0.9231 \t[0.92261]\n",
      "2027 0.9345 \t[0.93292]\n",
      "2028 0.92349 \t[0.92483]\n",
      "2029 0.94153 \t[0.942]\n",
      "2030 0.93054 \t[0.93122]\n",
      "2031 0.94193 \t[0.94241]\n",
      "2032 0.91494 \t[0.91519]\n",
      "2033 0.94248 \t[0.94316]\n",
      "2040 0.92331 \t[0.92479]\n",
      "2042 0.92328 \t[0.92505]\n",
      "2047 0.94212 \t[0.94181]\n",
      "2049 0.9994 \t[0.99943]\n",
      "2056 0.96283 \t[0.96281]\n",
      "2058 0.97922 \t[0.97906]\n",
      "2063 0.98261 \t[0.98284]\n",
      "2161 0.9906 \t[0.99071]\n",
      "2168 0.97006 \t[0.97017]\n",
      "2170 0.97043 \t[0.97057]\n",
      "2175 0.98982 \t[0.98989]\n",
      "2193 0.9978 \t[0.99772]\n",
      "2200 0.96128 \t[0.96122]\n",
      "2202 0.97765 \t[0.97763]\n",
      "2207 0.98103 \t[0.98104]\n",
      "2273 0.9898 \t[0.98994]\n",
      "2280 0.96928 \t[0.96948]\n",
      "2282 0.96965 \t[0.96948]\n",
      "2287 0.98903 \t[0.98914]\n",
      "2305 0.9834 \t[0.98339, 0.98366, 0.98343, 0.98324, 0.98356, 0.98321, 0.98309, 0.98378, 0.98364]\n",
      "2306 0.97158 \t[0.9719]\n",
      "2307 0.98347 \t[0.98351]\n",
      "2308 0.95565 \t[0.95684]\n",
      "2309 0.99081 \t[0.9906]\n",
      "2310 0.96299 \t[0.96299]\n",
      "2311 0.97488 \t[0.97548]\n",
      "2312 0.96307 \t[0.96325, 0.96355, 0.9629, 0.96307, 0.96264]\n",
      "2313 0.99121 \t[0.99128]\n",
      "2314 0.96338 \t[0.96376, 0.96409, 0.96233, 0.9639, 0.96396]\n",
      "2315 0.97528 \t[0.97523]\n",
      "2316 0.96345 \t[0.96479]\n",
      "2317 0.98261 \t[0.98285]\n",
      "2318 0.9708 \t[0.97093]\n",
      "2319 0.98269 \t[0.9828, 0.98256, 0.98264, 0.98297, 0.98268]\n",
      "2320 0.95487 \t[0.95619]\n",
      "2321 0.98241 \t[0.98209]\n",
      "2328 0.9621 \t[0.96197]\n",
      "2330 0.96241 \t[0.96132]\n",
      "2335 0.9817 \t[0.98188]\n",
      "2337 0.99061 \t[0.99079]\n",
      "2344 0.9543 \t[0.9554]\n",
      "2346 0.97061 \t[0.97088]\n",
      "2351 0.9739 \t[0.9742]\n",
      "2353 0.99081 \t[0.9909]\n",
      "2360 0.95449 \t[0.95424]\n",
      "2362 0.9708 \t[0.97116]\n",
      "2367 0.9741 \t[0.97387]\n",
      "2369 0.98321 \t[0.98292]\n",
      "2376 0.96287 \t[0.96273]\n",
      "2378 0.96319 \t[0.96212]\n",
      "2383 0.98249 \t[0.98251]\n",
      "2385 0.98222 \t[0.98198]\n",
      "2392 0.96191 \t[0.96177]\n",
      "2394 0.96222 \t[0.96108]\n",
      "2399 0.98151 \t[0.98182]\n",
      "2401 0.99041 \t[0.99034]\n",
      "2408 0.9541 \t[0.95492]\n",
      "2410 0.97041 \t[0.97084]\n",
      "2415 0.9737 \t[0.9737]\n",
      "2417 0.99061 \t[0.99064, 0.99078, 0.99049, 0.99059, 0.99054]\n",
      "2418 0.9628 \t[0.96333]\n",
      "2419 0.97469 \t[0.97434]\n",
      "2420 0.96287 \t[0.96322]\n",
      "2421 0.98202 \t[0.98196]\n",
      "2422 0.97022 \t[0.97052]\n",
      "2423 0.9821 \t[0.98276]\n",
      "2424 0.9543 \t[0.95555]\n",
      "2425 0.98241 \t[0.98215]\n",
      "2426 0.97061 \t[0.97074]\n",
      "2427 0.98249 \t[0.98255]\n",
      "2428 0.95468 \t[0.95596]\n",
      "2429 0.98982 \t[0.98981]\n",
      "2430 0.96202 \t[0.96254]\n",
      "2431 0.9739 \t[0.97363]\n",
      "2432 0.9621 \t[0.96279]\n",
      "2433 0.98281 \t[0.98317]\n",
      "2440 0.96249 \t[0.96218]\n",
      "2442 0.9628 \t[0.96306]\n",
      "2447 0.9821 \t[0.98227]\n",
      "2449 0.98182 \t[0.98173, 0.98214, 0.98201, 0.98149, 0.98193]\n",
      "2450 0.97002 \t[0.97049]\n",
      "2451 0.9819 \t[0.98197]\n",
      "2452 0.9541 \t[0.95531]\n",
      "2453 0.98923 \t[0.98912]\n",
      "2454 0.96144 \t[0.9618]\n",
      "2455 0.97331 \t[0.97409]\n",
      "2456 0.96153 \t[0.9616]\n",
      "2457 0.98962 \t[0.98958]\n",
      "2458 0.96183 \t[0.96159]\n",
      "2459 0.9737 \t[0.97363]\n",
      "2460 0.96191 \t[0.96384]\n",
      "2461 0.98103 \t[0.98125]\n",
      "2462 0.96925 \t[0.96961]\n",
      "2463 0.98112 \t[0.98115]\n",
      "2464 0.95333 \t[0.95474]\n",
      "2465 0.99002 \t[0.99015]\n",
      "2472 0.95372 \t[0.95451]\n",
      "2474 0.97002 \t[0.9698]\n",
      "2479 0.97331 \t[0.97335]\n",
      "2481 0.99022 \t[0.98989]\n",
      "2488 0.95391 \t[0.95494]\n",
      "2490 0.97022 \t[0.97082]\n",
      "2495 0.97351 \t[0.97329]\n",
      "2497 0.98261 \t[0.98281]\n",
      "2504 0.9623 \t[0.9618]\n",
      "2506 0.96261 \t[0.96332]\n",
      "2511 0.9819 \t[0.98171]\n",
      "2513 0.98162 \t[0.98141]\n",
      "2520 0.96133 \t[0.96158]\n",
      "2522 0.96163 \t[0.96225]\n",
      "2527 0.98092 \t[0.98075]\n",
      "2529 0.98982 \t[0.98988, 0.98995, 0.98975, 0.9898, 0.98975]\n",
      "2530 0.96202 \t[0.96235]\n",
      "2531 0.9739 \t[0.97386]\n",
      "2532 0.9621 \t[0.9629]\n",
      "2533 0.98123 \t[0.98121]\n",
      "2534 0.96944 \t[0.96963]\n",
      "2535 0.98131 \t[0.98193]\n",
      "2536 0.95353 \t[0.95451]\n",
      "2537 0.98162 \t[0.98138]\n",
      "2538 0.96983 \t[0.96987]\n",
      "2539 0.9817 \t[0.98195]\n",
      "2540 0.95391 \t[0.95514]\n",
      "2541 0.98903 \t[0.98907]\n",
      "2542 0.96125 \t[0.96167]\n",
      "2543 0.97312 \t[0.97294]\n",
      "2544 0.96133 \t[0.96237]\n",
      "2545 0.99002 \t[0.99006]\n",
      "2552 0.95372 \t[0.95373]\n",
      "2554 0.97002 \t[0.97015]\n",
      "2559 0.97331 \t[0.97296]\n",
      "2561 0.95142 \t[0.95128]\n",
      "2568 0.932 \t[0.93179]\n",
      "2570 0.93205 \t[0.93218]\n",
      "2575 0.95099 \t[0.9505]\n",
      "2673 0.95866 \t[0.95806]\n",
      "2680 0.92326 \t[0.9237]\n",
      "2682 0.9393 \t[0.93844]\n",
      "2687 0.94223 \t[0.94256]\n",
      "2705 0.94989 \t[0.9496]\n",
      "2712 0.93051 \t[0.93019]\n",
      "2714 0.93054 \t[0.93041]\n",
      "2719 0.94947 \t[0.94886]\n",
      "2785 0.95789 \t[0.95747]\n",
      "2792 0.92251 \t[0.92287]\n",
      "2794 0.93854 \t[0.93755]\n",
      "2799 0.94147 \t[0.94172]\n",
      "2817 0.95143 \t[0.95153]\n",
      "2824 0.91623 \t[0.91568]\n",
      "2826 0.93221 \t[0.93108]\n",
      "2831 0.93506 \t[0.93468]\n",
      "2929 0.94267 \t[0.9423]\n",
      "2936 0.92349 \t[0.92419]\n",
      "2938 0.92347 \t[0.92289]\n",
      "2943 0.94231 \t[0.94234]\n",
      "2961 0.94991 \t[0.95035]\n",
      "2968 0.91476 \t[0.91538]\n",
      "2970 0.93072 \t[0.93034]\n",
      "2975 0.93355 \t[0.93381]\n",
      "3041 0.94191 \t[0.94125]\n",
      "3048 0.92276 \t[0.92271]\n",
      "3050 0.92272 \t[0.9217]\n",
      "3055 0.94155 \t[0.94166]\n",
      "3073 0.9992 \t[0.99922]\n",
      "3080 0.96264 \t[0.96244]\n",
      "3082 0.97902 \t[0.97929]\n",
      "3087 0.98241 \t[0.98264]\n",
      "3185 0.9904 \t[0.99059]\n",
      "3192 0.96986 \t[0.96985]\n",
      "3194 0.97024 \t[0.971]\n",
      "3199 0.98962 \t[0.98978]\n",
      "3217 0.9976 \t[0.99761]\n",
      "3224 0.96109 \t[0.96122]\n",
      "3226 0.97745 \t[0.97779]\n",
      "3231 0.98083 \t[0.98131]\n",
      "3297 0.9896 \t[0.98974]\n",
      "3304 0.96909 \t[0.96902]\n",
      "3306 0.96945 \t[0.96998]\n",
      "3311 0.98883 \t[0.98882]\n",
      "3329 0.98321 \t[0.98341]\n",
      "3336 0.96287 \t[0.96342]\n",
      "3338 0.96319 \t[0.96341]\n",
      "3343 0.98249 \t[0.98281]\n",
      "3441 0.99041 \t[0.99088]\n",
      "3448 0.9541 \t[0.9553]\n",
      "3450 0.97041 \t[0.97053]\n",
      "3455 0.9737 \t[0.97418]\n",
      "3473 0.98162 \t[0.98196]\n",
      "3480 0.96133 \t[0.96198]\n",
      "3482 0.96163 \t[0.96195]\n",
      "3487 0.98092 \t[0.98138]\n",
      "3553 0.98962 \t[0.98999]\n",
      "3560 0.95333 \t[0.95393]\n",
      "3562 0.96963 \t[0.96981]\n",
      "3567 0.97292 \t[0.97362]\n",
      "3585 0.95123 \t[0.95148, 0.95154, 0.95103, 0.95167, 0.95158, 0.95104, 0.95147, 0.95099, 0.95201]\n",
      "3586 0.94005 \t[0.94102]\n",
      "3587 0.95156 \t[0.95162]\n",
      "3588 0.92437 \t[0.92421]\n",
      "3589 0.95866 \t[0.95905]\n",
      "3590 0.93148 \t[0.93216]\n",
      "3591 0.94299 \t[0.94381]\n",
      "3592 0.93181 \t[0.93264, 0.93092, 0.9328, 0.93195, 0.93312]\n",
      "3593 0.95904 \t[0.95941]\n",
      "3594 0.93186 \t[0.93225, 0.9307, 0.93205, 0.93236, 0.9337]\n",
      "3595 0.94337 \t[0.94345]\n",
      "3596 0.93219 \t[0.9332]\n",
      "3597 0.95046 \t[0.95082]\n",
      "3598 0.9393 \t[0.93948]\n",
      "3599 0.9508 \t[0.95153, 0.9505, 0.95127, 0.95043, 0.95112]\n",
      "3600 0.92363 \t[0.92336]\n",
      "3601 0.95027 \t[0.9506]\n",
      "3608 0.93088 \t[0.93246]\n",
      "3610 0.93092 \t[0.93133]\n",
      "3615 0.94985 \t[0.95029]\n",
      "3617 0.95846 \t[0.95802]\n",
      "3624 0.92307 \t[0.9233]\n",
      "3626 0.93911 \t[0.93874]\n",
      "3631 0.94204 \t[0.94163]\n",
      "3633 0.95866 \t[0.95912]\n",
      "3640 0.92325 \t[0.92468]\n",
      "3642 0.9393 \t[0.94051]\n",
      "3647 0.94223 \t[0.94247]\n",
      "3649 0.95104 \t[0.95115]\n",
      "3656 0.93163 \t[0.93291]\n",
      "3658 0.93167 \t[0.93232]\n",
      "3663 0.95061 \t[0.95112]\n",
      "3665 0.95008 \t[0.95025]\n",
      "3672 0.9307 \t[0.93246]\n",
      "3674 0.93073 \t[0.93159]\n",
      "3679 0.94966 \t[0.95008]\n",
      "3681 0.95827 \t[0.95843]\n",
      "3688 0.92288 \t[0.92209]\n",
      "3690 0.93892 \t[0.93801]\n",
      "3695 0.94185 \t[0.9408]\n",
      "3697 0.95846 \t[0.95861, 0.95866, 0.95819, 0.95868, 0.95778]\n",
      "3698 0.9313 \t[0.93153]\n",
      "3699 0.9428 \t[0.94284]\n",
      "3700 0.93163 \t[0.93041]\n",
      "3701 0.94989 \t[0.94942]\n",
      "3702 0.93873 \t[0.93963]\n",
      "3703 0.95023 \t[0.95076]\n",
      "3704 0.92307 \t[0.92418]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3705 0.95027 \t[0.95084]\n",
      "3706 0.93911 \t[0.93923]\n",
      "3707 0.95061 \t[0.95025]\n",
      "3708 0.92344 \t[0.92447]\n",
      "3709 0.9577 \t[0.95712]\n",
      "3710 0.93054 \t[0.93136]\n",
      "3711 0.94204 \t[0.94259]\n",
      "3712 0.93088 \t[0.92969]\n",
      "3713 0.95066 \t[0.95036]\n",
      "3720 0.93125 \t[0.9314]\n",
      "3722 0.9313 \t[0.9316]\n",
      "3727 0.95023 \t[0.94969]\n",
      "3729 0.9497 \t[0.94999, 0.95036, 0.94905, 0.9499, 0.94947]\n",
      "3730 0.93854 \t[0.93912]\n",
      "3731 0.95004 \t[0.94955]\n",
      "3732 0.92288 \t[0.92197]\n",
      "3733 0.95712 \t[0.95731]\n",
      "3734 0.92998 \t[0.9303]\n",
      "3735 0.94147 \t[0.94225]\n",
      "3736 0.93032 \t[0.93107]\n",
      "3737 0.95751 \t[0.95747]\n",
      "3738 0.93036 \t[0.93043]\n",
      "3739 0.94185 \t[0.9417]\n",
      "3740 0.9307 \t[0.93185]\n",
      "3741 0.94893 \t[0.94881]\n",
      "3742 0.93779 \t[0.93844]\n",
      "3743 0.94928 \t[0.95003]\n",
      "3744 0.92214 \t[0.9213]\n",
      "3745 0.95789 \t[0.95722]\n",
      "3752 0.92251 \t[0.92265]\n",
      "3754 0.93854 \t[0.93761]\n",
      "3759 0.94147 \t[0.94083]\n",
      "3761 0.95808 \t[0.95825]\n",
      "3768 0.9227 \t[0.92199]\n",
      "3770 0.93873 \t[0.93805]\n",
      "3775 0.94166 \t[0.94085]\n",
      "3777 0.95046 \t[0.95106]\n",
      "3784 0.93107 \t[0.93288]\n",
      "3786 0.93111 \t[0.9328]\n",
      "3791 0.95004 \t[0.95002]\n",
      "3793 0.94951 \t[0.94881]\n",
      "3800 0.93014 \t[0.92922]\n",
      "3802 0.93017 \t[0.92872]\n",
      "3807 0.94909 \t[0.94873]\n",
      "3809 0.9577 \t[0.95791, 0.95816, 0.95778, 0.95781, 0.95766]\n",
      "3810 0.93054 \t[0.93104]\n",
      "3811 0.94204 \t[0.94193]\n",
      "3812 0.93088 \t[0.93056]\n",
      "3813 0.94912 \t[0.9493]\n",
      "3814 0.93798 \t[0.93955]\n",
      "3815 0.94947 \t[0.95]\n",
      "3816 0.92232 \t[0.92291]\n",
      "3817 0.94951 \t[0.94962]\n",
      "3818 0.93836 \t[0.93853]\n",
      "3819 0.94985 \t[0.94959]\n",
      "3820 0.9227 \t[0.92437]\n",
      "3821 0.95693 \t[0.95713]\n",
      "3822 0.92979 \t[0.93113]\n",
      "3823 0.94128 \t[0.9418]\n",
      "3824 0.93014 \t[0.92989]\n",
      "3825 0.95789 \t[0.95791]\n",
      "3832 0.92251 \t[0.92411]\n",
      "3834 0.93854 \t[0.93945]\n",
      "3839 0.94147 \t[0.94162]\n",
      "3841 0.95124 \t[0.95228]\n",
      "3848 0.91605 \t[0.91584]\n",
      "3850 0.93203 \t[0.93288]\n",
      "3855 0.93487 \t[0.9351]\n",
      "3953 0.94248 \t[0.94266]\n",
      "3960 0.92331 \t[0.92275]\n",
      "3962 0.92328 \t[0.92347]\n",
      "3967 0.94212 \t[0.94212]\n",
      "3985 0.94972 \t[0.95038]\n",
      "3992 0.91457 \t[0.91486]\n",
      "3994 0.93054 \t[0.93119]\n",
      "3999 0.93337 \t[0.93337]\n",
      "4065 0.94172 \t[0.94233]\n",
      "4072 0.92257 \t[0.92296]\n",
      "4074 0.92254 \t[0.92375]\n",
      "4079 0.94137 \t[0.94211]\n"
     ]
    }
   ],
   "source": [
    "# our oracle so far\n",
    "for i in 1:4096\n",
    "    if estimateOracle[i]!=[]\n",
    "        print(\"$(string(i,pad=3)) $(round.(actualOracle[i],digits=5)) \\t$(round.(estimateOracle[i],digits=5))\\n\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12-element Array{Any,1}:\n",
       " Any[1, 14, 12, 7, 225, 238, 236, 231, 113, 126  …  2540, 2535, 2417, 2430, 2428, 2423, 2449, 2462, 2460, 2455]\n",
       " Any[1, 2, 5, 6, 225, 226, 229, 230, 113, 114  …  2533, 2534, 2417, 2418, 2421, 2422, 2449, 2450, 2453, 2454]\n",
       " Any[1, 3, 9, 11, 225, 227, 233, 235, 113, 115  …  2537, 2539, 2417, 2419, 2425, 2427, 2449, 2451, 2457, 2459]\n",
       " Any[1, 4, 13, 16, 225, 228, 237, 240, 113, 116  …  2541, 2544, 2417, 2420, 2429, 2432, 2449, 2452, 2461, 2464]\n",
       " Any[1, 15, 8, 10, 209, 223, 216, 218, 177, 191  …  2520, 2522, 2481, 2495, 2488, 2490, 2401, 2415, 2408, 2410]\n",
       " Any[1, 15, 8, 10, 17, 31, 24, 26, 65, 79  …  2328, 2330, 2369, 2383, 2376, 2378, 2385, 2399, 2392, 2394]\n",
       " Any[1, 15, 8, 10, 33, 47, 40, 42, 129, 143  …  2344, 2346, 2433, 2447, 2440, 2442, 2465, 2479, 2472, 2474]\n",
       " Any[1, 15, 8, 10, 49, 63, 56, 58, 193, 207  …  2360, 2362, 2497, 2511, 2504, 2506, 2545, 2559, 2552, 2554]\n",
       " Any[1, 15, 8, 10, 225, 239, 232, 234, 113, 127  …  1768, 1770, 1649, 1663, 1656, 1658, 1681, 1695, 1688, 1690]\n",
       " Any[1, 15, 8, 10, 225, 239, 232, 234, 113, 127  …  1512, 1514, 1393, 1407, 1400, 1402, 1425, 1439, 1432, 1434]\n",
       " Any[1, 15, 8, 10, 225, 239, 232, 234, 113, 127  …  2792, 2794, 2673, 2687, 2680, 2682, 2705, 2719, 2712, 2714]\n",
       " Any[1, 15, 8, 10, 225, 239, 232, 234, 113, 127  …  4072, 4074, 3953, 3967, 3960, 3962, 3985, 3999, 3992, 3994]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1_fidelity_extracted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Okay that is all of exeriment 1 and its offsets done. \n",
    "\n",
    "That leaves experiment 2 (we need two subsampling groups for the peeling decoder)\n",
    "\n",
    "Recall experiment 2 looks like this:\n",
    "\n",
    "# Experiment 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Tuple{Int64,Int64},1}:\n",
       " (1, 3)\n",
       " (2, 2)\n",
       " (2, 1)\n",
       " (1, 3)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "experiments[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mLengths: 100%|██████████████████████████████████████████| Time: 0:01:17\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "# So q1, has single qubit mub, q2&3 4&5 have a double mub experiment type 2 and q6 has a single mub, so lets set that up:\n",
    "\n",
    "initialGates = generateGates(experiments[2],[circuit1q,circuit2q])\n",
    "reverseGates = transpose(initialGates) \n",
    "# So at this point we have set up one of the 'new' experiments.\n",
    "\n",
    "experiment2 = []\n",
    "# Get the actual probabilities.\n",
    "@showprogress 1 \"Lengths: \" for m in lengths\n",
    "    wholeCircuit = reverseGates*noise^m*initialGates*rm*start./64 # Normalising our zs\n",
    "    probs = [z'*wholeCircuit for z in zs]\n",
    "    push!(experiment2,probs)\n",
    "end\n",
    "            \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64-element Array{Float64,1}:\n",
       " 1.0\n",
       " 0.9718492848668059\n",
       " 0.9992044876373045\n",
       " 0.9713105048705868\n",
       " 0.9981981062996419\n",
       " 0.9701024595100746\n",
       " 0.9985907483606172\n",
       " 0.9705630223407407\n",
       " 0.9517775779441707\n",
       " 0.9245733330744327\n",
       " 0.9512562769031969\n",
       " 0.9242646661745776\n",
       " 0.950147357210411\n",
       " ⋮\n",
       " 0.9488548623792893\n",
       " 0.9213777820094172\n",
       " 0.9497054630585438\n",
       " 0.9218973870298669\n",
       " 0.9822344066885326\n",
       " 0.9548523762940008\n",
       " 0.981512539397869\n",
       " 0.9541915237156421\n",
       " 0.9803364849752244\n",
       " 0.9533235904595504\n",
       " 0.980831313001577\n",
       " 0.953703278609339"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate shot limited stats\n",
    "\n",
    "cumMatrix = map(cumsum,experiment2)\n",
    "experiment2_observed = shotSimulator(64,shotsToDo,cumMatrix);\n",
    "# Fit and extract the fidelities\n",
    "(params,l, failed) = fitTheFidelities(lengths,experiment2_observed)\n",
    "experiment2_fidelities = vcat(1,[p[2] for p in params])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9999999999999999 : [1]\n",
      "0.972 : [2, 4]\n",
      "0.9992001200000001 : [57, 1153, 2113]\n",
      "0.9712225166 : [60, 1156, 2116]\n",
      "0.9982008000000001 : [29, 209, 3089]\n",
      "0.9702511776000001 : [32, 212, 3092]\n",
      "0.9986004800000002 : [37, 141, 2061, 2241, 3201]\n",
      "0.9706396666000001 : [40, 144, 2064, 2244, 3204]\n",
      "0.9518095999999999 : [833, 1793]\n",
      "0.9251589311999998 : [836, 1796]\n",
      "0.9510482665 : [889, 1849]\n",
      "0.9244189151 : [892, 1852]\n",
      "0.9500971041999999 : [861, 1821, 2001, 3921]\n",
      "0.9234943852999999 : [864, 1824, 2004, 3924]\n",
      "0.9504775233999999 : [869, 937, 1017, 1829, 1933, 2857, 2893, 3897]\n",
      "0.9238641527999998 : [872, 940, 1020, 1832, 1936, 2860, 2896, 3900]\n",
      "0.951232 : [525, 705, 3585]\n",
      "0.9243735040000001 : [528, 708, 3588]\n",
      "0.9504647295000003 : [613, 681, 761, 1573, 1677, 2601, 2637, 3641]\n",
      "0.9236277171000001 : [616, 684, 764, 1576, 1680, 2604, 2640, 3644]\n",
      "0.9495061498000001 : [733, 3613, 3793]\n",
      "0.9226959776000001 : [736, 3616, 3796]\n",
      "0.9498895356000002 : [741, 2765, 3621, 3725]\n",
      "0.9230686286 : [744, 2768, 3624, 3728]\n",
      "0.9834048 : [131, 385, 2051, 2305]\n",
      "0.9556454655999999 : [388, 2308]\n",
      "0.9826117951 : [119, 187, 373, 441, 1079, 1131, 1333, 1385, 2107, 2361]\n",
      "0.9548746649000001 : [376, 444, 1336, 1388, 2364]\n",
      "0.9816210645000001 : [159, 413, 2079, 2259, 2333, 2513, 3219, 3473]\n",
      "0.9539116747 : [416, 2336, 2516, 3476]\n",
      "0.9820173092000001 : [167, 247, 421, 501, 1259, 1513, 2087, 2191, 2341, 2445, 3127, 3179, 3381, 3433]\n",
      "0.9542968245 : [424, 504, 1516, 2344, 2448, 3384, 3436]\n",
      "0.9992 : [13, 193, 3073]\n",
      "0.9712224 : [16, 196, 3076]\n",
      "0.9984007599000001 : [101, 169, 249, 1061, 1165, 2089, 2125, 3129]\n",
      "0.9704455386 : [104, 172, 252, 1064, 1168, 2092, 2128, 3132]\n",
      "0.9974022394000001 : [221, 3101, 3281]\n",
      "0.9694749767 : [224, 3104, 3284]\n",
      "0.9978015996000001 : [229, 2253, 3109, 3213]\n",
      "0.9698631547999998 : [232, 2256, 3112, 3216]\n",
      "0.9510481523000002 : [809, 845, 1805, 1985, 3905]\n",
      "0.9244188041 : [812, 848, 1808, 1988, 3908]\n",
      "0.9502874279000002 : [949, 1893, 1961, 2041, 2869, 2921, 3961]\n",
      "0.9236793799000003 : [952, 1896, 1964, 2044, 2872, 2924, 3964]\n",
      "0.9493370265000001 : [2013, 3933]\n",
      "0.9227555897000002 : [2016, 3936]\n",
      "0.9497171414 : [2021, 3049, 3941, 4009, 4089]\n",
      "0.9231250615 : [2024, 3052, 3944, 4012, 4092]\n",
      "0.9504646143999999 : [717, 3597, 3777]\n",
      "0.9236276051999999 : [720, 3600, 3780]\n",
      "0.9496979577000001 : [1765, 2793, 3685, 3753, 3833]\n",
      "0.9228824149 : [1768, 2796, 3688, 3756, 3836]\n",
      "0.9487401449000001 : [3805]\n",
      "0.9219514208000001 : [3808]\n",
      "0.9491232240000002 : [3813]\n",
      "0.9223237736999998 : [3816]\n",
      "0.9826116762000001 : [39, 143, 293, 397, 2063, 2243, 2317, 2497, 3203, 3457]\n",
      "0.9548745492000003 : [296, 400, 2320, 2500, 3460]\n",
      "0.9818193057000002 : [1191, 1271, 1445, 1525, 2151, 2219, 2299, 2405, 2473, 2553, 3191, 3259, 3445, 3513]\n",
      "0.9541043651000002 : [1448, 1528, 2408, 2476, 2556, 3448, 3516]\n",
      "0.9808293676000002 : [2271, 2525, 3231, 3485]\n",
      "0.9531421453000002 : [2528, 3488]\n",
      "0.9812252953000004 : [2279, 2533, 3239, 3319, 3493, 3573]\n",
      "0.9535269870000002 : [2536, 3496, 3576]\n"
     ]
    }
   ],
   "source": [
    "xx = ifwht_natural([z'*reverseGates*noise*initialGates*start for z in zs]/64)\n",
    "for p in xx\n",
    "    print(\"$p : $(findall(x->isapprox(x,p),actualOracle))\\n\")\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64-element Array{String,1}:\n",
       " \"IIIIII\"\n",
       " \"IIIIIZ\"\n",
       " \"IIIZYI\"\n",
       " \"IIIZYZ\"\n",
       " \"IIIXZI\"\n",
       " \"IIIXZZ\"\n",
       " \"IIIYXI\"\n",
       " \"IIIYXZ\"\n",
       " \"IZXIII\"\n",
       " \"IZXIIZ\"\n",
       " \"IZXZYI\"\n",
       " \"IZXZYZ\"\n",
       " \"IZXXZI\"\n",
       " ⋮\n",
       " \"ZYZXZI\"\n",
       " \"ZYZXZZ\"\n",
       " \"ZYZYXI\"\n",
       " \"ZYZYXZ\"\n",
       " \"ZXYIII\"\n",
       " \"ZXYIIZ\"\n",
       " \"ZXYZYI\"\n",
       " \"ZXYZYZ\"\n",
       " \"ZXYXZI\"\n",
       " \"ZXYXZZ\"\n",
       " \"ZXYYXI\"\n",
       " \"ZXYYXZ\""
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fidelitiesExtracted = []\n",
    "for x1b in potentialSingles[experiments[2][4][2]] # Experiment 2, qubit division 3 (q1, q2&3, q4) the second part = exp number\n",
    "    p6 = binaryArrayToNumber(x1b)\n",
    "    for x2b in all2QlMuBs[experiments[2][3][2]]\n",
    "        p45 = binaryArrayToNumber(x2b)\n",
    "        for x2a in all2QlMuBs[experiments[2][2][2]]\n",
    "            p23 = binaryArrayToNumber(x2a)\n",
    "            for x1a in potentialSingles[experiments[2][1][2]]\n",
    "                p1 = binaryArrayToNumber(x1a)\n",
    "                push!(fidelitiesExtracted,p6*4^5+p45*4^3+p23*4^1+p1+1) # + 1 cause we index of 1 in Julia\n",
    "             end\n",
    "        end\n",
    "    end\n",
    "end\n",
    "map(x->fidelityLabels(x-1,qubits=6),fidelitiesExtracted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IIIIII (0):\tEstimate: 1.0 <-> 1.0 \tPercentage Error: 0.0%\n",
      "IIIIIZ (3):\tEstimate: 0.9718492848668059 <-> 0.972 \tPercentage Error: 0.0155%\n",
      "IIIZYI (56):\tEstimate: 0.9992044876373045 <-> 0.99920012 \tPercentage Error: 0.0004%\n",
      "IIIZYZ (59):\tEstimate: 0.9713105048705868 <-> 0.9712225166 \tPercentage Error: 0.0091%\n",
      "IIIXZI (28):\tEstimate: 0.9981981062996419 <-> 0.9982008 \tPercentage Error: 0.0003%\n",
      "IIIXZZ (31):\tEstimate: 0.9701024595100746 <-> 0.9702511776 \tPercentage Error: 0.0153%\n",
      "IIIYXI (36):\tEstimate: 0.9985907483606172 <-> 0.99860048 \tPercentage Error: 0.001%\n",
      "IIIYXZ (39):\tEstimate: 0.9705630223407407 <-> 0.9706396666 \tPercentage Error: 0.0079%\n",
      "IZXIII (832):\tEstimate: 0.9517775779441707 <-> 0.9518096 \tPercentage Error: 0.0034%\n",
      "IZXIIZ (835):\tEstimate: 0.9245733330744327 <-> 0.9251589312 \tPercentage Error: 0.0633%\n",
      "IZXZYI (888):\tEstimate: 0.9512562769031969 <-> 0.9510482665 \tPercentage Error: 0.0219%\n",
      "IZXZYZ (891):\tEstimate: 0.9242646661745776 <-> 0.9244189151 \tPercentage Error: 0.0167%\n",
      "IZXXZI (860):\tEstimate: 0.950147357210411 <-> 0.9500971042 \tPercentage Error: 0.0053%\n",
      "IZXXZZ (863):\tEstimate: 0.9228510771672417 <-> 0.9234943853 \tPercentage Error: 0.0697%\n",
      "IZXYXI (868):\tEstimate: 0.9509550062603832 <-> 0.9504775234 \tPercentage Error: 0.0502%\n",
      "IZXYXZ (871):\tEstimate: 0.9234245081258412 <-> 0.9238641528 \tPercentage Error: 0.0476%\n",
      "IYZIII (704):\tEstimate: 0.9509693776758223 <-> 0.951232 \tPercentage Error: 0.0276%\n",
      "IYZIIZ (707):\tEstimate: 0.9237571617539286 <-> 0.924373504 \tPercentage Error: 0.0667%\n",
      "IYZZYI (760):\tEstimate: 0.9506968275641192 <-> 0.9504647295 \tPercentage Error: 0.0244%\n",
      "IYZZYZ (763):\tEstimate: 0.9235819112253988 <-> 0.9236277171 \tPercentage Error: 0.005%\n",
      "IYZXZI (732):\tEstimate: 0.9496102218055714 <-> 0.9495061498 \tPercentage Error: 0.011%\n",
      "IYZXZZ (735):\tEstimate: 0.9221314737014048 <-> 0.9226959776 \tPercentage Error: 0.0612%\n",
      "IYZYXI (740):\tEstimate: 0.9504016799520018 <-> 0.9498895356 \tPercentage Error: 0.0539%\n",
      "IYZYXZ (743):\tEstimate: 0.9226123873106471 <-> 0.9230686286 \tPercentage Error: 0.0494%\n",
      "IXYIII (384):\tEstimate: 0.9831294394007184 <-> 0.9834048 \tPercentage Error: 0.028%\n",
      "IXYIIZ (387):\tEstimate: 0.9557896292882174 <-> 0.9556454656 \tPercentage Error: 0.0151%\n",
      "IXYZYI (440):\tEstimate: 0.9824020341673697 <-> 0.9826117951 \tPercentage Error: 0.0213%\n",
      "IXYZYZ (443):\tEstimate: 0.9551261143540881 <-> 0.9548746649 \tPercentage Error: 0.0263%\n",
      "IXYXZI (412):\tEstimate: 0.9812769722228375 <-> 0.9816210645 \tPercentage Error: 0.0351%\n",
      "IXYXZZ (415):\tEstimate: 0.9542270964263432 <-> 0.9539116747 \tPercentage Error: 0.0331%\n",
      "IXYYXI (420):\tEstimate: 0.9817477059842559 <-> 0.9820173092 \tPercentage Error: 0.0275%\n",
      "IXYYXZ (423):\tEstimate: 0.9545996003068581 <-> 0.9542968245 \tPercentage Error: 0.0317%\n",
      "ZIIIII (3072):\tEstimate: 0.9991867343374298 <-> 0.9992 \tPercentage Error: 0.0013%\n",
      "ZIIIIZ (3075):\tEstimate: 0.9710457018641796 <-> 0.9712224 \tPercentage Error: 0.0182%\n",
      "ZIIZYI (3128):\tEstimate: 0.998388910567334 <-> 0.9984007599 \tPercentage Error: 0.0012%\n",
      "ZIIZYZ (3131):\tEstimate: 0.9705023495825441 <-> 0.9704455386 \tPercentage Error: 0.0059%\n",
      "ZIIXZI (3100):\tEstimate: 0.9973797355262007 <-> 0.9974022394 \tPercentage Error: 0.0023%\n",
      "ZIIXZZ (3103):\tEstimate: 0.9693171746739611 <-> 0.9694749767 \tPercentage Error: 0.0163%\n",
      "ZIIYXI (3108):\tEstimate: 0.9977773222629968 <-> 0.9978015996 \tPercentage Error: 0.0024%\n",
      "ZIIYXZ (3111):\tEstimate: 0.9697209834263271 <-> 0.9698631548 \tPercentage Error: 0.0147%\n",
      "ZZXIII (3904):\tEstimate: 0.9508638020616145 <-> 0.9510481523 \tPercentage Error: 0.0194%\n",
      "ZZXIIZ (3907):\tEstimate: 0.9235900658142702 <-> 0.9244188041 \tPercentage Error: 0.0896%\n",
      "ZZXZYI (3960):\tEstimate: 0.9503518534725851 <-> 0.9502874279 \tPercentage Error: 0.0068%\n",
      "ZZXZYZ (3963):\tEstimate: 0.9233633889010356 <-> 0.9236793799 \tPercentage Error: 0.0342%\n",
      "ZZXXZI (3932):\tEstimate: 0.9493011695175068 <-> 0.9493370265 \tPercentage Error: 0.0038%\n",
      "ZZXXZZ (3935):\tEstimate: 0.9219140492893186 <-> 0.9227555897 \tPercentage Error: 0.0912%\n",
      "ZZXYXI (3940):\tEstimate: 0.9501258125442994 <-> 0.9497171414 \tPercentage Error: 0.043%\n",
      "ZZXYXZ (3943):\tEstimate: 0.9224895346040815 <-> 0.9231250615 \tPercentage Error: 0.0688%\n",
      "ZYZIII (3776):\tEstimate: 0.950188874313939 <-> 0.9504646144 \tPercentage Error: 0.029%\n",
      "ZYZIIZ (3779):\tEstimate: 0.9229840720963681 <-> 0.9236276052 \tPercentage Error: 0.0697%\n",
      "ZYZZYI (3832):\tEstimate: 0.9499311032332632 <-> 0.9496979577 \tPercentage Error: 0.0245%\n",
      "ZYZZYZ (3835):\tEstimate: 0.9228624353752058 <-> 0.9228824149 \tPercentage Error: 0.0022%\n",
      "ZYZXZI (3804):\tEstimate: 0.9488548623792893 <-> 0.9487401449 \tPercentage Error: 0.0121%\n",
      "ZYZXZZ (3807):\tEstimate: 0.9213777820094172 <-> 0.9219514208 \tPercentage Error: 0.0622%\n",
      "ZYZYXI (3812):\tEstimate: 0.9497054630585438 <-> 0.949123224 \tPercentage Error: 0.0613%\n",
      "ZYZYXZ (3815):\tEstimate: 0.9218973870298669 <-> 0.9223237737 \tPercentage Error: 0.0462%\n",
      "ZXYIII (3456):\tEstimate: 0.9822344066885326 <-> 0.9826116762 \tPercentage Error: 0.0384%\n",
      "ZXYIIZ (3459):\tEstimate: 0.9548523762940008 <-> 0.9548745492 \tPercentage Error: 0.0023%\n",
      "ZXYZYI (3512):\tEstimate: 0.981512539397869 <-> 0.9818193057 \tPercentage Error: 0.0312%\n",
      "ZXYZYZ (3515):\tEstimate: 0.9541915237156421 <-> 0.9541043651 \tPercentage Error: 0.0091%\n",
      "ZXYXZI (3484):\tEstimate: 0.9803364849752244 <-> 0.9808293676 \tPercentage Error: 0.0503%\n",
      "ZXYXZZ (3487):\tEstimate: 0.9533235904595504 <-> 0.9531421453 \tPercentage Error: 0.019%\n",
      "ZXYYXI (3492):\tEstimate: 0.980831313001577 <-> 0.9812252953 \tPercentage Error: 0.0402%\n",
      "ZXYYXZ (3495):\tEstimate: 0.953703278609339 <-> 0.953526987 \tPercentage Error: 0.0185%\n"
     ]
    }
   ],
   "source": [
    "# And (just out of interest we can compare the fidelities we extracted, with the actual values)\n",
    "for i in 1:64\n",
    "    print(\"$(fidelityLabels(fidelitiesExtracted[i]-1,qubits=6)) \",\n",
    "        \"($(fidelitiesExtracted[i]-1)):\\tEstimate: $(experiment2_fidelities[i]) \",\n",
    "        \"<-> $(actualOracle[fidelitiesExtracted[i]]) \\t\",\n",
    "        \"Percentage Error: $(round.(abs(actualOracle[fidelitiesExtracted[i]]-experiment2_fidelities[i])/(actualOracle[fidelitiesExtracted[i]])*100,digits=4))%\\n\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save you the sanity check and I will put these directly into the oracle\n",
    "\n",
    "for (fidelityIndex,fidelity)  in enumerate(fidelitiesExtracted)\n",
    "    push!(estimateOracle[fidelity],experiment2_fidelities[fidelityIndex])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "001 1.0 \t[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
      "002 0.972 \t[0.97245]\n",
      "003 0.984 \t[0.98379]\n",
      "004 0.972 \t[0.97222, 0.97185]\n",
      "005 0.9914 \t[0.99144]\n",
      "006 0.97941 \t[0.97957]\n",
      "007 0.9914 \t[0.99154]\n",
      "008 0.96342 \t[0.96466, 0.96398, 0.96294, 0.96325, 0.9632, 0.96397, 0.96343, 0.96334, 0.96326]\n",
      "009 0.9918 \t[0.99173]\n",
      "010 0.9798 \t[0.98004, 0.98015, 0.97996, 0.97959, 0.97987, 0.9798, 0.97983, 0.97964, 0.98009]\n",
      "011 0.9918 \t[0.99173]\n",
      "012 0.96381 \t[0.96422]\n",
      "013 0.9992 \t[0.99924]\n",
      "014 0.97122 \t[0.97099]\n",
      "015 0.98321 \t[0.98326, 0.98301, 0.98303, 0.98328, 0.98312, 0.98329, 0.98322, 0.98338, 0.98344]\n",
      "016 0.97122 \t[0.97164]\n",
      "017 0.999 \t[0.99905]\n",
      "024 0.96245 \t[0.9621]\n",
      "026 0.97882 \t[0.97902]\n",
      "029 0.9982 \t[0.9982]\n",
      "031 0.98222 \t[0.98198]\n",
      "032 0.97025 \t[0.9701]\n",
      "033 0.9912 \t[0.99122]\n",
      "037 0.9986 \t[0.99859]\n",
      "040 0.97064 \t[0.96982, 0.97056]\n",
      "042 0.97102 \t[0.97078]\n",
      "047 0.99041 \t[0.99034]\n",
      "049 0.9914 \t[0.99143]\n",
      "056 0.97083 \t[0.97072]\n",
      "057 0.9992 \t[0.9992]\n",
      "058 0.97122 \t[0.97188]\n",
      "060 0.97122 \t[0.97131]\n",
      "063 0.99061 \t[0.99061]\n",
      "065 0.9998 \t[0.99983]\n",
      "072 0.96322 \t[0.96257]\n",
      "074 0.97961 \t[0.97967]\n",
      "079 0.98301 \t[0.98293]\n",
      "081 0.9988 \t[0.99889]\n",
      "088 0.96225 \t[0.96175]\n",
      "090 0.97863 \t[0.97867]\n",
      "095 0.98202 \t[0.9819]\n",
      "097 0.991 \t[0.99091]\n",
      "104 0.97045 \t[0.97043]\n",
      "106 0.97082 \t[0.97099]\n",
      "111 0.99022 \t[0.99018]\n",
      "113 0.9912 \t[0.9911, 0.99132, 0.99138, 0.99103, 0.99118, 0.99143, 0.99122, 0.99126, 0.99144]\n",
      "114 0.97922 \t[0.97945]\n",
      "115 0.99121 \t[0.99099]\n",
      "116 0.96322 \t[0.96393]\n",
      "117 0.9986 \t[0.99861]\n",
      "118 0.97063 \t[0.97115]\n",
      "119 0.98261 \t[0.98272]\n",
      "120 0.97064 \t[0.97126, 0.9713, 0.97094, 0.97077, 0.97058]\n",
      "121 0.999 \t[0.99898]\n",
      "122 0.97102 \t[0.97163, 0.97103, 0.97088, 0.97107, 0.97178]\n",
      "123 0.98301 \t[0.98273]\n",
      "124 0.97103 \t[0.97133]\n",
      "125 0.9904 \t[0.99044]\n",
      "126 0.97843 \t[0.97817]\n",
      "127 0.99041 \t[0.99052, 0.99049, 0.99049, 0.9904, 0.99054]\n",
      "128 0.96245 \t[0.96317]\n",
      "129 0.9994 \t[0.99942]\n",
      "136 0.96283 \t[0.96246]\n",
      "138 0.97922 \t[0.9786]\n",
      "143 0.98261 \t[0.98276]\n",
      "145 0.9984 \t[0.99839, 0.99843, 0.99843, 0.99828, 0.99835, 0.99856, 0.99835, 0.9983, 0.99838]\n",
      "146 0.97043 \t[0.97101]\n",
      "147 0.98241 \t[0.98191]\n",
      "148 0.97045 \t[0.97054]\n",
      "149 0.9898 \t[0.98999]\n",
      "150 0.97785 \t[0.9781]\n",
      "151 0.98982 \t[0.98993]\n",
      "152 0.96186 \t[0.96303, 0.96228, 0.96186, 0.9618, 0.96182]\n",
      "153 0.9902 \t[0.99001]\n",
      "154 0.97824 \t[0.97831, 0.97833, 0.97787, 0.97816, 0.9784]\n",
      "155 0.99022 \t[0.98994]\n",
      "156 0.96225 \t[0.96273]\n",
      "157 0.9976 \t[0.99757]\n",
      "158 0.96965 \t[0.96954]\n",
      "159 0.98162 \t[0.98164, 0.98198, 0.98148, 0.98163, 0.98207]\n",
      "160 0.96967 \t[0.97002]\n",
      "161 0.9906 \t[0.99076]\n",
      "168 0.97006 \t[0.96884]\n",
      "170 0.97043 \t[0.96998]\n",
      "175 0.98982 \t[0.98971]\n",
      "177 0.9908 \t[0.99058]\n",
      "184 0.97025 \t[0.97032]\n",
      "186 0.97063 \t[0.97082]\n",
      "191 0.99002 \t[0.98983]\n",
      "193 0.9992 \t[0.99919]\n",
      "200 0.96264 \t[0.96275]\n",
      "202 0.97902 \t[0.97906]\n",
      "207 0.98241 \t[0.98238]\n",
      "209 0.9982 \t[0.99823]\n",
      "216 0.96167 \t[0.96222]\n",
      "218 0.97804 \t[0.9784]\n",
      "223 0.98142 \t[0.98127]\n",
      "225 0.9904 \t[0.99038, 0.99055, 0.99058, 0.99016, 0.99042, 0.99059, 0.99034, 0.99046, 0.99057]\n",
      "226 0.97843 \t[0.97859]\n",
      "227 0.99041 \t[0.99021]\n",
      "228 0.96245 \t[0.96336]\n",
      "229 0.9978 \t[0.99777]\n",
      "230 0.96985 \t[0.97035]\n",
      "231 0.98182 \t[0.98204]\n",
      "232 0.96986 \t[0.97036, 0.97029, 0.96985, 0.97001, 0.96985]\n",
      "233 0.9982 \t[0.99811]\n",
      "234 0.97024 \t[0.9708, 0.97016, 0.97003, 0.96999, 0.97078]\n",
      "235 0.98222 \t[0.9818]\n",
      "236 0.97025 \t[0.97049]\n",
      "237 0.9896 \t[0.98967]\n",
      "238 0.97765 \t[0.97746]\n",
      "239 0.98962 \t[0.98974, 0.98969, 0.9898, 0.98967, 0.98959]\n",
      "240 0.96167 \t[0.96259]\n",
      "241 0.9906 \t[0.99058]\n",
      "248 0.97006 \t[0.97013]\n",
      "250 0.97043 \t[0.97112]\n",
      "255 0.98982 \t[0.98974]\n",
      "257 0.984 \t[0.98416]\n",
      "264 0.96365 \t[0.96451]\n",
      "266 0.96397 \t[0.96369]\n",
      "271 0.98328 \t[0.98343]\n",
      "369 0.99121 \t[0.99107]\n",
      "376 0.95487 \t[0.95525]\n",
      "378 0.97119 \t[0.97133]\n",
      "383 0.97449 \t[0.97444]\n",
      "385 0.9834 \t[0.98313]\n",
      "388 0.95565 \t[0.95579]\n",
      "401 0.98241 \t[0.98228]\n",
      "408 0.9621 \t[0.96265]\n",
      "410 0.96241 \t[0.96167]\n",
      "413 0.98162 \t[0.98128]\n",
      "415 0.9817 \t[0.98183]\n",
      "416 0.95391 \t[0.95423]\n",
      "421 0.98202 \t[0.98175]\n",
      "424 0.9543 \t[0.9546]\n",
      "441 0.98261 \t[0.9824]\n",
      "444 0.95487 \t[0.95513]\n",
      "481 0.99041 \t[0.9903]\n",
      "488 0.9541 \t[0.95443]\n",
      "490 0.97041 \t[0.97051]\n",
      "495 0.9737 \t[0.97375]\n",
      "513 0.952 \t[0.95181]\n",
      "520 0.93256 \t[0.93235]\n",
      "522 0.93261 \t[0.93229]\n",
      "527 0.95156 \t[0.95112]\n",
      "625 0.95923 \t[0.95877]\n",
      "632 0.92381 \t[0.92436]\n",
      "634 0.93986 \t[0.93907]\n",
      "639 0.9428 \t[0.94314]\n",
      "657 0.95046 \t[0.95032]\n",
      "664 0.93107 \t[0.93085]\n",
      "666 0.93111 \t[0.93106]\n",
      "671 0.95004 \t[0.94956]\n",
      "705 0.95123 \t[0.95097]\n",
      "708 0.92437 \t[0.92376]\n",
      "733 0.94951 \t[0.94961]\n",
      "736 0.9227 \t[0.92213]\n",
      "737 0.95846 \t[0.95808]\n",
      "741 0.94989 \t[0.9504]\n",
      "744 0.92307 \t[0.92348, 0.92261]\n",
      "746 0.93911 \t[0.93804]\n",
      "751 0.94204 \t[0.94229]\n",
      "761 0.95046 \t[0.9507]\n",
      "764 0.92363 \t[0.92358]\n",
      "769 0.952 \t[0.95314]\n",
      "776 0.91679 \t[0.91672]\n",
      "778 0.93277 \t[0.9337]\n",
      "783 0.93563 \t[0.93591]\n",
      "833 0.95181 \t[0.95178]\n",
      "836 0.92516 \t[0.92457]\n",
      "861 0.9501 \t[0.95015]\n",
      "864 0.92349 \t[0.92285]\n",
      "869 0.95048 \t[0.95096]\n",
      "872 0.92386 \t[0.92342]\n",
      "881 0.94324 \t[0.94355]\n",
      "888 0.92405 \t[0.9236]\n",
      "889 0.95105 \t[0.95126]\n",
      "890 0.92403 \t[0.92427]\n",
      "892 0.92442 \t[0.92426]\n",
      "895 0.94287 \t[0.94297]\n",
      "913 0.95048 \t[0.95116]\n",
      "920 0.91531 \t[0.91568]\n",
      "922 0.93128 \t[0.9319]\n",
      "927 0.93412 \t[0.93411]\n",
      "993 0.94248 \t[0.94322]\n",
      "1000 0.92331 \t[0.92388]\n",
      "1002 0.92328 \t[0.92456]\n",
      "1007 0.94212 \t[0.943]\n",
      "1025 0.9998 \t[0.99981]\n",
      "1032 0.96322 \t[0.96318]\n",
      "1034 0.97961 \t[0.97964]\n",
      "1039 0.98301 \t[0.98303]\n",
      "1137 0.991 \t[0.99103]\n",
      "1144 0.97045 \t[0.97076]\n",
      "1146 0.97082 \t[0.97067]\n",
      "1151 0.99022 \t[0.99032]\n",
      "1169 0.9982 \t[0.99815]\n",
      "1176 0.96167 \t[0.96161]\n",
      "1178 0.97804 \t[0.97769]\n",
      "1183 0.98142 \t[0.98127]\n",
      "1249 0.9902 \t[0.99013]\n",
      "1256 0.96967 \t[0.96964]\n",
      "1258 0.97004 \t[0.96975]\n",
      "1263 0.98942 \t[0.98961]\n",
      "1281 0.9838 \t[0.98392]\n",
      "1288 0.96345 \t[0.96429]\n",
      "1290 0.96377 \t[0.96347]\n",
      "1295 0.98308 \t[0.98325]\n",
      "1393 0.99101 \t[0.99088]\n",
      "1400 0.95468 \t[0.95503]\n",
      "1402 0.97099 \t[0.97113]\n",
      "1407 0.97429 \t[0.97416]\n",
      "1425 0.98222 \t[0.98206]\n",
      "1432 0.96191 \t[0.96242]\n",
      "1434 0.96222 \t[0.96148]\n",
      "1439 0.98151 \t[0.98164]\n",
      "1505 0.99022 \t[0.99009]\n",
      "1512 0.95391 \t[0.95415]\n",
      "1514 0.97022 \t[0.97026]\n",
      "1519 0.97351 \t[0.97342]\n",
      "1537 0.95181 \t[0.95153]\n",
      "1544 0.93237 \t[0.93249]\n",
      "1546 0.93242 \t[0.93138]\n",
      "1551 0.95137 \t[0.9516]\n",
      "1649 0.95904 \t[0.95917]\n",
      "1656 0.92363 \t[0.92448]\n",
      "1658 0.93967 \t[0.93918]\n",
      "1663 0.94261 \t[0.94289]\n",
      "1681 0.95027 \t[0.94976]\n",
      "1688 0.93088 \t[0.93198]\n",
      "1690 0.93092 \t[0.93027]\n",
      "1695 0.94985 \t[0.9503]\n",
      "1761 0.95827 \t[0.95832]\n",
      "1768 0.92288 \t[0.92245]\n",
      "1770 0.93892 \t[0.93812]\n",
      "1775 0.94185 \t[0.94178]\n",
      "1793 0.95181 \t[0.95238, 0.95156, 0.95179, 0.95135, 0.95203, 0.9521, 0.9519, 0.95136, 0.95258]\n",
      "1794 0.92477 \t[0.92446]\n",
      "1795 0.9362 \t[0.93528]\n",
      "1796 0.92516 \t[0.92545]\n",
      "1797 0.94324 \t[0.94294]\n",
      "1798 0.93221 \t[0.93232]\n",
      "1799 0.94363 \t[0.94354]\n",
      "1800 0.9166 \t[0.91648, 0.91646, 0.91656, 0.91784, 0.9183]\n",
      "1801 0.94362 \t[0.94319]\n",
      "1802 0.93259 \t[0.93246, 0.93224, 0.93296, 0.93349, 0.93417]\n",
      "1803 0.94401 \t[0.94303]\n",
      "1804 0.91697 \t[0.91792]\n",
      "1805 0.95105 \t[0.95141]\n",
      "1806 0.92403 \t[0.92447]\n",
      "1807 0.93544 \t[0.9354, 0.93484, 0.93514, 0.93512, 0.93569]\n",
      "1808 0.92442 \t[0.9247]\n",
      "1809 0.95086 \t[0.951]\n",
      "1816 0.91568 \t[0.91548]\n",
      "1818 0.93165 \t[0.93214]\n",
      "1823 0.9345 \t[0.93388]\n",
      "1825 0.94305 \t[0.94298]\n",
      "1832 0.92386 \t[0.92431]\n",
      "1834 0.92384 \t[0.92486]\n",
      "1839 0.94269 \t[0.94205]\n",
      "1841 0.94324 \t[0.94415]\n",
      "1848 0.92405 \t[0.92538]\n",
      "1850 0.92403 \t[0.92629]\n",
      "1855 0.94287 \t[0.94276]\n",
      "1857 0.95162 \t[0.9515]\n",
      "1864 0.91642 \t[0.91693]\n",
      "1866 0.9324 \t[0.93311]\n",
      "1871 0.93525 \t[0.93491]\n",
      "1873 0.95067 \t[0.95053]\n",
      "1880 0.91549 \t[0.91576]\n",
      "1882 0.93147 \t[0.93215]\n",
      "1887 0.93431 \t[0.9336]\n",
      "1889 0.94286 \t[0.94235]\n",
      "1896 0.92368 \t[0.92356]\n",
      "1898 0.92365 \t[0.92281]\n",
      "1903 0.9425 \t[0.94212]\n",
      "1905 0.94305 \t[0.94339, 0.94273, 0.9423, 0.9423, 0.94314]\n",
      "1906 0.93203 \t[0.93152]\n",
      "1907 0.94344 \t[0.94238]\n",
      "1908 0.91642 \t[0.91613]\n",
      "1909 0.95048 \t[0.95032]\n",
      "1910 0.92347 \t[0.92295]\n",
      "1911 0.93487 \t[0.93504]\n",
      "1912 0.92386 \t[0.92416]\n",
      "1913 0.95086 \t[0.95001]\n",
      "1914 0.92384 \t[0.92337]\n",
      "1915 0.93525 \t[0.93367]\n",
      "1916 0.92423 \t[0.92525]\n",
      "1917 0.94229 \t[0.9425]\n",
      "1918 0.93128 \t[0.93184]\n",
      "1919 0.94269 \t[0.94333]\n",
      "1920 0.91568 \t[0.91546]\n",
      "1921 0.95124 \t[0.95061]\n",
      "1928 0.91605 \t[0.91689]\n",
      "1930 0.93203 \t[0.93251]\n",
      "1935 0.93487 \t[0.93434]\n",
      "1937 0.95029 \t[0.9507, 0.95027, 0.94995, 0.94922, 0.94962]\n",
      "1938 0.92328 \t[0.92244]\n",
      "1939 0.93468 \t[0.93311]\n",
      "1940 0.92368 \t[0.92291]\n",
      "1941 0.94172 \t[0.94114]\n",
      "1942 0.93072 \t[0.93039]\n",
      "1943 0.94212 \t[0.94191]\n",
      "1944 0.91513 \t[0.9153]\n",
      "1945 0.9421 \t[0.94118]\n",
      "1946 0.9311 \t[0.9307]\n",
      "1947 0.9425 \t[0.94089]\n",
      "1948 0.91549 \t[0.91673]\n",
      "1949 0.94953 \t[0.94918]\n",
      "1950 0.92254 \t[0.92334]\n",
      "1951 0.93393 \t[0.93375]\n",
      "1952 0.92294 \t[0.92233]\n",
      "1953 0.94248 \t[0.94202]\n",
      "1960 0.92331 \t[0.92313]\n",
      "1962 0.92328 \t[0.92369]\n",
      "1967 0.94212 \t[0.94103]\n",
      "1969 0.94267 \t[0.94262]\n",
      "1976 0.92349 \t[0.92362]\n",
      "1978 0.92347 \t[0.92327]\n",
      "1983 0.94231 \t[0.94203]\n",
      "1985 0.95105 \t[0.95136]\n",
      "1992 0.91586 \t[0.9177]\n",
      "1994 0.93184 \t[0.93347]\n",
      "1999 0.93469 \t[0.93516]\n",
      "2001 0.9501 \t[0.95018]\n",
      "2008 0.91494 \t[0.91412]\n",
      "2010 0.93091 \t[0.93001]\n",
      "2015 0.93374 \t[0.93245]\n",
      "2017 0.94229 \t[0.94288, 0.94269, 0.94172, 0.94149, 0.94266]\n",
      "2018 0.93128 \t[0.93103]\n",
      "2019 0.94269 \t[0.94167]\n",
      "2020 0.91568 \t[0.91585]\n",
      "2021 0.94972 \t[0.94985]\n",
      "2022 0.92272 \t[0.92263]\n",
      "2023 0.93412 \t[0.93443]\n",
      "2024 0.92313 \t[0.92311]\n",
      "2025 0.9501 \t[0.94919]\n",
      "2026 0.9231 \t[0.92261]\n",
      "2027 0.9345 \t[0.93292]\n",
      "2028 0.92349 \t[0.92483]\n",
      "2029 0.94153 \t[0.942]\n",
      "2030 0.93054 \t[0.93122]\n",
      "2031 0.94193 \t[0.94241]\n",
      "2032 0.91494 \t[0.91519]\n",
      "2033 0.94248 \t[0.94316]\n",
      "2040 0.92331 \t[0.92479]\n",
      "2042 0.92328 \t[0.92505]\n",
      "2047 0.94212 \t[0.94181]\n",
      "2049 0.9994 \t[0.99943]\n",
      "2056 0.96283 \t[0.96281]\n",
      "2058 0.97922 \t[0.97906]\n",
      "2063 0.98261 \t[0.98284]\n",
      "2161 0.9906 \t[0.99071]\n",
      "2168 0.97006 \t[0.97017]\n",
      "2170 0.97043 \t[0.97057]\n",
      "2175 0.98982 \t[0.98989]\n",
      "2193 0.9978 \t[0.99772]\n",
      "2200 0.96128 \t[0.96122]\n",
      "2202 0.97765 \t[0.97763]\n",
      "2207 0.98103 \t[0.98104]\n",
      "2273 0.9898 \t[0.98994]\n",
      "2280 0.96928 \t[0.96948]\n",
      "2282 0.96965 \t[0.96948]\n",
      "2287 0.98903 \t[0.98914]\n",
      "2305 0.9834 \t[0.98339, 0.98366, 0.98343, 0.98324, 0.98356, 0.98321, 0.98309, 0.98378, 0.98364]\n",
      "2306 0.97158 \t[0.9719]\n",
      "2307 0.98347 \t[0.98351]\n",
      "2308 0.95565 \t[0.95684]\n",
      "2309 0.99081 \t[0.9906]\n",
      "2310 0.96299 \t[0.96299]\n",
      "2311 0.97488 \t[0.97548]\n",
      "2312 0.96307 \t[0.96325, 0.96355, 0.9629, 0.96307, 0.96264]\n",
      "2313 0.99121 \t[0.99128]\n",
      "2314 0.96338 \t[0.96376, 0.96409, 0.96233, 0.9639, 0.96396]\n",
      "2315 0.97528 \t[0.97523]\n",
      "2316 0.96345 \t[0.96479]\n",
      "2317 0.98261 \t[0.98285]\n",
      "2318 0.9708 \t[0.97093]\n",
      "2319 0.98269 \t[0.9828, 0.98256, 0.98264, 0.98297, 0.98268]\n",
      "2320 0.95487 \t[0.95619]\n",
      "2321 0.98241 \t[0.98209]\n",
      "2328 0.9621 \t[0.96197]\n",
      "2330 0.96241 \t[0.96132]\n",
      "2335 0.9817 \t[0.98188]\n",
      "2337 0.99061 \t[0.99079]\n",
      "2344 0.9543 \t[0.9554]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2346 0.97061 \t[0.97088]\n",
      "2351 0.9739 \t[0.9742]\n",
      "2353 0.99081 \t[0.9909]\n",
      "2360 0.95449 \t[0.95424]\n",
      "2362 0.9708 \t[0.97116]\n",
      "2367 0.9741 \t[0.97387]\n",
      "2369 0.98321 \t[0.98292]\n",
      "2376 0.96287 \t[0.96273]\n",
      "2378 0.96319 \t[0.96212]\n",
      "2383 0.98249 \t[0.98251]\n",
      "2385 0.98222 \t[0.98198]\n",
      "2392 0.96191 \t[0.96177]\n",
      "2394 0.96222 \t[0.96108]\n",
      "2399 0.98151 \t[0.98182]\n",
      "2401 0.99041 \t[0.99034]\n",
      "2408 0.9541 \t[0.95492]\n",
      "2410 0.97041 \t[0.97084]\n",
      "2415 0.9737 \t[0.9737]\n",
      "2417 0.99061 \t[0.99064, 0.99078, 0.99049, 0.99059, 0.99054]\n",
      "2418 0.9628 \t[0.96333]\n",
      "2419 0.97469 \t[0.97434]\n",
      "2420 0.96287 \t[0.96322]\n",
      "2421 0.98202 \t[0.98196]\n",
      "2422 0.97022 \t[0.97052]\n",
      "2423 0.9821 \t[0.98276]\n",
      "2424 0.9543 \t[0.95555]\n",
      "2425 0.98241 \t[0.98215]\n",
      "2426 0.97061 \t[0.97074]\n",
      "2427 0.98249 \t[0.98255]\n",
      "2428 0.95468 \t[0.95596]\n",
      "2429 0.98982 \t[0.98981]\n",
      "2430 0.96202 \t[0.96254]\n",
      "2431 0.9739 \t[0.97363]\n",
      "2432 0.9621 \t[0.96279]\n",
      "2433 0.98281 \t[0.98317]\n",
      "2440 0.96249 \t[0.96218]\n",
      "2442 0.9628 \t[0.96306]\n",
      "2447 0.9821 \t[0.98227]\n",
      "2449 0.98182 \t[0.98173, 0.98214, 0.98201, 0.98149, 0.98193]\n",
      "2450 0.97002 \t[0.97049]\n",
      "2451 0.9819 \t[0.98197]\n",
      "2452 0.9541 \t[0.95531]\n",
      "2453 0.98923 \t[0.98912]\n",
      "2454 0.96144 \t[0.9618]\n",
      "2455 0.97331 \t[0.97409]\n",
      "2456 0.96153 \t[0.9616]\n",
      "2457 0.98962 \t[0.98958]\n",
      "2458 0.96183 \t[0.96159]\n",
      "2459 0.9737 \t[0.97363]\n",
      "2460 0.96191 \t[0.96384]\n",
      "2461 0.98103 \t[0.98125]\n",
      "2462 0.96925 \t[0.96961]\n",
      "2463 0.98112 \t[0.98115]\n",
      "2464 0.95333 \t[0.95474]\n",
      "2465 0.99002 \t[0.99015]\n",
      "2472 0.95372 \t[0.95451]\n",
      "2474 0.97002 \t[0.9698]\n",
      "2479 0.97331 \t[0.97335]\n",
      "2481 0.99022 \t[0.98989]\n",
      "2488 0.95391 \t[0.95494]\n",
      "2490 0.97022 \t[0.97082]\n",
      "2495 0.97351 \t[0.97329]\n",
      "2497 0.98261 \t[0.98281]\n",
      "2504 0.9623 \t[0.9618]\n",
      "2506 0.96261 \t[0.96332]\n",
      "2511 0.9819 \t[0.98171]\n",
      "2513 0.98162 \t[0.98141]\n",
      "2520 0.96133 \t[0.96158]\n",
      "2522 0.96163 \t[0.96225]\n",
      "2527 0.98092 \t[0.98075]\n",
      "2529 0.98982 \t[0.98988, 0.98995, 0.98975, 0.9898, 0.98975]\n",
      "2530 0.96202 \t[0.96235]\n",
      "2531 0.9739 \t[0.97386]\n",
      "2532 0.9621 \t[0.9629]\n",
      "2533 0.98123 \t[0.98121]\n",
      "2534 0.96944 \t[0.96963]\n",
      "2535 0.98131 \t[0.98193]\n",
      "2536 0.95353 \t[0.95451]\n",
      "2537 0.98162 \t[0.98138]\n",
      "2538 0.96983 \t[0.96987]\n",
      "2539 0.9817 \t[0.98195]\n",
      "2540 0.95391 \t[0.95514]\n",
      "2541 0.98903 \t[0.98907]\n",
      "2542 0.96125 \t[0.96167]\n",
      "2543 0.97312 \t[0.97294]\n",
      "2544 0.96133 \t[0.96237]\n",
      "2545 0.99002 \t[0.99006]\n",
      "2552 0.95372 \t[0.95373]\n",
      "2554 0.97002 \t[0.97015]\n",
      "2559 0.97331 \t[0.97296]\n",
      "2561 0.95142 \t[0.95128]\n",
      "2568 0.932 \t[0.93179]\n",
      "2570 0.93205 \t[0.93218]\n",
      "2575 0.95099 \t[0.9505]\n",
      "2673 0.95866 \t[0.95806]\n",
      "2680 0.92326 \t[0.9237]\n",
      "2682 0.9393 \t[0.93844]\n",
      "2687 0.94223 \t[0.94256]\n",
      "2705 0.94989 \t[0.9496]\n",
      "2712 0.93051 \t[0.93019]\n",
      "2714 0.93054 \t[0.93041]\n",
      "2719 0.94947 \t[0.94886]\n",
      "2785 0.95789 \t[0.95747]\n",
      "2792 0.92251 \t[0.92287]\n",
      "2794 0.93854 \t[0.93755]\n",
      "2799 0.94147 \t[0.94172]\n",
      "2817 0.95143 \t[0.95153]\n",
      "2824 0.91623 \t[0.91568]\n",
      "2826 0.93221 \t[0.93108]\n",
      "2831 0.93506 \t[0.93468]\n",
      "2929 0.94267 \t[0.9423]\n",
      "2936 0.92349 \t[0.92419]\n",
      "2938 0.92347 \t[0.92289]\n",
      "2943 0.94231 \t[0.94234]\n",
      "2961 0.94991 \t[0.95035]\n",
      "2968 0.91476 \t[0.91538]\n",
      "2970 0.93072 \t[0.93034]\n",
      "2975 0.93355 \t[0.93381]\n",
      "3041 0.94191 \t[0.94125]\n",
      "3048 0.92276 \t[0.92271]\n",
      "3050 0.92272 \t[0.9217]\n",
      "3055 0.94155 \t[0.94166]\n",
      "3073 0.9992 \t[0.99922, 0.99919]\n",
      "3076 0.97122 \t[0.97105]\n",
      "3080 0.96264 \t[0.96244]\n",
      "3082 0.97902 \t[0.97929]\n",
      "3087 0.98241 \t[0.98264]\n",
      "3101 0.9974 \t[0.99738]\n",
      "3104 0.96947 \t[0.96932]\n",
      "3109 0.9978 \t[0.99778]\n",
      "3112 0.96986 \t[0.96972]\n",
      "3129 0.9984 \t[0.99839]\n",
      "3132 0.97045 \t[0.9705]\n",
      "3185 0.9904 \t[0.99059]\n",
      "3192 0.96986 \t[0.96985]\n",
      "3194 0.97024 \t[0.971]\n",
      "3199 0.98962 \t[0.98978]\n",
      "3217 0.9976 \t[0.99761]\n",
      "3224 0.96109 \t[0.96122]\n",
      "3226 0.97745 \t[0.97779]\n",
      "3231 0.98083 \t[0.98131]\n",
      "3297 0.9896 \t[0.98974]\n",
      "3304 0.96909 \t[0.96902]\n",
      "3306 0.96945 \t[0.96998]\n",
      "3311 0.98883 \t[0.98882]\n",
      "3329 0.98321 \t[0.98341]\n",
      "3336 0.96287 \t[0.96342]\n",
      "3338 0.96319 \t[0.96341]\n",
      "3343 0.98249 \t[0.98281]\n",
      "3441 0.99041 \t[0.99088]\n",
      "3448 0.9541 \t[0.9553]\n",
      "3450 0.97041 \t[0.97053]\n",
      "3455 0.9737 \t[0.97418]\n",
      "3457 0.98261 \t[0.98223]\n",
      "3460 0.95487 \t[0.95485]\n",
      "3473 0.98162 \t[0.98196]\n",
      "3480 0.96133 \t[0.96198]\n",
      "3482 0.96163 \t[0.96195]\n",
      "3485 0.98083 \t[0.98034]\n",
      "3487 0.98092 \t[0.98138]\n",
      "3488 0.95314 \t[0.95332]\n",
      "3493 0.98123 \t[0.98083]\n",
      "3496 0.95353 \t[0.9537]\n",
      "3513 0.98182 \t[0.98151]\n",
      "3516 0.9541 \t[0.95419]\n",
      "3553 0.98962 \t[0.98999]\n",
      "3560 0.95333 \t[0.95393]\n",
      "3562 0.96963 \t[0.96981]\n",
      "3567 0.97292 \t[0.97362]\n",
      "3585 0.95123 \t[0.95148, 0.95154, 0.95103, 0.95167, 0.95158, 0.95104, 0.95147, 0.95099, 0.95201]\n",
      "3586 0.94005 \t[0.94102]\n",
      "3587 0.95156 \t[0.95162]\n",
      "3588 0.92437 \t[0.92421]\n",
      "3589 0.95866 \t[0.95905]\n",
      "3590 0.93148 \t[0.93216]\n",
      "3591 0.94299 \t[0.94381]\n",
      "3592 0.93181 \t[0.93264, 0.93092, 0.9328, 0.93195, 0.93312]\n",
      "3593 0.95904 \t[0.95941]\n",
      "3594 0.93186 \t[0.93225, 0.9307, 0.93205, 0.93236, 0.9337]\n",
      "3595 0.94337 \t[0.94345]\n",
      "3596 0.93219 \t[0.9332]\n",
      "3597 0.95046 \t[0.95082]\n",
      "3598 0.9393 \t[0.93948]\n",
      "3599 0.9508 \t[0.95153, 0.9505, 0.95127, 0.95043, 0.95112]\n",
      "3600 0.92363 \t[0.92336]\n",
      "3601 0.95027 \t[0.9506]\n",
      "3608 0.93088 \t[0.93246]\n",
      "3610 0.93092 \t[0.93133]\n",
      "3615 0.94985 \t[0.95029]\n",
      "3617 0.95846 \t[0.95802]\n",
      "3624 0.92307 \t[0.9233]\n",
      "3626 0.93911 \t[0.93874]\n",
      "3631 0.94204 \t[0.94163]\n",
      "3633 0.95866 \t[0.95912]\n",
      "3640 0.92325 \t[0.92468]\n",
      "3642 0.9393 \t[0.94051]\n",
      "3647 0.94223 \t[0.94247]\n",
      "3649 0.95104 \t[0.95115]\n",
      "3656 0.93163 \t[0.93291]\n",
      "3658 0.93167 \t[0.93232]\n",
      "3663 0.95061 \t[0.95112]\n",
      "3665 0.95008 \t[0.95025]\n",
      "3672 0.9307 \t[0.93246]\n",
      "3674 0.93073 \t[0.93159]\n",
      "3679 0.94966 \t[0.95008]\n",
      "3681 0.95827 \t[0.95843]\n",
      "3688 0.92288 \t[0.92209]\n",
      "3690 0.93892 \t[0.93801]\n",
      "3695 0.94185 \t[0.9408]\n",
      "3697 0.95846 \t[0.95861, 0.95866, 0.95819, 0.95868, 0.95778]\n",
      "3698 0.9313 \t[0.93153]\n",
      "3699 0.9428 \t[0.94284]\n",
      "3700 0.93163 \t[0.93041]\n",
      "3701 0.94989 \t[0.94942]\n",
      "3702 0.93873 \t[0.93963]\n",
      "3703 0.95023 \t[0.95076]\n",
      "3704 0.92307 \t[0.92418]\n",
      "3705 0.95027 \t[0.95084]\n",
      "3706 0.93911 \t[0.93923]\n",
      "3707 0.95061 \t[0.95025]\n",
      "3708 0.92344 \t[0.92447]\n",
      "3709 0.9577 \t[0.95712]\n",
      "3710 0.93054 \t[0.93136]\n",
      "3711 0.94204 \t[0.94259]\n",
      "3712 0.93088 \t[0.92969]\n",
      "3713 0.95066 \t[0.95036]\n",
      "3720 0.93125 \t[0.9314]\n",
      "3722 0.9313 \t[0.9316]\n",
      "3727 0.95023 \t[0.94969]\n",
      "3729 0.9497 \t[0.94999, 0.95036, 0.94905, 0.9499, 0.94947]\n",
      "3730 0.93854 \t[0.93912]\n",
      "3731 0.95004 \t[0.94955]\n",
      "3732 0.92288 \t[0.92197]\n",
      "3733 0.95712 \t[0.95731]\n",
      "3734 0.92998 \t[0.9303]\n",
      "3735 0.94147 \t[0.94225]\n",
      "3736 0.93032 \t[0.93107]\n",
      "3737 0.95751 \t[0.95747]\n",
      "3738 0.93036 \t[0.93043]\n",
      "3739 0.94185 \t[0.9417]\n",
      "3740 0.9307 \t[0.93185]\n",
      "3741 0.94893 \t[0.94881]\n",
      "3742 0.93779 \t[0.93844]\n",
      "3743 0.94928 \t[0.95003]\n",
      "3744 0.92214 \t[0.9213]\n",
      "3745 0.95789 \t[0.95722]\n",
      "3752 0.92251 \t[0.92265]\n",
      "3754 0.93854 \t[0.93761]\n",
      "3759 0.94147 \t[0.94083]\n",
      "3761 0.95808 \t[0.95825]\n",
      "3768 0.9227 \t[0.92199]\n",
      "3770 0.93873 \t[0.93805]\n",
      "3775 0.94166 \t[0.94085]\n",
      "3777 0.95046 \t[0.95106, 0.95019]\n",
      "3780 0.92363 \t[0.92298]\n",
      "3784 0.93107 \t[0.93288]\n",
      "3786 0.93111 \t[0.9328]\n",
      "3791 0.95004 \t[0.95002]\n",
      "3793 0.94951 \t[0.94881]\n",
      "3800 0.93014 \t[0.92922]\n",
      "3802 0.93017 \t[0.92872]\n",
      "3805 0.94874 \t[0.94885]\n",
      "3807 0.94909 \t[0.94873]\n",
      "3808 0.92195 \t[0.92138]\n",
      "3809 0.9577 \t[0.95791, 0.95816, 0.95778, 0.95781, 0.95766]\n",
      "3810 0.93054 \t[0.93104]\n",
      "3811 0.94204 \t[0.94193]\n",
      "3812 0.93088 \t[0.93056]\n",
      "3813 0.94912 \t[0.9493, 0.94971]\n",
      "3814 0.93798 \t[0.93955]\n",
      "3815 0.94947 \t[0.95]\n",
      "3816 0.92232 \t[0.92291, 0.9219]\n",
      "3817 0.94951 \t[0.94962]\n",
      "3818 0.93836 \t[0.93853]\n",
      "3819 0.94985 \t[0.94959]\n",
      "3820 0.9227 \t[0.92437]\n",
      "3821 0.95693 \t[0.95713]\n",
      "3822 0.92979 \t[0.93113]\n",
      "3823 0.94128 \t[0.9418]\n",
      "3824 0.93014 \t[0.92989]\n",
      "3825 0.95789 \t[0.95791]\n",
      "3832 0.92251 \t[0.92411]\n",
      "3833 0.9497 \t[0.94993]\n",
      "3834 0.93854 \t[0.93945]\n",
      "3836 0.92288 \t[0.92286]\n",
      "3839 0.94147 \t[0.94162]\n",
      "3841 0.95124 \t[0.95228]\n",
      "3848 0.91605 \t[0.91584]\n",
      "3850 0.93203 \t[0.93288]\n",
      "3855 0.93487 \t[0.9351]\n",
      "3905 0.95105 \t[0.95086]\n",
      "3908 0.92442 \t[0.92359]\n",
      "3933 0.94934 \t[0.9493]\n",
      "3936 0.92276 \t[0.92191]\n",
      "3941 0.94972 \t[0.95013]\n",
      "3944 0.92313 \t[0.92249]\n",
      "3953 0.94248 \t[0.94266]\n",
      "3960 0.92331 \t[0.92275]\n",
      "3961 0.95029 \t[0.95035]\n",
      "3962 0.92328 \t[0.92347]\n",
      "3964 0.92368 \t[0.92336]\n",
      "3967 0.94212 \t[0.94212]\n",
      "3985 0.94972 \t[0.95038]\n",
      "3992 0.91457 \t[0.91486]\n",
      "3994 0.93054 \t[0.93119]\n",
      "3999 0.93337 \t[0.93337]\n",
      "4065 0.94172 \t[0.94233]\n",
      "4072 0.92257 \t[0.92296]\n",
      "4074 0.92254 \t[0.92375]\n",
      "4079 0.94137 \t[0.94211]\n"
     ]
    }
   ],
   "source": [
    "# our oracle so far\n",
    "for i in 1:4096\n",
    "    if estimateOracle[i]!=[]\n",
    "        print(\"$(string(i,pad=3)) $(round.(actualOracle[i],digits=5)) \\t$(round.(estimateOracle[i],digits=5))\\n\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### And super finally we just need to create the offsets to get their fidelities.\n",
    "\n",
    "For the single qubit Mubs, we need the other 2 mubs, for the two qubit Mubs the other four.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32mQGroup 1 Exp: 1: 100%|██████████████████████████████████| Time: 0:01:16\u001b[39m\n",
      "\u001b[32mQGroup 1 Exp: 2: 100%|██████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup 2 Exp: 1: 100%|██████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup 2 Exp: 3: 100%|██████████████████████████████████| Time: 0:01:16\u001b[39m\n",
      "\u001b[32mQGroup 2 Exp: 4: 100%|██████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup 2 Exp: 5: 100%|██████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup 3 Exp: 2: 100%|██████████████████████████████████| Time: 0:01:18\u001b[39m\n",
      "\u001b[32mQGroup 3 Exp: 3: 100%|██████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup 3 Exp: 4: 100%|██████████████████████████████████| Time: 0:01:16\u001b[39m\n",
      "\u001b[32mQGroup 3 Exp: 5: 100%|██████████████████████████████████| Time: 0:01:16\u001b[39m\n",
      "\u001b[32mQGroup 4 Exp: 1: 100%|██████████████████████████████████| Time: 0:01:17\u001b[39m\n",
      "\u001b[32mQGroup 4 Exp: 2: 100%|██████████████████████████████████| Time: 0:01:16\u001b[39m\n",
      "\u001b[32mQubits: 100%|███████████████████████████████████████████| Time: 0:15:26\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "\n",
    "e2_all_additional_fidelities = []\n",
    "e2_fidelity_extracted = []\n",
    "# Note here I am hard coding that we have single qubit twirls on 1 and 4.\n",
    "e_count = 0\n",
    "e2_all_actualProbabilities = []\n",
    "@showprogress 1 \"Qubits: \" for qubitOn in 1:4 # qubits we can be \"On\" here are 1, 2&3 4&5 and 6\n",
    "    \n",
    "    if qubitOn == 2 || qubitOn == 3\n",
    "        noOfExperiments = 5\n",
    "    else \n",
    "        noOfExperiments = 3 # Only 3 if its a single qubit.\n",
    "    end\n",
    "    for experimentType = 1:noOfExperiments\n",
    "        if experiments[2][qubitOn][2] != experimentType\n",
    "            # Its one we haven't done\n",
    "            expOnFirstSet = experiments[2][1][2]\n",
    "            expOnSecondSet = experiments[2][2][2]\n",
    "            expOnThirdSet = experiments[2][3][2]\n",
    "            expOnFourthSet = experiments[2][4][2]\n",
    "\n",
    "\n",
    "            if qubitOn == 1\n",
    "                expOnFirstSet = experimentType\n",
    "            elseif qubitOn == 2\n",
    "                expOnSecondSet = experimentType\n",
    "            elseif qubitOn ==3 \n",
    "                expOnThirdSet = experimentType\n",
    "            else \n",
    "                expOnFourthSet = experimentType\n",
    "            end\n",
    "                \n",
    "            initialGates = circuit1q[expOnFourthSet]⊗circuit2q[expOnThirdSet]⊗circuit2q[expOnSecondSet]⊗circuit1q[expOnFirstSet]\n",
    "\n",
    "            reverseGates = transpose(initialGates) # yay superoperators.\n",
    "            # So at this point we have set up one of the 'new' experiments.\n",
    "            additionalExperiment = []\n",
    "            # Get the actual probabilities.\n",
    "            @showprogress 1 \"QGroup $qubitOn Exp: $experimentType: \" for m in lengths\n",
    "                wholeCircuit = reverseGates*noise^m*initialGates*rm*start./64 # Normalising our zs\n",
    "                probs = [z'*wholeCircuit for z in zs]\n",
    "                push!(additionalExperiment,probs)\n",
    "            end\n",
    "            push!(e2_all_actualProbabilities,additionalExperiment)\n",
    "            \n",
    "            # Generate the measurement statistics\n",
    "            cumMatrix = map(cumsum,additionalExperiment)\n",
    "            experiment2_additional_observed =  shotSimulator(64,shotsToDo,cumMatrix);\n",
    "            # Fit and extract the fidelities\n",
    "            (params,l, failed) = fitTheFidelities(lengths,experiment2_additional_observed)\n",
    "            experiment2_additional_fidelities = vcat(1,[p[2] for p in params])\n",
    "            push!(e2_all_additional_fidelities,experiment2_additional_fidelities)\n",
    "            fidelitiesExtracted=[]\n",
    "            for x1 in potentialSingles[expOnFourthSet] # Experiment 2, qubit division 3 (q1, q2&3, q4&5 q6) the second part = exp number\n",
    "                p6 = binaryArrayToNumber(x1)\n",
    "                for x2b in all2QlMuBs[expOnThirdSet]\n",
    "                    p45 = binaryArrayToNumber(x2b)\n",
    "                    for x2 in all2QlMuBs[expOnSecondSet]\n",
    "                        p23 = binaryArrayToNumber(x2)\n",
    "                        for x3 in potentialSingles[expOnFirstSet]\n",
    "                            p1 = binaryArrayToNumber(x3)\n",
    "                            push!(fidelitiesExtracted,p6*4^5+p45*4^3+p23*4+p1+1) # + 1 cause we index of 1 in Julia\n",
    "                        end\n",
    "                     end\n",
    "                end\n",
    "            end\n",
    "            push!(e2_fidelity_extracted,fidelitiesExtracted)\n",
    "        end\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64-element Array{Float64,1}:\n",
       " 1.0\n",
       " 0.9717523697451188\n",
       " 0.9991676369755909\n",
       " 0.9709244723454289\n",
       " 0.9981766764813327\n",
       " 0.9699284238623218\n",
       " 0.9986231009644055\n",
       " 0.9702564827175163\n",
       " 0.9512418846043682\n",
       " 0.9236218399391224\n",
       " 0.9508934528804082\n",
       " 0.9232719057295831\n",
       " 0.9495534658317248\n",
       " ⋮\n",
       " 0.9487124039115584\n",
       " 0.9369045824609961\n",
       " 0.9492380011931869\n",
       " 0.9374605064621049\n",
       " 0.982588164588106\n",
       " 0.9704544251064045\n",
       " 0.98176033631428\n",
       " 0.9697576995707274\n",
       " 0.9807633296559303\n",
       " 0.968580298226486\n",
       " 0.9812418357678202\n",
       " 0.9690889216859961"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2_all_additional_fidelities[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IIIIII (1): \tEstimate: 1.0 <-> 1.0 \tPercentage Error: 0.0%\n",
      "IIIIIZ (4): \tEstimate: 0.97211 <-> 0.972 \tPercentage Error: 0.011%\n",
      "IIIZYI (57): \tEstimate: 0.99915 <-> 0.9992 \tPercentage Error: 0.0049%\n",
      "IIIZYZ (60): \tEstimate: 0.97114 <-> 0.97122 \tPercentage Error: 0.0086%\n",
      "IIIXZI (29): \tEstimate: 0.99812 <-> 0.9982 \tPercentage Error: 0.0085%\n",
      "IIIXZZ (32): \tEstimate: 0.97031 <-> 0.97025 \tPercentage Error: 0.0062%\n",
      "IIIYXI (37): \tEstimate: 0.99859 <-> 0.9986 \tPercentage Error: 0.0007%\n",
      "IIIYXZ (40): \tEstimate: 0.97072 <-> 0.97064 \tPercentage Error: 0.0081%\n",
      "IIXIII (65): \tEstimate: 0.99976 <-> 0.9998 \tPercentage Error: 0.0043%\n",
      "IIXIIZ (68): \tEstimate: 0.97172 <-> 0.97181 \tPercentage Error: 0.0092%\n",
      "IIXZYI (121): \tEstimate: 0.99891 <-> 0.999 \tPercentage Error: 0.0095%\n",
      "IIXZYZ (124): \tEstimate: 0.97079 <-> 0.97103 \tPercentage Error: 0.0241%\n",
      "IIXXZI (93): \tEstimate: 0.99786 <-> 0.998 \tPercentage Error: 0.0137%\n",
      "IIXXZZ (96): \tEstimate: 0.97 <-> 0.97006 \tPercentage Error: 0.0062%\n",
      "IIXYXI (101): \tEstimate: 0.99833 <-> 0.9984 \tPercentage Error: 0.0072%\n",
      "IIXYXZ (104): \tEstimate: 0.97046 <-> 0.97045 \tPercentage Error: 0.0015%\n",
      "IXIIII (257): \tEstimate: 0.98445 <-> 0.984 \tPercentage Error: 0.0457%\n",
      "IXIIIZ (260): \tEstimate: 0.95649 <-> 0.95622 \tPercentage Error: 0.0282%\n",
      "IXIZYI (313): \tEstimate: 0.98355 <-> 0.98321 \tPercentage Error: 0.0348%\n",
      "IXIZYZ (316): \tEstimate: 0.95548 <-> 0.95545 \tPercentage Error: 0.0031%\n",
      "IXIXZI (285): \tEstimate: 0.98261 <-> 0.98222 \tPercentage Error: 0.0401%\n",
      "IXIXZZ (288): \tEstimate: 0.95473 <-> 0.95449 \tPercentage Error: 0.0248%\n",
      "IXIYXI (293): \tEstimate: 0.98299 <-> 0.98261 \tPercentage Error: 0.0384%\n",
      "IXIYXZ (296): \tEstimate: 0.95473 <-> 0.95487 \tPercentage Error: 0.0149%\n",
      "IXXIII (321): \tEstimate: 0.98407 <-> 0.9838 \tPercentage Error: 0.0271%\n",
      "IXXIIZ (324): \tEstimate: 0.95597 <-> 0.95603 \tPercentage Error: 0.0063%\n",
      "IXXZYI (377): \tEstimate: 0.98315 <-> 0.98301 \tPercentage Error: 0.0145%\n",
      "IXXZYZ (380): \tEstimate: 0.95497 <-> 0.95526 \tPercentage Error: 0.0301%\n",
      "IXXXZI (349): \tEstimate: 0.98218 <-> 0.98202 \tPercentage Error: 0.0166%\n",
      "IXXXZZ (352): \tEstimate: 0.95408 <-> 0.9543 \tPercentage Error: 0.0222%\n",
      "IXXYXI (357): \tEstimate: 0.98256 <-> 0.98241 \tPercentage Error: 0.0145%\n",
      "IXXYXZ (360): \tEstimate: 0.9542 <-> 0.95468 \tPercentage Error: 0.0509%\n",
      "ZIIIII (3073): \tEstimate: 0.99926 <-> 0.9992 \tPercentage Error: 0.0056%\n",
      "ZIIIIZ (3076): \tEstimate: 0.97128 <-> 0.97122 \tPercentage Error: 0.0063%\n",
      "ZIIZYI (3129): \tEstimate: 0.9984 <-> 0.9984 \tPercentage Error: 0.0001%\n",
      "ZIIZYZ (3132): \tEstimate: 0.97035 <-> 0.97045 \tPercentage Error: 0.0094%\n",
      "ZIIXZI (3101): \tEstimate: 0.99738 <-> 0.9974 \tPercentage Error: 0.0024%\n",
      "ZIIXZZ (3104): \tEstimate: 0.96949 <-> 0.96947 \tPercentage Error: 0.0021%\n",
      "ZIIYXI (3109): \tEstimate: 0.99785 <-> 0.9978 \tPercentage Error: 0.0048%\n",
      "ZIIYXZ (3112): \tEstimate: 0.96989 <-> 0.96986 \tPercentage Error: 0.0025%\n",
      "ZIXIII (3137): \tEstimate: 0.99901 <-> 0.999 \tPercentage Error: 0.0006%\n",
      "ZIXIIZ (3140): \tEstimate: 0.9709 <-> 0.97103 \tPercentage Error: 0.013%\n",
      "ZIXZYI (3193): \tEstimate: 0.99816 <-> 0.9982 \tPercentage Error: 0.0045%\n",
      "ZIXZYZ (3196): \tEstimate: 0.97004 <-> 0.97025 \tPercentage Error: 0.022%\n",
      "ZIXXZI (3165): \tEstimate: 0.99713 <-> 0.9972 \tPercentage Error: 0.0074%\n",
      "ZIXXZZ (3168): \tEstimate: 0.96922 <-> 0.96928 \tPercentage Error: 0.0067%\n",
      "ZIXYXI (3173): \tEstimate: 0.99758 <-> 0.9976 \tPercentage Error: 0.0017%\n",
      "ZIXYXZ (3176): \tEstimate: 0.96966 <-> 0.96967 \tPercentage Error: 0.0013%\n",
      "ZXIIII (3329): \tEstimate: 0.98362 <-> 0.98321 \tPercentage Error: 0.0418%\n",
      "ZXIIIZ (3332): \tEstimate: 0.95567 <-> 0.95545 \tPercentage Error: 0.023%\n",
      "ZXIZYI (3385): \tEstimate: 0.98272 <-> 0.98241 \tPercentage Error: 0.0316%\n",
      "ZXIZYZ (3388): \tEstimate: 0.95465 <-> 0.95468 \tPercentage Error: 0.003%\n",
      "ZXIXZI (3357): \tEstimate: 0.98183 <-> 0.98142 \tPercentage Error: 0.041%\n",
      "ZXIXZZ (3360): \tEstimate: 0.95389 <-> 0.95372 \tPercentage Error: 0.0179%\n",
      "ZXIYXI (3365): \tEstimate: 0.98219 <-> 0.98182 \tPercentage Error: 0.0379%\n",
      "ZXIYXZ (3368): \tEstimate: 0.95385 <-> 0.9541 \tPercentage Error: 0.0267%\n",
      "ZXXIII (3393): \tEstimate: 0.98325 <-> 0.98301 \tPercentage Error: 0.0247%\n",
      "ZXXIIZ (3396): \tEstimate: 0.95515 <-> 0.95526 \tPercentage Error: 0.0116%\n",
      "ZXXZYI (3449): \tEstimate: 0.98235 <-> 0.98222 \tPercentage Error: 0.0138%\n",
      "ZXXZYZ (3452): \tEstimate: 0.95413 <-> 0.95449 \tPercentage Error: 0.038%\n",
      "ZXXXZI (3421): \tEstimate: 0.98142 <-> 0.98123 \tPercentage Error: 0.0197%\n",
      "ZXXXZZ (3424): \tEstimate: 0.95324 <-> 0.95353 \tPercentage Error: 0.0299%\n",
      "ZXXYXI (3429): \tEstimate: 0.98178 <-> 0.98162 \tPercentage Error: 0.0159%\n",
      "ZXXYXZ (3432): \tEstimate: 0.95333 <-> 0.95391 \tPercentage Error: 0.0613%\n"
     ]
    }
   ],
   "source": [
    "# So for example, if we look experiment 8 of these additional experiments, we see\n",
    "toExtract = 8\n",
    "\n",
    "# And (just out of interest we can compare the fidelities we extracted, with the actual values)\n",
    "for i in 1:64\n",
    "    print(\"$(fidelityLabels(e2_fidelity_extracted[toExtract][i]-1,qubits=6)) \",\n",
    "          \"($(e2_fidelity_extracted[toExtract][i])): \",\n",
    "          \"\\tEstimate: $(round(e2_all_additional_fidelities[toExtract][i],digits=5))\",\n",
    "          \" <-> $(round(actualOracle[e2_fidelity_extracted[toExtract][i]],digits=5)) \",\n",
    "          \"\\tPercentage Error: $(round.(abs(actualOracle[e2_fidelity_extracted[toExtract][i]]-e2_all_additional_fidelities[toExtract][i])/(actualOracle[e2_fidelity_extracted[toExtract][i]])*100,digits=4))%\\n\")\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Okay load them all up into the oracle\n",
    "\n",
    "for (expNo,x) in enumerate(e2_fidelity_extracted)\n",
    "    for (fidelityIndex,fidelity)  in enumerate(x)\n",
    "        push!(estimateOracle[fidelity],e2_all_additional_fidelities[expNo][fidelityIndex])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "001 1.0 \t[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
      "002 0.972 \t[0.97245, 0.97175]\n",
      "003 0.984 \t[0.98379, 0.98434]\n",
      "004 0.972 \t[0.97222, 0.97185, 0.97194, 0.97223, 0.97192, 0.97228, 0.97207, 0.97211, 0.97152, 0.97182, 0.97204, 0.97236]\n",
      "005 0.9914 \t[0.99144, 0.99129]\n",
      "006 0.97941 \t[0.97957]\n",
      "007 0.9914 \t[0.99154]\n",
      "008 0.96342 \t[0.96466, 0.96398, 0.96294, 0.96325, 0.9632, 0.96397, 0.96343, 0.96334, 0.96326, 0.96409]\n",
      "009 0.9918 \t[0.99173, 0.99173]\n",
      "010 0.9798 \t[0.98004, 0.98015, 0.97996, 0.97959, 0.97987, 0.9798, 0.97983, 0.97964, 0.98009]\n",
      "011 0.9918 \t[0.99173]\n",
      "012 0.96381 \t[0.96422, 0.96408]\n",
      "013 0.9992 \t[0.99924, 0.99917]\n",
      "014 0.97122 \t[0.97099]\n",
      "015 0.98321 \t[0.98326, 0.98301, 0.98303, 0.98328, 0.98312, 0.98329, 0.98322, 0.98338, 0.98344]\n",
      "016 0.97122 \t[0.97164, 0.97164]\n",
      "017 0.999 \t[0.99905, 0.99899]\n",
      "020 0.97103 \t[0.97143]\n",
      "021 0.9904 \t[0.99029]\n",
      "024 0.96245 \t[0.9621, 0.96326]\n",
      "025 0.9908 \t[0.99083]\n",
      "026 0.97882 \t[0.97902]\n",
      "028 0.96283 \t[0.96294]\n",
      "029 0.9982 \t[0.9982, 0.99818, 0.99815, 0.99821, 0.99812, 0.99822, 0.99821, 0.9982, 0.99819]\n",
      "030 0.97024 \t[0.96993]\n",
      "031 0.98222 \t[0.98198, 0.98257]\n",
      "032 0.97025 \t[0.9701, 0.97018, 0.97031, 0.96956, 0.97029, 0.97036, 0.97099]\n",
      "033 0.9912 \t[0.99122, 0.99117]\n",
      "036 0.96322 \t[0.96366]\n",
      "037 0.9986 \t[0.99859, 0.99862, 0.99852, 0.99864, 0.99859, 0.99861, 0.99864, 0.99859, 0.99862]\n",
      "038 0.97063 \t[0.97026]\n",
      "039 0.98261 \t[0.9829]\n",
      "040 0.97064 \t[0.96982, 0.97056, 0.97076, 0.97072, 0.97013, 0.97058, 0.97082, 0.97129]\n",
      "041 0.999 \t[0.99902]\n",
      "042 0.97102 \t[0.97078]\n",
      "044 0.97103 \t[0.97108]\n",
      "045 0.9904 \t[0.99044]\n",
      "047 0.99041 \t[0.99034]\n",
      "048 0.96245 \t[0.96289]\n",
      "049 0.9914 \t[0.99143, 0.99137]\n",
      "052 0.96342 \t[0.96381]\n",
      "053 0.9988 \t[0.99885]\n",
      "056 0.97083 \t[0.97072, 0.97095]\n",
      "057 0.9992 \t[0.9992, 0.99917, 0.99916, 0.99924, 0.99915, 0.99923, 0.99924, 0.99921, 0.9992]\n",
      "058 0.97122 \t[0.97188, 0.97092]\n",
      "059 0.98321 \t[0.9836]\n",
      "060 0.97122 \t[0.97131, 0.97122, 0.97114, 0.97065, 0.97113, 0.9713, 0.97159]\n",
      "061 0.9906 \t[0.99053]\n",
      "063 0.99061 \t[0.99061]\n",
      "064 0.96264 \t[0.96339]\n",
      "065 0.9998 \t[0.99983, 0.99976]\n",
      "068 0.97181 \t[0.97172]\n",
      "072 0.96322 \t[0.96257]\n",
      "074 0.97961 \t[0.97967]\n",
      "079 0.98301 \t[0.98293]\n",
      "081 0.9988 \t[0.99889]\n",
      "088 0.96225 \t[0.96175]\n",
      "090 0.97863 \t[0.97867]\n",
      "093 0.998 \t[0.99786]\n",
      "095 0.98202 \t[0.9819]\n",
      "096 0.97006 \t[0.97]\n",
      "097 0.991 \t[0.99091]\n",
      "101 0.9984 \t[0.99833]\n",
      "104 0.97045 \t[0.97043, 0.97046]\n",
      "106 0.97082 \t[0.97099]\n",
      "111 0.99022 \t[0.99018]\n",
      "113 0.9912 \t[0.9911, 0.99132, 0.99138, 0.99103, 0.99118, 0.99143, 0.99122, 0.99126, 0.99144]\n",
      "114 0.97922 \t[0.97945]\n",
      "115 0.99121 \t[0.99099]\n",
      "116 0.96322 \t[0.96393]\n",
      "117 0.9986 \t[0.99861]\n",
      "118 0.97063 \t[0.97115]\n",
      "119 0.98261 \t[0.98272]\n",
      "120 0.97064 \t[0.97126, 0.9713, 0.97094, 0.97077, 0.97058]\n",
      "121 0.999 \t[0.99898, 0.99891]\n",
      "122 0.97102 \t[0.97163, 0.97103, 0.97088, 0.97107, 0.97178]\n",
      "123 0.98301 \t[0.98273]\n",
      "124 0.97103 \t[0.97133, 0.97079]\n",
      "125 0.9904 \t[0.99044]\n",
      "126 0.97843 \t[0.97817]\n",
      "127 0.99041 \t[0.99052, 0.99049, 0.99049, 0.9904, 0.99054]\n",
      "128 0.96245 \t[0.96317]\n",
      "129 0.9994 \t[0.99942, 0.99941]\n",
      "132 0.97142 \t[0.97059]\n",
      "136 0.96283 \t[0.96246]\n",
      "138 0.97922 \t[0.9786]\n",
      "143 0.98261 \t[0.98276]\n",
      "145 0.9984 \t[0.99839, 0.99843, 0.99843, 0.99828, 0.99835, 0.99856, 0.99835, 0.9983, 0.99838]\n",
      "146 0.97043 \t[0.97101]\n",
      "147 0.98241 \t[0.98191]\n",
      "148 0.97045 \t[0.97054]\n",
      "149 0.9898 \t[0.98999]\n",
      "150 0.97785 \t[0.9781]\n",
      "151 0.98982 \t[0.98993]\n",
      "152 0.96186 \t[0.96303, 0.96228, 0.96186, 0.9618, 0.96182]\n",
      "153 0.9902 \t[0.99001]\n",
      "154 0.97824 \t[0.97831, 0.97833, 0.97787, 0.97816, 0.9784]\n",
      "155 0.99022 \t[0.98994]\n",
      "156 0.96225 \t[0.96273]\n",
      "157 0.9976 \t[0.99757, 0.99769]\n",
      "158 0.96965 \t[0.96954]\n",
      "159 0.98162 \t[0.98164, 0.98198, 0.98148, 0.98163, 0.98207]\n",
      "160 0.96967 \t[0.97002, 0.96858]\n",
      "161 0.9906 \t[0.99076]\n",
      "165 0.998 \t[0.99808]\n",
      "168 0.97006 \t[0.96884, 0.9693]\n",
      "170 0.97043 \t[0.96998]\n",
      "175 0.98982 \t[0.98971]\n",
      "177 0.9908 \t[0.99058]\n",
      "184 0.97025 \t[0.97032]\n",
      "185 0.9986 \t[0.99866]\n",
      "186 0.97063 \t[0.97082]\n",
      "188 0.97064 \t[0.96972]\n",
      "191 0.99002 \t[0.98983]\n",
      "193 0.9992 \t[0.99919, 0.99922]\n",
      "196 0.97122 \t[0.97118]\n",
      "200 0.96264 \t[0.96275]\n",
      "202 0.97902 \t[0.97906]\n",
      "207 0.98241 \t[0.98238]\n",
      "209 0.9982 \t[0.99823]\n",
      "216 0.96167 \t[0.96222]\n",
      "218 0.97804 \t[0.9784]\n",
      "221 0.9974 \t[0.99739]\n",
      "223 0.98142 \t[0.98127]\n",
      "224 0.96947 \t[0.96958]\n",
      "225 0.9904 \t[0.99038, 0.99055, 0.99058, 0.99016, 0.99042, 0.99059, 0.99034, 0.99046, 0.99057]\n",
      "226 0.97843 \t[0.97859]\n",
      "227 0.99041 \t[0.99021]\n",
      "228 0.96245 \t[0.96336]\n",
      "229 0.9978 \t[0.99777, 0.99782]\n",
      "230 0.96985 \t[0.97035]\n",
      "231 0.98182 \t[0.98204]\n",
      "232 0.96986 \t[0.97036, 0.97029, 0.96985, 0.97001, 0.96985, 0.96982]\n",
      "233 0.9982 \t[0.99811]\n",
      "234 0.97024 \t[0.9708, 0.97016, 0.97003, 0.96999, 0.97078]\n",
      "235 0.98222 \t[0.9818]\n",
      "236 0.97025 \t[0.97049]\n",
      "237 0.9896 \t[0.98967]\n",
      "238 0.97765 \t[0.97746]\n",
      "239 0.98962 \t[0.98974, 0.98969, 0.9898, 0.98967, 0.98959]\n",
      "240 0.96167 \t[0.96259]\n",
      "241 0.9906 \t[0.99058]\n",
      "248 0.97006 \t[0.97013]\n",
      "249 0.9984 \t[0.99843]\n",
      "250 0.97043 \t[0.97112]\n",
      "252 0.97045 \t[0.97051]\n",
      "255 0.98982 \t[0.98974]\n",
      "257 0.984 \t[0.98416, 0.98445]\n",
      "260 0.95622 \t[0.95649]\n",
      "264 0.96365 \t[0.96451]\n",
      "266 0.96397 \t[0.96369]\n",
      "271 0.98328 \t[0.98343]\n",
      "285 0.98222 \t[0.98261]\n",
      "288 0.95449 \t[0.95473]\n",
      "293 0.98261 \t[0.98299]\n",
      "296 0.95487 \t[0.95473]\n",
      "313 0.98321 \t[0.98355]\n",
      "316 0.95545 \t[0.95548]\n",
      "321 0.9838 \t[0.98407]\n",
      "324 0.95603 \t[0.95597]\n",
      "349 0.98202 \t[0.98218]\n",
      "352 0.9543 \t[0.95408]\n",
      "357 0.98241 \t[0.98256]\n",
      "360 0.95468 \t[0.9542]\n",
      "369 0.99121 \t[0.99107]\n",
      "376 0.95487 \t[0.95525]\n",
      "377 0.98301 \t[0.98315]\n",
      "378 0.97119 \t[0.97133]\n",
      "380 0.95526 \t[0.95497]\n",
      "383 0.97449 \t[0.97444]\n",
      "385 0.9834 \t[0.98313, 0.98329, 0.98327, 0.98327, 0.98332, 0.98336, 0.98347, 0.9832, 0.98324]\n",
      "386 0.97158 \t[0.97107]\n",
      "387 0.98347 \t[0.98317]\n",
      "388 0.95565 \t[0.95579, 0.95631, 0.95641, 0.95696, 0.95579, 0.95409, 0.95602]\n",
      "389 0.99081 \t[0.99081]\n",
      "392 0.96307 \t[0.96389]\n",
      "393 0.99121 \t[0.99119]\n",
      "396 0.96345 \t[0.96467]\n",
      "397 0.98261 \t[0.98263]\n",
      "400 0.95487 \t[0.9554]\n",
      "401 0.98241 \t[0.98228, 0.98244]\n",
      "404 0.95468 \t[0.95573]\n",
      "405 0.98982 \t[0.98981]\n",
      "408 0.9621 \t[0.96265, 0.96318]\n",
      "409 0.99022 \t[0.99031]\n",
      "410 0.96241 \t[0.96167]\n",
      "412 0.96249 \t[0.96321]\n",
      "413 0.98162 \t[0.98128, 0.98139, 0.98159, 0.98135, 0.98154]\n",
      "414 0.96983 \t[0.96917]\n",
      "415 0.9817 \t[0.98183, 0.98139]\n",
      "416 0.95391 \t[0.95423, 0.95222, 0.95465]\n",
      "417 0.99061 \t[0.99058]\n",
      "420 0.96287 \t[0.96432]\n",
      "421 0.98202 \t[0.98175, 0.98191, 0.98193, 0.98172, 0.9819]\n",
      "422 0.97022 \t[0.96963]\n",
      "423 0.9821 \t[0.9818]\n",
      "424 0.9543 \t[0.9546, 0.95264, 0.9551]\n",
      "425 0.98241 \t[0.98247]\n",
      "428 0.95468 \t[0.95651]\n",
      "429 0.98982 \t[0.98991]\n",
      "432 0.9621 \t[0.96303]\n",
      "433 0.99081 \t[0.99094]\n",
      "436 0.96307 \t[0.96301]\n",
      "437 0.98222 \t[0.98213]\n",
      "440 0.95449 \t[0.95528]\n",
      "441 0.98261 \t[0.9824, 0.98243, 0.98264, 0.9824, 0.98253]\n",
      "442 0.9708 \t[0.97031]\n",
      "443 0.98269 \t[0.98238]\n",
      "444 0.95487 \t[0.95513, 0.95351, 0.95539]\n",
      "445 0.99002 \t[0.99005]\n",
      "448 0.9623 \t[0.96255]\n",
      "449 0.98321 \t[0.98361]\n",
      "452 0.95545 \t[0.95564]\n",
      "477 0.98142 \t[0.9817]\n",
      "480 0.95372 \t[0.9535]\n",
      "481 0.99041 \t[0.9903]\n",
      "485 0.98182 \t[0.98219]\n",
      "488 0.9541 \t[0.95443, 0.95382]\n",
      "490 0.97041 \t[0.97051]\n",
      "495 0.9737 \t[0.97375]\n",
      "505 0.98241 \t[0.98281]\n",
      "508 0.95468 \t[0.9546]\n",
      "513 0.952 \t[0.95181, 0.95145]\n",
      "516 0.92512 \t[0.92298]\n",
      "520 0.93256 \t[0.93235]\n",
      "522 0.93261 \t[0.93229]\n",
      "527 0.95156 \t[0.95112]\n",
      "541 0.95027 \t[0.94949]\n",
      "544 0.92344 \t[0.92113]\n",
      "549 0.95066 \t[0.9494]\n",
      "552 0.92381 \t[0.92138]\n",
      "569 0.95123 \t[0.95032]\n",
      "572 0.92437 \t[0.9221]\n",
      "577 0.95181 \t[0.95238]\n",
      "580 0.92493 \t[0.92492]\n",
      "605 0.95008 \t[0.95053]\n",
      "608 0.92325 \t[0.92298]\n",
      "613 0.95046 \t[0.95091]\n",
      "616 0.92363 \t[0.92339]\n",
      "625 0.95923 \t[0.95877]\n",
      "632 0.92381 \t[0.92436]\n",
      "633 0.95104 \t[0.95155]\n",
      "634 0.93986 \t[0.93907]\n",
      "636 0.92419 \t[0.92388]\n",
      "639 0.9428 \t[0.94314]\n",
      "641 0.95142 \t[0.95071]\n",
      "644 0.92456 \t[0.92257]\n",
      "657 0.95046 \t[0.95032]\n",
      "664 0.93107 \t[0.93085]\n",
      "666 0.93111 \t[0.93106]\n",
      "669 0.9497 \t[0.9489]\n",
      "671 0.95004 \t[0.94956]\n",
      "672 0.92288 \t[0.92086]\n",
      "677 0.95008 \t[0.94871]\n",
      "680 0.92325 \t[0.92105]\n",
      "697 0.95066 \t[0.94967]\n",
      "700 0.92381 \t[0.92168]\n",
      "705 0.95123 \t[0.95097, 0.95114, 0.95151, 0.95197, 0.95197, 0.95114, 0.95159, 0.95061, 0.95225]\n",
      "706 0.94005 \t[0.93963]\n",
      "707 0.95156 \t[0.95194]\n",
      "708 0.92437 \t[0.92376, 0.92586, 0.92511, 0.92437, 0.92485, 0.92348, 0.92578]\n",
      "709 0.95866 \t[0.95939]\n",
      "712 0.93181 \t[0.93286]\n",
      "713 0.95904 \t[0.95885]\n",
      "716 0.93219 \t[0.93177]\n",
      "717 0.95046 \t[0.9508]\n",
      "720 0.92363 \t[0.92421]\n",
      "721 0.95027 \t[0.95143]\n",
      "724 0.92344 \t[0.92471]\n",
      "725 0.9577 \t[0.95876]\n",
      "728 0.93088 \t[0.93218]\n",
      "729 0.95808 \t[0.95879]\n",
      "732 0.93125 \t[0.93287]\n",
      "733 0.94951 \t[0.94961, 0.9491, 0.94991, 0.9492, 0.95115]\n",
      "734 0.93836 \t[0.93741]\n",
      "735 0.94985 \t[0.95015]\n",
      "736 0.9227 \t[0.92213, 0.92149, 0.9251]\n",
      "737 0.95846 \t[0.95808, 0.95829]\n",
      "740 0.93163 \t[0.93164]\n",
      "741 0.94989 \t[0.9504, 0.94964, 0.95042, 0.94962, 0.95145]\n",
      "742 0.93873 \t[0.93793]\n",
      "743 0.95023 \t[0.95083]\n",
      "744 0.92307 \t[0.92348, 0.92261, 0.9221, 0.92536]\n",
      "745 0.95027 \t[0.95034]\n",
      "746 0.93911 \t[0.93804]\n",
      "748 0.92344 \t[0.92395]\n",
      "749 0.9577 \t[0.95828]\n",
      "751 0.94204 \t[0.94229]\n",
      "752 0.93088 \t[0.93273]\n",
      "753 0.95866 \t[0.95877]\n",
      "756 0.93181 \t[0.9322]\n",
      "757 0.95008 \t[0.95081]\n",
      "760 0.92325 \t[0.9247]\n",
      "761 0.95046 \t[0.9507, 0.95071, 0.95088, 0.95017, 0.95167]\n",
      "762 0.9393 \t[0.93919]\n",
      "763 0.9508 \t[0.9516]\n",
      "764 0.92363 \t[0.92358, 0.92281, 0.92518]\n",
      "765 0.95789 \t[0.95803]\n",
      "768 0.93107 \t[0.93162]\n",
      "769 0.952 \t[0.95314, 0.95203]\n",
      "772 0.92534 \t[0.92457]\n",
      "776 0.91679 \t[0.91672]\n",
      "778 0.93277 \t[0.9337]\n",
      "783 0.93563 \t[0.93591]\n",
      "797 0.95029 \t[0.9506]\n",
      "800 0.92368 \t[0.92338]\n",
      "805 0.95067 \t[0.95108]\n",
      "808 0.92405 \t[0.92383]\n",
      "825 0.95124 \t[0.95148]\n",
      "828 0.9246 \t[0.92427]\n",
      "833 0.95181 \t[0.95178, 0.95124, 0.95247, 0.9528, 0.95211, 0.95176, 0.95215, 0.95142, 0.95287]\n",
      "834 0.92477 \t[0.92362]\n",
      "835 0.9362 \t[0.93736]\n",
      "836 0.92516 \t[0.92457, 0.92722, 0.92628, 0.926, 0.92566, 0.92445, 0.92598]\n",
      "837 0.94324 \t[0.94421]\n",
      "840 0.9166 \t[0.91822]\n",
      "841 0.94362 \t[0.94378]\n",
      "844 0.91697 \t[0.91825]\n",
      "845 0.95105 \t[0.95115]\n",
      "848 0.92442 \t[0.92497]\n",
      "849 0.95086 \t[0.95173]\n",
      "852 0.92423 \t[0.92595]\n",
      "853 0.94229 \t[0.9439]\n",
      "856 0.91568 \t[0.91808]\n",
      "857 0.94267 \t[0.94341]\n",
      "860 0.91605 \t[0.91763]\n",
      "861 0.9501 \t[0.95015, 0.94955, 0.95046, 0.94985, 0.95136]\n",
      "862 0.9231 \t[0.92226]\n",
      "863 0.9345 \t[0.93569]\n",
      "864 0.92349 \t[0.92285, 0.9227, 0.92533]\n",
      "865 0.94305 \t[0.94318]\n",
      "868 0.91642 \t[0.91805]\n",
      "869 0.95048 \t[0.95096, 0.95013, 0.95097, 0.95024, 0.95135]\n",
      "870 0.92347 \t[0.9226]\n",
      "871 0.93487 \t[0.93612]\n",
      "872 0.92386 \t[0.92342, 0.92331, 0.92517]\n",
      "873 0.95086 \t[0.95105]\n",
      "876 0.92423 \t[0.92586]\n",
      "877 0.94229 \t[0.94311]\n",
      "880 0.91568 \t[0.91768]\n",
      "881 0.94324 \t[0.94355, 0.94298]\n",
      "884 0.9166 \t[0.91645]\n",
      "885 0.95067 \t[0.95199]\n",
      "888 0.92405 \t[0.9236, 0.92641]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "889 0.95105 \t[0.95126, 0.95089, 0.95194, 0.95104, 0.95206]\n",
      "890 0.92403 \t[0.92427, 0.92327]\n",
      "891 0.93544 \t[0.93674]\n",
      "892 0.92442 \t[0.92426, 0.92422, 0.92522]\n",
      "893 0.94248 \t[0.94212]\n",
      "895 0.94287 \t[0.94297]\n",
      "896 0.91586 \t[0.91589]\n",
      "897 0.95143 \t[0.95155]\n",
      "900 0.92479 \t[0.92352]\n",
      "913 0.95048 \t[0.95116]\n",
      "920 0.91531 \t[0.91568]\n",
      "922 0.93128 \t[0.9319]\n",
      "925 0.94972 \t[0.94999]\n",
      "927 0.93412 \t[0.93411]\n",
      "928 0.92312 \t[0.92169]\n",
      "933 0.9501 \t[0.95036]\n",
      "936 0.92349 \t[0.92212]\n",
      "953 0.95067 \t[0.95086]\n",
      "956 0.92405 \t[0.92276]\n",
      "961 0.95124 \t[0.95116]\n",
      "964 0.9246 \t[0.92459]\n",
      "989 0.94953 \t[0.94989]\n",
      "992 0.92294 \t[0.92334]\n",
      "993 0.94248 \t[0.94322]\n",
      "997 0.94991 \t[0.95032]\n",
      "1000 0.92331 \t[0.92388, 0.92401]\n",
      "1002 0.92328 \t[0.92456]\n",
      "1007 0.94212 \t[0.943]\n",
      "1017 0.95048 \t[0.95059]\n",
      "1020 0.92386 \t[0.92422]\n",
      "1025 0.9998 \t[0.99981, 0.99979]\n",
      "1028 0.97181 \t[0.97185]\n",
      "1032 0.96322 \t[0.96318]\n",
      "1034 0.97961 \t[0.97964]\n",
      "1039 0.98301 \t[0.98303]\n",
      "1053 0.998 \t[0.998]\n",
      "1056 0.97006 \t[0.97017]\n",
      "1061 0.9984 \t[0.99837]\n",
      "1064 0.97045 \t[0.97063]\n",
      "1081 0.999 \t[0.999]\n",
      "1084 0.97103 \t[0.97109]\n",
      "1137 0.991 \t[0.99103]\n",
      "1144 0.97045 \t[0.97076]\n",
      "1146 0.97082 \t[0.97067]\n",
      "1151 0.99022 \t[0.99032]\n",
      "1169 0.9982 \t[0.99815]\n",
      "1176 0.96167 \t[0.96161]\n",
      "1178 0.97804 \t[0.97769]\n",
      "1183 0.98142 \t[0.98127]\n",
      "1249 0.9902 \t[0.99013]\n",
      "1256 0.96967 \t[0.96964]\n",
      "1258 0.97004 \t[0.96975]\n",
      "1263 0.98942 \t[0.98961]\n",
      "1281 0.9838 \t[0.98392]\n",
      "1288 0.96345 \t[0.96429]\n",
      "1290 0.96377 \t[0.96347]\n",
      "1295 0.98308 \t[0.98325]\n",
      "1393 0.99101 \t[0.99088]\n",
      "1400 0.95468 \t[0.95503]\n",
      "1402 0.97099 \t[0.97113]\n",
      "1407 0.97429 \t[0.97416]\n",
      "1409 0.98321 \t[0.98296]\n",
      "1412 0.95545 \t[0.95398]\n",
      "1425 0.98222 \t[0.98206]\n",
      "1432 0.96191 \t[0.96242]\n",
      "1434 0.96222 \t[0.96148]\n",
      "1437 0.98142 \t[0.98112]\n",
      "1439 0.98151 \t[0.98164]\n",
      "1440 0.95372 \t[0.95209]\n",
      "1445 0.98182 \t[0.98148]\n",
      "1448 0.9541 \t[0.95255]\n",
      "1465 0.98241 \t[0.98217]\n",
      "1468 0.95468 \t[0.95336]\n",
      "1505 0.99022 \t[0.99009]\n",
      "1512 0.95391 \t[0.95415]\n",
      "1514 0.97022 \t[0.97026]\n",
      "1519 0.97351 \t[0.97342]\n",
      "1537 0.95181 \t[0.95153]\n",
      "1544 0.93237 \t[0.93249]\n",
      "1546 0.93242 \t[0.93138]\n",
      "1551 0.95137 \t[0.9516]\n",
      "1649 0.95904 \t[0.95917]\n",
      "1656 0.92363 \t[0.92448]\n",
      "1658 0.93967 \t[0.93918]\n",
      "1663 0.94261 \t[0.94289]\n",
      "1681 0.95027 \t[0.94976]\n",
      "1688 0.93088 \t[0.93198]\n",
      "1690 0.93092 \t[0.93027]\n",
      "1695 0.94985 \t[0.9503]\n",
      "1729 0.95104 \t[0.95037]\n",
      "1732 0.92419 \t[0.92326]\n",
      "1757 0.94931 \t[0.94896]\n",
      "1760 0.92251 \t[0.92119]\n",
      "1761 0.95827 \t[0.95832]\n",
      "1765 0.9497 \t[0.94939]\n",
      "1768 0.92288 \t[0.92245, 0.92182]\n",
      "1770 0.93892 \t[0.93812]\n",
      "1775 0.94185 \t[0.94178]\n",
      "1785 0.95027 \t[0.9499]\n",
      "1788 0.92344 \t[0.92255]\n",
      "1793 0.95181 \t[0.95238, 0.95156, 0.95179, 0.95135, 0.95203, 0.9521, 0.9519, 0.95136, 0.95258]\n",
      "1794 0.92477 \t[0.92446]\n",
      "1795 0.9362 \t[0.93528]\n",
      "1796 0.92516 \t[0.92545]\n",
      "1797 0.94324 \t[0.94294]\n",
      "1798 0.93221 \t[0.93232]\n",
      "1799 0.94363 \t[0.94354]\n",
      "1800 0.9166 \t[0.91648, 0.91646, 0.91656, 0.91784, 0.9183]\n",
      "1801 0.94362 \t[0.94319]\n",
      "1802 0.93259 \t[0.93246, 0.93224, 0.93296, 0.93349, 0.93417]\n",
      "1803 0.94401 \t[0.94303]\n",
      "1804 0.91697 \t[0.91792]\n",
      "1805 0.95105 \t[0.95141]\n",
      "1806 0.92403 \t[0.92447]\n",
      "1807 0.93544 \t[0.9354, 0.93484, 0.93514, 0.93512, 0.93569]\n",
      "1808 0.92442 \t[0.9247]\n",
      "1809 0.95086 \t[0.951]\n",
      "1816 0.91568 \t[0.91548]\n",
      "1818 0.93165 \t[0.93214]\n",
      "1823 0.9345 \t[0.93388]\n",
      "1825 0.94305 \t[0.94298]\n",
      "1832 0.92386 \t[0.92431]\n",
      "1834 0.92384 \t[0.92486]\n",
      "1839 0.94269 \t[0.94205]\n",
      "1841 0.94324 \t[0.94415]\n",
      "1848 0.92405 \t[0.92538]\n",
      "1850 0.92403 \t[0.92629]\n",
      "1855 0.94287 \t[0.94276]\n",
      "1857 0.95162 \t[0.9515, 0.95114]\n",
      "1860 0.92497 \t[0.92429]\n",
      "1864 0.91642 \t[0.91693]\n",
      "1866 0.9324 \t[0.93311]\n",
      "1871 0.93525 \t[0.93491]\n",
      "1873 0.95067 \t[0.95053]\n",
      "1880 0.91549 \t[0.91576]\n",
      "1882 0.93147 \t[0.93215]\n",
      "1885 0.94991 \t[0.94955]\n",
      "1887 0.93431 \t[0.9336]\n",
      "1888 0.92331 \t[0.92249]\n",
      "1889 0.94286 \t[0.94235]\n",
      "1893 0.95029 \t[0.94992]\n",
      "1896 0.92368 \t[0.92356, 0.92312]\n",
      "1898 0.92365 \t[0.92281]\n",
      "1903 0.9425 \t[0.94212]\n",
      "1905 0.94305 \t[0.94339, 0.94273, 0.9423, 0.9423, 0.94314]\n",
      "1906 0.93203 \t[0.93152]\n",
      "1907 0.94344 \t[0.94238]\n",
      "1908 0.91642 \t[0.91613]\n",
      "1909 0.95048 \t[0.95032]\n",
      "1910 0.92347 \t[0.92295]\n",
      "1911 0.93487 \t[0.93504]\n",
      "1912 0.92386 \t[0.92416]\n",
      "1913 0.95086 \t[0.95001, 0.95076]\n",
      "1914 0.92384 \t[0.92337]\n",
      "1915 0.93525 \t[0.93367]\n",
      "1916 0.92423 \t[0.92525, 0.92403]\n",
      "1917 0.94229 \t[0.9425]\n",
      "1918 0.93128 \t[0.93184]\n",
      "1919 0.94269 \t[0.94333]\n",
      "1920 0.91568 \t[0.91546]\n",
      "1921 0.95124 \t[0.95061]\n",
      "1928 0.91605 \t[0.91689]\n",
      "1930 0.93203 \t[0.93251]\n",
      "1935 0.93487 \t[0.93434]\n",
      "1937 0.95029 \t[0.9507, 0.95027, 0.94995, 0.94922, 0.94962]\n",
      "1938 0.92328 \t[0.92244]\n",
      "1939 0.93468 \t[0.93311]\n",
      "1940 0.92368 \t[0.92291]\n",
      "1941 0.94172 \t[0.94114]\n",
      "1942 0.93072 \t[0.93039]\n",
      "1943 0.94212 \t[0.94191]\n",
      "1944 0.91513 \t[0.9153]\n",
      "1945 0.9421 \t[0.94118]\n",
      "1946 0.9311 \t[0.9307]\n",
      "1947 0.9425 \t[0.94089]\n",
      "1948 0.91549 \t[0.91673]\n",
      "1949 0.94953 \t[0.94918]\n",
      "1950 0.92254 \t[0.92334]\n",
      "1951 0.93393 \t[0.93375]\n",
      "1952 0.92294 \t[0.92233]\n",
      "1953 0.94248 \t[0.94202]\n",
      "1960 0.92331 \t[0.92313]\n",
      "1962 0.92328 \t[0.92369]\n",
      "1967 0.94212 \t[0.94103]\n",
      "1969 0.94267 \t[0.94262]\n",
      "1976 0.92349 \t[0.92362]\n",
      "1978 0.92347 \t[0.92327]\n",
      "1983 0.94231 \t[0.94203]\n",
      "1985 0.95105 \t[0.95136]\n",
      "1992 0.91586 \t[0.9177]\n",
      "1994 0.93184 \t[0.93347]\n",
      "1999 0.93469 \t[0.93516]\n",
      "2001 0.9501 \t[0.95018]\n",
      "2008 0.91494 \t[0.91412]\n",
      "2010 0.93091 \t[0.93001]\n",
      "2015 0.93374 \t[0.93245]\n",
      "2017 0.94229 \t[0.94288, 0.94269, 0.94172, 0.94149, 0.94266]\n",
      "2018 0.93128 \t[0.93103]\n",
      "2019 0.94269 \t[0.94167]\n",
      "2020 0.91568 \t[0.91585]\n",
      "2021 0.94972 \t[0.94985]\n",
      "2022 0.92272 \t[0.92263]\n",
      "2023 0.93412 \t[0.93443]\n",
      "2024 0.92313 \t[0.92311]\n",
      "2025 0.9501 \t[0.94919]\n",
      "2026 0.9231 \t[0.92261]\n",
      "2027 0.9345 \t[0.93292]\n",
      "2028 0.92349 \t[0.92483]\n",
      "2029 0.94153 \t[0.942]\n",
      "2030 0.93054 \t[0.93122]\n",
      "2031 0.94193 \t[0.94241]\n",
      "2032 0.91494 \t[0.91519]\n",
      "2033 0.94248 \t[0.94316]\n",
      "2040 0.92331 \t[0.92479]\n",
      "2042 0.92328 \t[0.92505]\n",
      "2047 0.94212 \t[0.94181]\n",
      "2049 0.9994 \t[0.99943, 0.99938]\n",
      "2052 0.97142 \t[0.97184]\n",
      "2056 0.96283 \t[0.96281]\n",
      "2058 0.97922 \t[0.97906]\n",
      "2063 0.98261 \t[0.98284]\n",
      "2077 0.9976 \t[0.99757]\n",
      "2080 0.96967 \t[0.97049]\n",
      "2085 0.998 \t[0.99798]\n",
      "2088 0.97006 \t[0.97073]\n",
      "2105 0.9986 \t[0.99858]\n",
      "2108 0.97064 \t[0.9711]\n",
      "2161 0.9906 \t[0.99071]\n",
      "2168 0.97006 \t[0.97017]\n",
      "2170 0.97043 \t[0.97057]\n",
      "2175 0.98982 \t[0.98989]\n",
      "2193 0.9978 \t[0.99772]\n",
      "2200 0.96128 \t[0.96122]\n",
      "2202 0.97765 \t[0.97763]\n",
      "2207 0.98103 \t[0.98104]\n",
      "2273 0.9898 \t[0.98994]\n",
      "2280 0.96928 \t[0.96948]\n",
      "2282 0.96965 \t[0.96948]\n",
      "2287 0.98903 \t[0.98914]\n",
      "2305 0.9834 \t[0.98339, 0.98366, 0.98343, 0.98324, 0.98356, 0.98321, 0.98309, 0.98378, 0.98364]\n",
      "2306 0.97158 \t[0.9719]\n",
      "2307 0.98347 \t[0.98351]\n",
      "2308 0.95565 \t[0.95684]\n",
      "2309 0.99081 \t[0.9906]\n",
      "2310 0.96299 \t[0.96299]\n",
      "2311 0.97488 \t[0.97548]\n",
      "2312 0.96307 \t[0.96325, 0.96355, 0.9629, 0.96307, 0.96264]\n",
      "2313 0.99121 \t[0.99128]\n",
      "2314 0.96338 \t[0.96376, 0.96409, 0.96233, 0.9639, 0.96396]\n",
      "2315 0.97528 \t[0.97523]\n",
      "2316 0.96345 \t[0.96479]\n",
      "2317 0.98261 \t[0.98285]\n",
      "2318 0.9708 \t[0.97093]\n",
      "2319 0.98269 \t[0.9828, 0.98256, 0.98264, 0.98297, 0.98268]\n",
      "2320 0.95487 \t[0.95619]\n",
      "2321 0.98241 \t[0.98209]\n",
      "2328 0.9621 \t[0.96197]\n",
      "2330 0.96241 \t[0.96132]\n",
      "2335 0.9817 \t[0.98188]\n",
      "2337 0.99061 \t[0.99079]\n",
      "2344 0.9543 \t[0.9554]\n",
      "2346 0.97061 \t[0.97088]\n",
      "2351 0.9739 \t[0.9742]\n",
      "2353 0.99081 \t[0.9909]\n",
      "2360 0.95449 \t[0.95424]\n",
      "2362 0.9708 \t[0.97116]\n",
      "2367 0.9741 \t[0.97387]\n",
      "2369 0.98321 \t[0.98292]\n",
      "2376 0.96287 \t[0.96273]\n",
      "2378 0.96319 \t[0.96212]\n",
      "2383 0.98249 \t[0.98251]\n",
      "2385 0.98222 \t[0.98198]\n",
      "2392 0.96191 \t[0.96177]\n",
      "2394 0.96222 \t[0.96108]\n",
      "2399 0.98151 \t[0.98182]\n",
      "2401 0.99041 \t[0.99034]\n",
      "2408 0.9541 \t[0.95492]\n",
      "2410 0.97041 \t[0.97084]\n",
      "2415 0.9737 \t[0.9737]\n",
      "2417 0.99061 \t[0.99064, 0.99078, 0.99049, 0.99059, 0.99054]\n",
      "2418 0.9628 \t[0.96333]\n",
      "2419 0.97469 \t[0.97434]\n",
      "2420 0.96287 \t[0.96322]\n",
      "2421 0.98202 \t[0.98196]\n",
      "2422 0.97022 \t[0.97052]\n",
      "2423 0.9821 \t[0.98276]\n",
      "2424 0.9543 \t[0.95555]\n",
      "2425 0.98241 \t[0.98215]\n",
      "2426 0.97061 \t[0.97074]\n",
      "2427 0.98249 \t[0.98255]\n",
      "2428 0.95468 \t[0.95596]\n",
      "2429 0.98982 \t[0.98981]\n",
      "2430 0.96202 \t[0.96254]\n",
      "2431 0.9739 \t[0.97363]\n",
      "2432 0.9621 \t[0.96279]\n",
      "2433 0.98281 \t[0.98317, 0.98257]\n",
      "2436 0.95507 \t[0.95549]\n",
      "2440 0.96249 \t[0.96218]\n",
      "2442 0.9628 \t[0.96306]\n",
      "2447 0.9821 \t[0.98227]\n",
      "2449 0.98182 \t[0.98173, 0.98214, 0.98201, 0.98149, 0.98193]\n",
      "2450 0.97002 \t[0.97049]\n",
      "2451 0.9819 \t[0.98197]\n",
      "2452 0.9541 \t[0.95531]\n",
      "2453 0.98923 \t[0.98912]\n",
      "2454 0.96144 \t[0.9618]\n",
      "2455 0.97331 \t[0.97409]\n",
      "2456 0.96153 \t[0.9616]\n",
      "2457 0.98962 \t[0.98958]\n",
      "2458 0.96183 \t[0.96159]\n",
      "2459 0.9737 \t[0.97363]\n",
      "2460 0.96191 \t[0.96384]\n",
      "2461 0.98103 \t[0.98125, 0.9809]\n",
      "2462 0.96925 \t[0.96961]\n",
      "2463 0.98112 \t[0.98115]\n",
      "2464 0.95333 \t[0.95474, 0.95415]\n",
      "2465 0.99002 \t[0.99015]\n",
      "2469 0.98142 \t[0.98122]\n",
      "2472 0.95372 \t[0.95451, 0.95459]\n",
      "2474 0.97002 \t[0.9698]\n",
      "2479 0.97331 \t[0.97335]\n",
      "2481 0.99022 \t[0.98989]\n",
      "2488 0.95391 \t[0.95494]\n",
      "2489 0.98202 \t[0.98187]\n",
      "2490 0.97022 \t[0.97082]\n",
      "2492 0.9543 \t[0.95488]\n",
      "2495 0.97351 \t[0.97329]\n",
      "2497 0.98261 \t[0.98281]\n",
      "2504 0.9623 \t[0.9618]\n",
      "2506 0.96261 \t[0.96332]\n",
      "2511 0.9819 \t[0.98171]\n",
      "2513 0.98162 \t[0.98141]\n",
      "2520 0.96133 \t[0.96158]\n",
      "2522 0.96163 \t[0.96225]\n",
      "2527 0.98092 \t[0.98075]\n",
      "2529 0.98982 \t[0.98988, 0.98995, 0.98975, 0.9898, 0.98975]\n",
      "2530 0.96202 \t[0.96235]\n",
      "2531 0.9739 \t[0.97386]\n",
      "2532 0.9621 \t[0.9629]\n",
      "2533 0.98123 \t[0.98121]\n",
      "2534 0.96944 \t[0.96963]\n",
      "2535 0.98131 \t[0.98193]\n",
      "2536 0.95353 \t[0.95451]\n",
      "2537 0.98162 \t[0.98138]\n",
      "2538 0.96983 \t[0.96987]\n",
      "2539 0.9817 \t[0.98195]\n",
      "2540 0.95391 \t[0.95514]\n",
      "2541 0.98903 \t[0.98907]\n",
      "2542 0.96125 \t[0.96167]\n",
      "2543 0.97312 \t[0.97294]\n",
      "2544 0.96133 \t[0.96237]\n",
      "2545 0.99002 \t[0.99006]\n",
      "2552 0.95372 \t[0.95373]\n",
      "2554 0.97002 \t[0.97015]\n",
      "2559 0.97331 \t[0.97296]\n",
      "2561 0.95142 \t[0.95128]\n",
      "2568 0.932 \t[0.93179]\n",
      "2570 0.93205 \t[0.93218]\n",
      "2575 0.95099 \t[0.9505]\n",
      "2673 0.95866 \t[0.95806]\n",
      "2680 0.92326 \t[0.9237]\n",
      "2682 0.9393 \t[0.93844]\n",
      "2687 0.94223 \t[0.94256]\n",
      "2705 0.94989 \t[0.9496]\n",
      "2712 0.93051 \t[0.93019]\n",
      "2714 0.93054 \t[0.93041]\n",
      "2719 0.94947 \t[0.94886]\n",
      "2753 0.95066 \t[0.95175]\n",
      "2756 0.92381 \t[0.92554]\n",
      "2781 0.94893 \t[0.95066]\n",
      "2784 0.92214 \t[0.9249]\n",
      "2785 0.95789 \t[0.95747]\n",
      "2789 0.94931 \t[0.95097]\n",
      "2792 0.92251 \t[0.92287, 0.92521]\n",
      "2794 0.93854 \t[0.93755]\n",
      "2799 0.94147 \t[0.94172]\n",
      "2809 0.94989 \t[0.95116]\n",
      "2812 0.92307 \t[0.92498]\n",
      "2817 0.95143 \t[0.95153]\n",
      "2824 0.91623 \t[0.91568]\n",
      "2826 0.93221 \t[0.93108]\n",
      "2831 0.93506 \t[0.93468]\n",
      "2881 0.95124 \t[0.95232]\n",
      "2884 0.9246 \t[0.92575]\n",
      "2909 0.94953 \t[0.95077]\n",
      "2912 0.92294 \t[0.92516]\n",
      "2917 0.94991 \t[0.95076]\n",
      "2920 0.92331 \t[0.92505]\n",
      "2929 0.94267 \t[0.9423]\n",
      "2936 0.92349 \t[0.92419]\n",
      "2937 0.95048 \t[0.95148]\n",
      "2938 0.92347 \t[0.92289]\n",
      "2940 0.92386 \t[0.92504]\n",
      "2943 0.94231 \t[0.94234]\n",
      "2961 0.94991 \t[0.95035]\n",
      "2968 0.91476 \t[0.91538]\n",
      "2970 0.93072 \t[0.93034]\n",
      "2975 0.93355 \t[0.93381]\n",
      "3041 0.94191 \t[0.94125]\n",
      "3048 0.92276 \t[0.92271]\n",
      "3050 0.92272 \t[0.9217]\n",
      "3055 0.94155 \t[0.94166]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3073 0.9992 \t[0.99922, 0.99919, 0.99923, 0.99924, 0.99919, 0.99918, 0.99918, 0.99924, 0.99918, 0.99926, 0.9992, 0.99917]\n",
      "3074 0.97122 \t[0.97113]\n",
      "3075 0.98321 \t[0.98355]\n",
      "3076 0.97122 \t[0.97105, 0.97112, 0.97148, 0.97114, 0.97145, 0.9714, 0.97128, 0.9709, 0.9712]\n",
      "3077 0.9906 \t[0.99054]\n",
      "3080 0.96264 \t[0.96244, 0.96334]\n",
      "3081 0.991 \t[0.99093]\n",
      "3082 0.97902 \t[0.97929]\n",
      "3084 0.96303 \t[0.96346]\n",
      "3085 0.9984 \t[0.99841]\n",
      "3087 0.98241 \t[0.98264]\n",
      "3088 0.97045 \t[0.97077]\n",
      "3089 0.9982 \t[0.99817]\n",
      "3092 0.97025 \t[0.9707]\n",
      "3093 0.9896 \t[0.98956]\n",
      "3096 0.96167 \t[0.96257]\n",
      "3097 0.99 \t[0.99001]\n",
      "3100 0.96206 \t[0.9619]\n",
      "3101 0.9974 \t[0.99738, 0.99742, 0.99736, 0.9974, 0.99738, 0.99741, 0.99737]\n",
      "3102 0.96945 \t[0.96936]\n",
      "3103 0.98142 \t[0.98177]\n",
      "3104 0.96947 \t[0.96932, 0.96952, 0.96949, 0.96893, 0.96962]\n",
      "3105 0.9904 \t[0.99036]\n",
      "3108 0.96245 \t[0.96308]\n",
      "3109 0.9978 \t[0.99778, 0.99786, 0.99772, 0.99782, 0.99785, 0.99781, 0.99777]\n",
      "3110 0.96985 \t[0.96968]\n",
      "3111 0.98182 \t[0.98209]\n",
      "3112 0.96986 \t[0.96972, 0.97003, 0.96989, 0.96954, 0.96994]\n",
      "3113 0.9982 \t[0.99823]\n",
      "3116 0.97025 \t[0.97031]\n",
      "3117 0.9896 \t[0.98963]\n",
      "3120 0.96167 \t[0.96191]\n",
      "3121 0.9906 \t[0.99059]\n",
      "3124 0.96264 \t[0.9629]\n",
      "3125 0.998 \t[0.99803]\n",
      "3128 0.97006 \t[0.97011]\n",
      "3129 0.9984 \t[0.99839, 0.9984, 0.99838, 0.99842, 0.9984, 0.99843, 0.99841]\n",
      "3130 0.97043 \t[0.97035]\n",
      "3131 0.98241 \t[0.98284]\n",
      "3132 0.97045 \t[0.9705, 0.97054, 0.97035, 0.97005, 0.97053]\n",
      "3133 0.9898 \t[0.98976]\n",
      "3136 0.96186 \t[0.96248]\n",
      "3137 0.999 \t[0.99901]\n",
      "3140 0.97103 \t[0.9709]\n",
      "3165 0.9972 \t[0.99713]\n",
      "3168 0.96928 \t[0.96922]\n",
      "3173 0.9976 \t[0.99758]\n",
      "3176 0.96967 \t[0.96966]\n",
      "3185 0.9904 \t[0.99059]\n",
      "3192 0.96986 \t[0.96985]\n",
      "3193 0.9982 \t[0.99816]\n",
      "3194 0.97024 \t[0.971]\n",
      "3196 0.97025 \t[0.97004]\n",
      "3199 0.98962 \t[0.98978]\n",
      "3201 0.9986 \t[0.99859]\n",
      "3204 0.97064 \t[0.96999]\n",
      "3217 0.9976 \t[0.99761]\n",
      "3224 0.96109 \t[0.96122]\n",
      "3226 0.97745 \t[0.97779]\n",
      "3229 0.9968 \t[0.99686]\n",
      "3231 0.98083 \t[0.98131]\n",
      "3232 0.96889 \t[0.96795]\n",
      "3237 0.9972 \t[0.99726]\n",
      "3240 0.96928 \t[0.9687]\n",
      "3257 0.9978 \t[0.99785]\n",
      "3260 0.96986 \t[0.96915]\n",
      "3265 0.9984 \t[0.99839]\n",
      "3268 0.97045 \t[0.97058]\n",
      "3293 0.9966 \t[0.99655]\n",
      "3296 0.9687 \t[0.96895]\n",
      "3297 0.9896 \t[0.98974]\n",
      "3301 0.997 \t[0.99696]\n",
      "3304 0.96909 \t[0.96902, 0.96919]\n",
      "3306 0.96945 \t[0.96998]\n",
      "3311 0.98883 \t[0.98882]\n",
      "3321 0.9976 \t[0.99759]\n",
      "3324 0.96967 \t[0.96994]\n",
      "3329 0.98321 \t[0.98341, 0.98362]\n",
      "3332 0.95545 \t[0.95567]\n",
      "3336 0.96287 \t[0.96342]\n",
      "3338 0.96319 \t[0.96341]\n",
      "3343 0.98249 \t[0.98281]\n",
      "3357 0.98142 \t[0.98183]\n",
      "3360 0.95372 \t[0.95389]\n",
      "3365 0.98182 \t[0.98219]\n",
      "3368 0.9541 \t[0.95385]\n",
      "3385 0.98241 \t[0.98272]\n",
      "3388 0.95468 \t[0.95465]\n",
      "3393 0.98301 \t[0.98325]\n",
      "3396 0.95526 \t[0.95515]\n",
      "3421 0.98123 \t[0.98142]\n",
      "3424 0.95353 \t[0.95324]\n",
      "3429 0.98162 \t[0.98178]\n",
      "3432 0.95391 \t[0.95333]\n",
      "3441 0.99041 \t[0.99088]\n",
      "3448 0.9541 \t[0.9553]\n",
      "3449 0.98222 \t[0.98235]\n",
      "3450 0.97041 \t[0.97053]\n",
      "3452 0.95449 \t[0.95413]\n",
      "3455 0.9737 \t[0.97418]\n",
      "3457 0.98261 \t[0.98223, 0.98259, 0.98257, 0.9825, 0.98267, 0.98254, 0.98272]\n",
      "3458 0.9708 \t[0.97045]\n",
      "3459 0.98269 \t[0.98245]\n",
      "3460 0.95487 \t[0.95485, 0.95517, 0.95556, 0.9564, 0.95468]\n",
      "3461 0.99002 \t[0.99013]\n",
      "3464 0.9623 \t[0.96319]\n",
      "3465 0.99041 \t[0.99037]\n",
      "3468 0.96268 \t[0.96406]\n",
      "3469 0.98182 \t[0.98192]\n",
      "3472 0.9541 \t[0.95429]\n",
      "3473 0.98162 \t[0.98196, 0.9818]\n",
      "3476 0.95391 \t[0.95495]\n",
      "3477 0.98903 \t[0.98911]\n",
      "3480 0.96133 \t[0.96198, 0.96247]\n",
      "3481 0.98942 \t[0.98958]\n",
      "3482 0.96163 \t[0.96195]\n",
      "3484 0.96172 \t[0.96217]\n",
      "3485 0.98083 \t[0.98034, 0.98076, 0.98089]\n",
      "3486 0.96905 \t[0.96858]\n",
      "3487 0.98092 \t[0.98138, 0.9807]\n",
      "3488 0.95314 \t[0.95332]\n",
      "3489 0.98982 \t[0.98977]\n",
      "3492 0.9621 \t[0.96372]\n",
      "3493 0.98123 \t[0.98083, 0.98124, 0.98124]\n",
      "3494 0.96944 \t[0.96909]\n",
      "3495 0.98131 \t[0.98107]\n",
      "3496 0.95353 \t[0.9537]\n",
      "3497 0.98162 \t[0.98167]\n",
      "3500 0.95391 \t[0.95599]\n",
      "3501 0.98903 \t[0.98918]\n",
      "3504 0.96133 \t[0.962]\n",
      "3505 0.99002 \t[0.99023]\n",
      "3508 0.9623 \t[0.96211]\n",
      "3509 0.98142 \t[0.98133]\n",
      "3512 0.95372 \t[0.95416]\n",
      "3513 0.98182 \t[0.98151, 0.98176, 0.98192]\n",
      "3514 0.97002 \t[0.96976]\n",
      "3515 0.9819 \t[0.98166]\n",
      "3516 0.9541 \t[0.95419]\n",
      "3517 0.98923 \t[0.98937]\n",
      "3520 0.96153 \t[0.9616]\n",
      "3521 0.98241 \t[0.98285]\n",
      "3524 0.95468 \t[0.95489]\n",
      "3549 0.98063 \t[0.98093]\n",
      "3552 0.95295 \t[0.95267]\n",
      "3553 0.98962 \t[0.98999]\n",
      "3557 0.98103 \t[0.98139]\n",
      "3560 0.95333 \t[0.95393, 0.95296]\n",
      "3562 0.96963 \t[0.96981]\n",
      "3567 0.97292 \t[0.97362]\n",
      "3577 0.98162 \t[0.98205]\n",
      "3580 0.95391 \t[0.9538]\n",
      "3585 0.95123 \t[0.95148, 0.95154, 0.95103, 0.95167, 0.95158, 0.95104, 0.95147, 0.95099, 0.95201, 0.95059]\n",
      "3586 0.94005 \t[0.94102]\n",
      "3587 0.95156 \t[0.95162]\n",
      "3588 0.92437 \t[0.92421, 0.92235]\n",
      "3589 0.95866 \t[0.95905]\n",
      "3590 0.93148 \t[0.93216]\n",
      "3591 0.94299 \t[0.94381]\n",
      "3592 0.93181 \t[0.93264, 0.93092, 0.9328, 0.93195, 0.93312]\n",
      "3593 0.95904 \t[0.95941]\n",
      "3594 0.93186 \t[0.93225, 0.9307, 0.93205, 0.93236, 0.9337]\n",
      "3595 0.94337 \t[0.94345]\n",
      "3596 0.93219 \t[0.9332]\n",
      "3597 0.95046 \t[0.95082]\n",
      "3598 0.9393 \t[0.93948]\n",
      "3599 0.9508 \t[0.95153, 0.9505, 0.95127, 0.95043, 0.95112]\n",
      "3600 0.92363 \t[0.92336]\n",
      "3601 0.95027 \t[0.9506]\n",
      "3608 0.93088 \t[0.93246]\n",
      "3610 0.93092 \t[0.93133]\n",
      "3613 0.94951 \t[0.94862]\n",
      "3615 0.94985 \t[0.95029]\n",
      "3616 0.9227 \t[0.9205]\n",
      "3617 0.95846 \t[0.95802]\n",
      "3621 0.94989 \t[0.94856]\n",
      "3624 0.92307 \t[0.9233, 0.92073]\n",
      "3626 0.93911 \t[0.93874]\n",
      "3631 0.94204 \t[0.94163]\n",
      "3633 0.95866 \t[0.95912]\n",
      "3640 0.92325 \t[0.92468]\n",
      "3641 0.95046 \t[0.94951]\n",
      "3642 0.9393 \t[0.94051]\n",
      "3644 0.92363 \t[0.9215]\n",
      "3647 0.94223 \t[0.94247]\n",
      "3649 0.95104 \t[0.95115, 0.9515]\n",
      "3652 0.92419 \t[0.92404]\n",
      "3656 0.93163 \t[0.93291]\n",
      "3658 0.93167 \t[0.93232]\n",
      "3663 0.95061 \t[0.95112]\n",
      "3665 0.95008 \t[0.95025]\n",
      "3672 0.9307 \t[0.93246]\n",
      "3674 0.93073 \t[0.93159]\n",
      "3677 0.94931 \t[0.94961]\n",
      "3679 0.94966 \t[0.95008]\n",
      "3680 0.92251 \t[0.92203]\n",
      "3681 0.95827 \t[0.95843]\n",
      "3685 0.9497 \t[0.94998]\n",
      "3688 0.92288 \t[0.92209, 0.92246]\n",
      "3690 0.93892 \t[0.93801]\n",
      "3695 0.94185 \t[0.9408]\n",
      "3697 0.95846 \t[0.95861, 0.95866, 0.95819, 0.95868, 0.95778]\n",
      "3698 0.9313 \t[0.93153]\n",
      "3699 0.9428 \t[0.94284]\n",
      "3700 0.93163 \t[0.93041]\n",
      "3701 0.94989 \t[0.94942]\n",
      "3702 0.93873 \t[0.93963]\n",
      "3703 0.95023 \t[0.95076]\n",
      "3704 0.92307 \t[0.92418]\n",
      "3705 0.95027 \t[0.95084, 0.95068]\n",
      "3706 0.93911 \t[0.93923]\n",
      "3707 0.95061 \t[0.95025]\n",
      "3708 0.92344 \t[0.92447, 0.92303]\n",
      "3709 0.9577 \t[0.95712]\n",
      "3710 0.93054 \t[0.93136]\n",
      "3711 0.94204 \t[0.94259]\n",
      "3712 0.93088 \t[0.92969]\n",
      "3713 0.95066 \t[0.95036, 0.94986]\n",
      "3716 0.92381 \t[0.9219]\n",
      "3720 0.93125 \t[0.9314]\n",
      "3722 0.9313 \t[0.9316]\n",
      "3727 0.95023 \t[0.94969]\n",
      "3729 0.9497 \t[0.94999, 0.95036, 0.94905, 0.9499, 0.94947]\n",
      "3730 0.93854 \t[0.93912]\n",
      "3731 0.95004 \t[0.94955]\n",
      "3732 0.92288 \t[0.92197]\n",
      "3733 0.95712 \t[0.95731]\n",
      "3734 0.92998 \t[0.9303]\n",
      "3735 0.94147 \t[0.94225]\n",
      "3736 0.93032 \t[0.93107]\n",
      "3737 0.95751 \t[0.95747]\n",
      "3738 0.93036 \t[0.93043]\n",
      "3739 0.94185 \t[0.9417]\n",
      "3740 0.9307 \t[0.93185]\n",
      "3741 0.94893 \t[0.94881, 0.94804]\n",
      "3742 0.93779 \t[0.93844]\n",
      "3743 0.94928 \t[0.95003]\n",
      "3744 0.92214 \t[0.9213, 0.92018]\n",
      "3745 0.95789 \t[0.95722]\n",
      "3749 0.94931 \t[0.94786]\n",
      "3752 0.92251 \t[0.92265, 0.92034]\n",
      "3754 0.93854 \t[0.93761]\n",
      "3759 0.94147 \t[0.94083]\n",
      "3761 0.95808 \t[0.95825]\n",
      "3768 0.9227 \t[0.92199]\n",
      "3769 0.94989 \t[0.94885]\n",
      "3770 0.93873 \t[0.93805]\n",
      "3772 0.92307 \t[0.92103]\n",
      "3775 0.94166 \t[0.94085]\n",
      "3777 0.95046 \t[0.95106, 0.95019, 0.95063, 0.95079, 0.95102, 0.9513, 0.95026, 0.95076]\n",
      "3778 0.9393 \t[0.93904]\n",
      "3779 0.9508 \t[0.9511]\n",
      "3780 0.92363 \t[0.92298, 0.92503, 0.92414, 0.92375, 0.92395]\n",
      "3781 0.95789 \t[0.95881]\n",
      "3784 0.93107 \t[0.93288, 0.93192]\n",
      "3785 0.95827 \t[0.95791]\n",
      "3786 0.93111 \t[0.9328]\n",
      "3788 0.93144 \t[0.93111]\n",
      "3789 0.9497 \t[0.94994]\n",
      "3791 0.95004 \t[0.95002]\n",
      "3792 0.92288 \t[0.92334]\n",
      "3793 0.94951 \t[0.94881, 0.95078]\n",
      "3796 0.9227 \t[0.92378]\n",
      "3797 0.95693 \t[0.95816]\n",
      "3800 0.93014 \t[0.92922, 0.93121]\n",
      "3801 0.95731 \t[0.95795]\n",
      "3802 0.93017 \t[0.92872]\n",
      "3804 0.93051 \t[0.93204]\n",
      "3805 0.94874 \t[0.94885, 0.94871, 0.94919]\n",
      "3806 0.93761 \t[0.9369]\n",
      "3807 0.94909 \t[0.94873, 0.94936]\n",
      "3808 0.92195 \t[0.92138]\n",
      "3809 0.9577 \t[0.95791, 0.95816, 0.95778, 0.95781, 0.95766, 0.9573]\n",
      "3810 0.93054 \t[0.93104]\n",
      "3811 0.94204 \t[0.94193]\n",
      "3812 0.93088 \t[0.93056, 0.931]\n",
      "3813 0.94912 \t[0.9493, 0.94971, 0.94924, 0.94972]\n",
      "3814 0.93798 \t[0.93955, 0.93746]\n",
      "3815 0.94947 \t[0.95, 0.95004]\n",
      "3816 0.92232 \t[0.92291, 0.9219]\n",
      "3817 0.94951 \t[0.94962, 0.9495]\n",
      "3818 0.93836 \t[0.93853]\n",
      "3819 0.94985 \t[0.94959]\n",
      "3820 0.9227 \t[0.92437, 0.9234]\n",
      "3821 0.95693 \t[0.95713, 0.95752]\n",
      "3822 0.92979 \t[0.93113]\n",
      "3823 0.94128 \t[0.9418]\n",
      "3824 0.93014 \t[0.92989, 0.93195]\n",
      "3825 0.95789 \t[0.95791, 0.95812]\n",
      "3828 0.93107 \t[0.93142]\n",
      "3829 0.94931 \t[0.94988]\n",
      "3832 0.92251 \t[0.92411, 0.92389]\n",
      "3833 0.9497 \t[0.94993, 0.95018, 0.95017]\n",
      "3834 0.93854 \t[0.93945, 0.93861]\n",
      "3835 0.95004 \t[0.95079]\n",
      "3836 0.92288 \t[0.92286]\n",
      "3837 0.95712 \t[0.95735]\n",
      "3839 0.94147 \t[0.94162]\n",
      "3840 0.93032 \t[0.93085]\n",
      "3841 0.95124 \t[0.95228, 0.95137]\n",
      "3844 0.9246 \t[0.92402]\n",
      "3848 0.91605 \t[0.91584]\n",
      "3850 0.93203 \t[0.93288]\n",
      "3855 0.93487 \t[0.9351]\n",
      "3869 0.94953 \t[0.94987]\n",
      "3872 0.92294 \t[0.92279]\n",
      "3877 0.94991 \t[0.95037]\n",
      "3880 0.92331 \t[0.92315]\n",
      "3897 0.95048 \t[0.95084]\n",
      "3900 0.92386 \t[0.92364]\n",
      "3905 0.95105 \t[0.95086, 0.95068, 0.95182, 0.95203, 0.95155, 0.95093, 0.95128]\n",
      "3906 0.92403 \t[0.92317]\n",
      "3907 0.93544 \t[0.93669]\n",
      "3908 0.92442 \t[0.92359, 0.92645, 0.92547, 0.92545, 0.92466]\n",
      "3909 0.94248 \t[0.94348]\n",
      "3912 0.91586 \t[0.91725]\n",
      "3913 0.94286 \t[0.94295]\n",
      "3916 0.91623 \t[0.91769]\n",
      "3917 0.95029 \t[0.95029]\n",
      "3920 0.92368 \t[0.924]\n",
      "3921 0.9501 \t[0.95119]\n",
      "3924 0.92349 \t[0.92516]\n",
      "3925 0.94153 \t[0.94325]\n",
      "3928 0.91494 \t[0.91712]\n",
      "3929 0.94191 \t[0.94259]\n",
      "3932 0.91531 \t[0.91701]\n",
      "3933 0.94934 \t[0.9493, 0.94906, 0.94978]\n",
      "3934 0.92235 \t[0.92189]\n",
      "3935 0.93374 \t[0.93505]\n",
      "3936 0.92276 \t[0.92191]\n",
      "3937 0.94229 \t[0.9424]\n",
      "3940 0.91568 \t[0.91753]\n",
      "3941 0.94972 \t[0.95013, 0.94966, 0.95028]\n",
      "3942 0.92272 \t[0.92221]\n",
      "3943 0.93412 \t[0.93549]\n",
      "3944 0.92313 \t[0.92249]\n",
      "3945 0.9501 \t[0.95019]\n",
      "3948 0.92349 \t[0.92539]\n",
      "3949 0.94153 \t[0.94236]\n",
      "3952 0.91494 \t[0.91712]\n",
      "3953 0.94248 \t[0.94266, 0.94211]\n",
      "3956 0.91586 \t[0.91541]\n",
      "3957 0.94991 \t[0.95116]\n",
      "3960 0.92331 \t[0.92275, 0.92566]\n",
      "3961 0.95029 \t[0.95035, 0.95035, 0.95131]\n",
      "3962 0.92328 \t[0.92347, 0.92282]\n",
      "3963 0.93469 \t[0.93607]\n",
      "3964 0.92368 \t[0.92336]\n",
      "3965 0.94172 \t[0.94125]\n",
      "3967 0.94212 \t[0.94212]\n",
      "3968 0.91513 \t[0.91485]\n",
      "3969 0.95067 \t[0.95066]\n",
      "3972 0.92405 \t[0.92267]\n",
      "3985 0.94972 \t[0.95038]\n",
      "3992 0.91457 \t[0.91486]\n",
      "3994 0.93054 \t[0.93119]\n",
      "3997 0.94896 \t[0.94918]\n",
      "3999 0.93337 \t[0.93337]\n",
      "4000 0.92239 \t[0.92086]\n",
      "4005 0.94934 \t[0.94955]\n",
      "4008 0.92276 \t[0.92131]\n",
      "4025 0.94991 \t[0.94997]\n",
      "4028 0.92331 \t[0.92194]\n",
      "4033 0.95048 \t[0.95048]\n",
      "4036 0.92386 \t[0.92393]\n",
      "4061 0.94877 \t[0.94914]\n",
      "4064 0.9222 \t[0.92265]\n",
      "4065 0.94172 \t[0.94233]\n",
      "4069 0.94915 \t[0.94962]\n",
      "4072 0.92257 \t[0.92296, 0.92321]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4074 0.92254 \t[0.92375]\n",
      "4079 0.94137 \t[0.94211]\n",
      "4089 0.94972 \t[0.94995]\n",
      "4092 0.92313 \t[0.92349]\n"
     ]
    }
   ],
   "source": [
    "# our oracle so far\n",
    "for i in 1:4096\n",
    "    if estimateOracle[i]!=[]\n",
    "        print(\"$(string(i,pad=3)) $(round.(actualOracle[i],digits=5)) \\t$(round.(estimateOracle[i],digits=5))\\n\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: 0.0\n",
      "2: 2.4015768904846784e-7\n",
      "3: 1.50785789761816e-7\n",
      "4: 5.5323714558751604e-8\n",
      "5: 1.067059598645194e-8\n",
      "8: 2.8531740381809753e-7\n",
      "9: 2.178518349875181e-12\n",
      "10: 3.6463511391561535e-8\n",
      "12: 8.978581756069673e-9\n",
      "13: 2.225255542883944e-9\n",
      "15: 2.1334208117480867e-8\n",
      "16: 6.926519921658443e-13\n",
      "17: 1.5312982745800985e-9\n",
      "24: 6.749229610940465e-7\n",
      "29: 1.2017293611320204e-9\n",
      "31: 1.707874061484662e-7\n",
      "32: 1.7969543035492927e-7\n",
      "33: 1.104222462654191e-9\n",
      "37: 1.4479145023763648e-9\n",
      "40: 1.984939430390262e-7\n",
      "49: 1.6723242151334215e-9\n",
      "56: 2.5639669134587785e-8\n",
      "57: 1.0830137763592448e-9\n",
      "58: 4.5784731421970874e-7\n",
      "60: 8.16176005244911e-8\n",
      "65: 2.6193734717542385e-9\n",
      "104: 3.2508179925329365e-10\n",
      "113: 2.088257528286289e-8\n",
      "120: 9.614037103990904e-8\n",
      "121: 2.6409037014116985e-9\n",
      "122: 1.603564240416226e-7\n",
      "124: 1.4375850654322247e-7\n",
      "127: 2.708235179784811e-9\n",
      "129: 4.537805434562285e-11\n",
      "145: 7.090932120682458e-9\n",
      "152: 2.7684564203310423e-7\n",
      "154: 4.446460426170507e-8\n",
      "157: 6.808220002016595e-9\n",
      "159: 6.338869342992565e-8\n",
      "160: 1.0377913238822297e-6\n",
      "168: 1.053571970697729e-7\n",
      "193: 6.385078601262505e-10\n",
      "225: 2.0420629355926066e-8\n",
      "229: 1.29750825040717e-9\n",
      "232: 5.8631577914400964e-8\n",
      "234: 1.620010835872509e-7\n",
      "239: 5.992564289762187e-9\n",
      "257: 4.2664148076160086e-8\n",
      "385: 9.330785330151773e-9\n",
      "388: 8.093561334264893e-7\n",
      "401: 1.2327582034808143e-8\n",
      "408: 1.3775346123569166e-7\n",
      "413: 1.7159497368997825e-8\n",
      "415: 9.69019431535846e-8\n",
      "416: 1.6891119253041878e-6\n",
      "421: 9.941836291993947e-9\n",
      "424: 1.6829423975779585e-6\n",
      "441: 1.0868289754517585e-8\n",
      "444: 1.0382655030055923e-6\n",
      "488: 1.8559240997940965e-7\n",
      "513: 6.408912777328474e-8\n",
      "705: 2.922239960522234e-7\n",
      "708: 8.641818862476931e-7\n",
      "733: 6.803089511462973e-7\n",
      "736: 3.7090480128720713e-6\n",
      "737: 2.1830126153255827e-8\n",
      "741: 5.617714951240028e-7\n",
      "744: 2.0538835547566247e-6\n",
      "761: 2.918328786678761e-7\n",
      "764: 1.4721605883543292e-6\n",
      "769: 6.073159664694409e-7\n",
      "833: 3.28943748507194e-7\n",
      "836: 9.400011863840682e-7\n",
      "861: 4.823371021199301e-7\n",
      "864: 2.177962934752857e-6\n",
      "869: 2.730425286072919e-7\n",
      "872: 1.0820167043890086e-6\n",
      "881: 1.6383379811744987e-7\n",
      "888: 3.954249261521601e-6\n",
      "889: 2.795444133184951e-7\n",
      "890: 4.970629739022461e-7\n",
      "892: 3.1970290341035076e-7\n",
      "1000: 8.306363002285679e-9\n",
      "1025: 2.3873333841197416e-10\n",
      "1768: 1.9931300494325615e-7\n",
      "1793: 1.8410736567586368e-7\n",
      "1800: 7.66154639475543e-7\n",
      "1802: 6.188337397599058e-7\n",
      "1807: 1.0306511447215306e-7\n",
      "1857: 6.714753517726496e-8\n",
      "1896: 9.694711692774297e-8\n",
      "1905: 2.420756496712187e-7\n",
      "1913: 2.863919891504028e-7\n",
      "1916: 7.440184193767592e-7\n",
      "1937: 3.2789342654248177e-7\n",
      "2017: 4.0223842218355667e-7\n",
      "2049: 1.3078797438694954e-9\n",
      "2305: 5.4670779945779684e-8\n",
      "2312: 1.1822062634335761e-7\n",
      "2314: 5.267996550510961e-7\n",
      "2319: 2.5713191119883205e-8\n",
      "2417: 1.288276161223577e-8\n",
      "2433: 1.8490205581463577e-7\n",
      "2449: 6.54066058081546e-8\n",
      "2461: 6.133449024574238e-8\n",
      "2464: 1.733303941173275e-7\n",
      "2472: 3.4357097001563734e-9\n",
      "2529: 7.096928855038355e-9\n",
      "2792: 2.7502707036739298e-6\n",
      "3073: 8.723738208658598e-10\n",
      "3076: 3.8355519333863964e-8\n",
      "3080: 4.046492125637285e-7\n",
      "3101: 4.48153615520223e-10\n",
      "3104: 7.515189020295687e-8\n",
      "3109: 2.3351707709582795e-9\n",
      "3112: 3.8060291542554694e-8\n",
      "3129: 2.780038721462716e-10\n",
      "3132: 4.37952840295822e-8\n",
      "3304: 1.497099267723311e-8\n",
      "3329: 2.2179417299015104e-8\n",
      "3457: 2.458976713148626e-8\n",
      "3460: 4.7003710011808296e-7\n",
      "3473: 1.227166523407743e-8\n",
      "3480: 1.1884852181649184e-7\n",
      "3485: 8.33161475432735e-8\n",
      "3487: 2.2853536877679304e-7\n",
      "3493: 5.5624271403751925e-8\n",
      "3513: 4.277733871629999e-8\n",
      "3560: 4.732738521807581e-7\n",
      "3585: 1.7286320075454504e-7\n",
      "3588: 1.7227208847230142e-6\n",
      "3592: 7.641249503764565e-7\n",
      "3594: 1.1409508023945698e-6\n",
      "3599: 2.3653396514852813e-7\n",
      "3624: 3.3189234193274346e-6\n",
      "3649: 6.38890928970502e-8\n",
      "3688: 6.579179851124789e-8\n",
      "3697: 1.5494455279657186e-7\n",
      "3705: 1.3672483987419606e-8\n",
      "3708: 1.0392572166708177e-6\n",
      "3713: 1.269578984479865e-7\n",
      "3729: 2.572206123381697e-7\n",
      "3741: 2.921706243673055e-7\n",
      "3744: 6.280704050813674e-7\n",
      "3752: 2.6677781876079027e-6\n",
      "3777: 1.4775148266121797e-7\n",
      "3780: 5.445666410423697e-7\n",
      "3784: 4.643694515894267e-7\n",
      "3793: 1.939967938361251e-6\n",
      "3800: 1.9722413112912866e-6\n",
      "3805: 6.095236110019247e-8\n",
      "3807: 2.0312418117816616e-7\n",
      "3809: 7.981508547007415e-8\n",
      "3812: 9.932768029113756e-8\n",
      "3813: 6.726989098052332e-8\n",
      "3814: 2.1850046833112867e-6\n",
      "3815: 1.2121559016753712e-9\n",
      "3816: 5.130463314441521e-7\n",
      "3817: 6.518124781276381e-9\n",
      "3820: 4.7126618875536286e-7\n",
      "3821: 7.668441123901582e-8\n",
      "3824: 2.129909051743053e-6\n",
      "3825: 2.2417024928082872e-8\n",
      "3832: 2.4408009838343956e-8\n",
      "3833: 2.016529939682111e-8\n",
      "3834: 3.4590110716898126e-7\n",
      "3841: 4.103363701392373e-7\n",
      "3905: 2.620348419302889e-7\n",
      "3908: 1.1362440348252749e-6\n",
      "3933: 1.3572608238795897e-7\n",
      "3941: 1.0144306995629207e-7\n",
      "3953: 1.505988073883599e-7\n",
      "3960: 4.242270907107228e-6\n",
      "3961: 3.026229944607843e-7\n",
      "3962: 2.1207015172951415e-7\n",
      "4072: 3.198161859483364e-8\n"
     ]
    }
   ],
   "source": [
    "using Statistics\n",
    "# So we can get an idea of the variance in the oracle (where we have fidelities)\n",
    "# This is based off 1,000 shots per 'experiment sequence'\n",
    "for (ix,i) in enumerate(estimateOracle)\n",
    "    if length(i) > 1 \n",
    "        print(\"$ix: $(var(i))\\n\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4096-element Array{Real,1}:\n",
       " 1.0\n",
       " 0.9720988936902138\n",
       " 0.9840623974961618\n",
       " 0.9720291467193548\n",
       " 0.9913625817827061\n",
       " 0.9795678213424949\n",
       " 0.99153629425895\n",
       " 0.9636106976757578\n",
       " 0.9917309645128152\n",
       " 0.9798848056702893\n",
       " 0.9917306043528243\n",
       " 0.9641518473962647\n",
       " 0.9992037586930189\n",
       " ⋮\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0.9499529053266064\n",
       " 0\n",
       " 0\n",
       " 0.9234866856425643\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get our oracle single figure\n",
    "oracleToUse = [length(x) > 0 ? mean(x) : 0 for x in estimateOracle]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual error in the eigenvalues estimated\n",
      "0001: IIIIII: 0.0%\n",
      "0002: IIIIIX: 0.01%\n",
      "0003: IIIIIY: 0.006%\n",
      "0004: IIIIIZ: 0.003%\n",
      "0005: IIIIXI: -0.004%\n",
      "0006: IIIIXX: 0.016%\n",
      "0007: IIIIXY: 0.013%\n",
      "0008: IIIIXZ: 0.02%\n",
      "0009: IIIIYI: -0.007%\n",
      "0010: IIIIYX: 0.008%\n",
      "0011: IIIIYY: -0.007%\n",
      "0012: IIIIYZ: 0.036%\n",
      "0013: IIIIZI: 0.0%\n",
      "0014: IIIIZX: -0.023%\n",
      "0015: IIIIZY: 0.002%\n",
      "0016: IIIIZZ: 0.043%\n",
      "0017: IIIXII: 0.002%\n",
      "0020: IIIXIZ: 0.041%\n",
      "0021: IIIXXI: -0.011%\n",
      "0024: IIIXXZ: 0.025%\n",
      "0025: IIIXYI: 0.003%\n",
      "0026: IIIXYX: 0.02%\n",
      "0028: IIIXYZ: 0.011%\n",
      "0029: IIIXZI: -0.002%\n",
      "0030: IIIXZX: -0.032%\n",
      "0031: IIIXZY: 0.006%\n",
      "0032: IIIXZZ: 0.001%\n",
      "0033: IIIYII: -0.001%\n",
      "0036: IIIYIZ: 0.045%\n",
      "0037: IIIYXI: 0.0%\n",
      "0038: IIIYXX: -0.038%\n",
      "0039: IIIYXY: 0.029%\n",
      "0040: IIIYXZ: -0.006%\n",
      "0041: IIIYYI: 0.002%\n",
      "0042: IIIYYX: -0.024%\n",
      "0044: IIIYYZ: 0.005%\n",
      "0045: IIIYZI: 0.004%\n",
      "0047: IIIYZY: -0.007%\n",
      "0048: IIIYZZ: 0.046%\n",
      "0049: IIIZII: -0.0%\n",
      "0052: IIIZIZ: 0.041%\n",
      "0053: IIIZXI: 0.005%\n",
      "0056: IIIZXZ: -0.0%\n",
      "0057: IIIZYI: -0.0%\n",
      "0058: IIIZYX: 0.019%\n",
      "0059: IIIZYY: 0.04%\n",
      "0060: IIIZYZ: -0.003%\n",
      "0061: IIIZZI: -0.007%\n",
      "0063: IIIZZY: -0.001%\n",
      "0064: IIIZZZ: 0.078%\n",
      "0065: IIXIII: -0.001%\n",
      "0068: IIXIIZ: -0.009%\n",
      "0072: IIXIXZ: -0.068%\n",
      "0074: IIXIYX: 0.006%\n",
      "0079: IIXIZY: -0.008%\n",
      "0081: IIXXII: 0.009%\n",
      "0088: IIXXXZ: -0.052%\n",
      "0090: IIXXYX: 0.004%\n",
      "0093: IIXXZI: -0.014%\n",
      "0095: IIXXZY: -0.012%\n",
      "0096: IIXXZZ: -0.006%\n",
      "0097: IIXYII: -0.009%\n",
      "0101: IIXYXI: -0.007%\n",
      "0104: IIXYXZ: 0.0%\n",
      "0106: IIXYYX: 0.017%\n",
      "0111: IIXYZY: -0.004%\n",
      "0113: IIXZII: 0.006%\n",
      "0114: IIXZIX: 0.024%\n",
      "0115: IIXZIY: -0.022%\n",
      "0116: IIXZIZ: 0.074%\n",
      "0117: IIXZXI: 0.001%\n",
      "0118: IIXZXX: 0.054%\n",
      "0119: IIXZXY: 0.011%\n",
      "0120: IIXZXZ: 0.034%\n",
      "0121: IIXZYI: -0.006%\n",
      "0122: IIXZYX: 0.027%\n",
      "0123: IIXZYY: -0.029%\n",
      "0124: IIXZYZ: 0.003%\n",
      "0125: IIXZZI: 0.004%\n",
      "0126: IIXZZX: -0.027%\n",
      "0127: IIXZZY: 0.007%\n",
      "0128: IIXZZZ: 0.076%\n",
      "0129: IIYIII: 0.002%\n",
      "0132: IIYIIZ: -0.085%\n",
      "0136: IIYIXZ: -0.039%\n",
      "0138: IIYIYX: -0.063%\n",
      "0143: IIYIZY: 0.016%\n",
      "0145: IIYXII: -0.001%\n",
      "0146: IIYXIX: 0.06%\n",
      "0147: IIYXIY: -0.051%\n",
      "0148: IIYXIZ: 0.01%\n",
      "0149: IIYXXI: 0.019%\n",
      "0150: IIYXXX: 0.026%\n",
      "0151: IIYXXY: 0.011%\n",
      "0152: IIYXXZ: 0.031%\n",
      "0153: IIYXYI: -0.02%\n",
      "0154: IIYXYX: -0.003%\n",
      "0155: IIYXYY: -0.028%\n",
      "0156: IIYXYZ: 0.049%\n",
      "0157: IIYXZI: 0.003%\n",
      "0158: IIYXZX: -0.011%\n",
      "0159: IIYXZY: 0.014%\n",
      "0160: IIYXZZ: -0.038%\n",
      "0161: IIYYII: 0.017%\n",
      "0165: IIYYXI: 0.008%\n",
      "0168: IIYYXZ: -0.102%\n",
      "0170: IIYYYX: -0.047%\n",
      "0175: IIYYZY: -0.011%\n",
      "0177: IIYZII: -0.023%\n",
      "0184: IIYZXZ: 0.007%\n",
      "0185: IIYZYI: 0.006%\n",
      "0186: IIYZYX: 0.02%\n",
      "0188: IIYZYZ: -0.094%\n",
      "0191: IIYZZY: -0.019%\n",
      "0193: IIZIII: 0.0%\n",
      "0196: IIZIIZ: -0.005%\n",
      "0200: IIZIXZ: 0.012%\n",
      "0202: IIZIYX: 0.004%\n",
      "0207: IIZIZY: -0.003%\n",
      "0209: IIZXII: 0.003%\n",
      "0216: IIZXXZ: 0.057%\n",
      "0218: IIZXYX: 0.037%\n",
      "0221: IIZXZI: -0.001%\n",
      "0223: IIZXZY: -0.016%\n",
      "0224: IIZXZZ: 0.011%\n",
      "0225: IIZYII: 0.005%\n",
      "0226: IIZYIX: 0.016%\n",
      "0227: IIZYIY: -0.02%\n",
      "0228: IIZYIZ: 0.095%\n",
      "0229: IIZYXI: -0.0%\n",
      "0230: IIZYXX: 0.052%\n",
      "0231: IIZYXY: 0.022%\n",
      "0232: IIZYXZ: 0.017%\n",
      "0233: IIZYYI: -0.009%\n",
      "0234: IIZYYX: 0.012%\n",
      "0235: IIZYYY: -0.042%\n",
      "0236: IIZYYZ: 0.025%\n",
      "0237: IIZYZI: 0.007%\n",
      "0238: IIZYZX: -0.02%\n",
      "0239: IIZYZY: 0.008%\n",
      "0240: IIZYZZ: 0.095%\n",
      "0241: IIZZII: -0.002%\n",
      "0248: IIZZXZ: 0.008%\n",
      "0249: IIZZYI: 0.003%\n",
      "0250: IIZZYX: 0.071%\n",
      "0252: IIZZYZ: 0.007%\n",
      "0255: IIZZZY: -0.008%\n",
      "0257: IXIIII: 0.031%\n",
      "0260: IXIIIZ: 0.028%\n",
      "0264: IXIIXZ: 0.09%\n",
      "0266: IXIIYX: -0.029%\n",
      "0271: IXIIZY: 0.015%\n",
      "0285: IXIXZI: 0.04%\n",
      "0288: IXIXZZ: 0.025%\n",
      "0293: IXIYXI: 0.038%\n",
      "0296: IXIYXZ: -0.015%\n",
      "0313: IXIZYI: 0.035%\n",
      "0316: IXIZYZ: 0.003%\n",
      "0321: IXXIII: 0.027%\n",
      "0324: IXXIIZ: -0.006%\n",
      "0349: IXXXZI: 0.017%\n",
      "0352: IXXXZZ: -0.022%\n",
      "0357: IXXYXI: 0.014%\n",
      "0360: IXXYXZ: -0.051%\n",
      "0369: IXXZII: -0.014%\n",
      "0376: IXXZXZ: 0.04%\n",
      "0377: IXXZYI: 0.014%\n",
      "0378: IXXZYX: 0.015%\n",
      "0380: IXXZYZ: -0.03%\n",
      "0383: IXXZZY: -0.006%\n",
      "0385: IXYIII: -0.012%\n",
      "0386: IXYIIX: -0.052%\n",
      "0387: IXYIIY: -0.03%\n",
      "0388: IXYIIZ: 0.027%\n",
      "0389: IXYIXI: 0.0%\n",
      "0392: IXYIXZ: 0.086%\n",
      "0393: IXYIYI: -0.002%\n",
      "0396: IXYIYZ: 0.126%\n",
      "0397: IXYIZI: 0.002%\n",
      "0400: IXYIZZ: 0.055%\n",
      "0401: IXYXII: -0.005%\n",
      "0404: IXYXIZ: 0.109%\n",
      "0405: IXYXXI: -0.001%\n",
      "0408: IXYXXZ: 0.084%\n",
      "0409: IXYXYI: 0.009%\n",
      "0410: IXYXYX: -0.077%\n",
      "0412: IXYXYZ: 0.075%\n",
      "0413: IXYXZI: -0.019%\n",
      "0414: IXYXZX: -0.068%\n",
      "0415: IXYXZY: -0.01%\n",
      "0416: IXYXZZ: -0.023%\n",
      "0417: IXYYII: -0.003%\n",
      "0420: IXYYIZ: 0.15%\n",
      "0421: IXYYXI: -0.018%\n",
      "0422: IXYYXX: -0.06%\n",
      "0423: IXYYXY: -0.031%\n",
      "0424: IXYYXZ: -0.019%\n",
      "0425: IXYYYI: 0.006%\n",
      "0428: IXYYYZ: 0.192%\n",
      "0429: IXYYZI: 0.009%\n",
      "0432: IXYYZZ: 0.096%\n",
      "0433: IXYZII: 0.013%\n",
      "0436: IXYZIZ: -0.006%\n",
      "0437: IXYZXI: -0.009%\n",
      "0440: IXYZXZ: 0.083%\n",
      "0441: IXYZYI: -0.013%\n",
      "0442: IXYZYX: -0.051%\n",
      "0443: IXYZYY: -0.031%\n",
      "0444: IXYZYZ: -0.021%\n",
      "0445: IXYZZI: 0.004%\n",
      "0448: IXYZZZ: 0.026%\n",
      "0449: IXZIII: 0.042%\n",
      "0452: IXZIIZ: 0.02%\n",
      "0477: IXZXZI: 0.028%\n",
      "0480: IXZXZZ: -0.023%\n",
      "0481: IXZYII: -0.012%\n",
      "0485: IXZYXI: 0.038%\n",
      "0488: IXZYXZ: 0.002%\n",
      "0490: IXZYYX: 0.01%\n",
      "0495: IXZYZY: 0.005%\n",
      "0505: IXZZYI: 0.04%\n",
      "0508: IXZZYZ: -0.009%\n",
      "0513: IYIIII: -0.039%\n",
      "0516: IYIIIZ: -0.232%\n",
      "0520: IYIIXZ: -0.022%\n",
      "0522: IYIIYX: -0.034%\n",
      "0527: IYIIZY: -0.046%\n",
      "0541: IYIXZI: -0.083%\n",
      "0544: IYIXZZ: -0.251%\n",
      "0549: IYIYXI: -0.132%\n",
      "0552: IYIYXZ: -0.263%\n",
      "0569: IYIZYI: -0.096%\n",
      "0572: IYIZYZ: -0.246%\n",
      "0577: IYXIII: 0.06%\n",
      "0580: IYXIIZ: -0.002%\n",
      "0605: IYXXZI: 0.047%\n",
      "0608: IYXXZZ: -0.03%\n",
      "0613: IYXYXI: 0.046%\n",
      "0616: IYXYXZ: -0.025%\n",
      "0625: IYXZII: -0.048%\n",
      "0632: IYXZXZ: 0.059%\n",
      "0633: IYXZYI: 0.053%\n",
      "0634: IYXZYX: -0.084%\n",
      "0636: IYXZYZ: -0.033%\n",
      "0639: IYXZZY: 0.037%\n",
      "0641: IYYIII: -0.075%\n",
      "0644: IYYIIZ: -0.215%\n",
      "0657: IYYXII: -0.016%\n",
      "0664: IYYXXZ: -0.024%\n",
      "0666: IYYXYX: -0.005%\n",
      "0669: IYYXZI: -0.084%\n",
      "0671: IYYXZY: -0.05%\n",
      "0672: IYYXZZ: -0.219%\n",
      "0677: IYYYXI: -0.144%\n",
      "0680: IYYYXZ: -0.239%\n",
      "0697: IYYZYI: -0.104%\n",
      "0700: IYYZYZ: -0.231%\n",
      "0705: IYZIII: 0.024%\n",
      "0706: IYZIIX: -0.045%\n",
      "0707: IYZIIY: 0.04%\n",
      "0708: IYZIIZ: 0.04%\n",
      "0709: IYZIXI: 0.077%\n",
      "0712: IYZIXZ: 0.112%\n",
      "0713: IYZIYI: -0.02%\n",
      "0716: IYZIYZ: -0.045%\n",
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     "name": "stdout",
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      "2554: YXZZYX: 0.013%\n",
      "2559: YXZZZY: -0.036%\n",
      "2561: YYIIII: -0.015%\n",
      "2568: YYIIXZ: -0.023%\n",
      "2570: YYIIYX: 0.014%\n",
      "2575: YYIIZY: -0.051%\n",
      "2673: YYXZII: -0.062%\n",
      "2680: YYXZXZ: 0.048%\n",
      "2682: YYXZYX: -0.091%\n",
      "2687: YYXZZY: 0.035%\n",
      "2705: YYYXII: -0.031%\n",
      "2712: YYYXXZ: -0.035%\n",
      "2714: YYYXYX: -0.014%\n",
      "2719: YYYXZY: -0.064%\n",
      "2753: YYZIII: 0.115%\n",
      "2756: YYZIIZ: 0.186%\n",
      "2781: YYZXZI: 0.182%\n",
      "2784: YYZXZZ: 0.3%\n",
      "2785: YYZYII: -0.043%\n",
      "2789: YYZYXI: 0.174%\n",
      "2792: YYZYXZ: 0.166%\n",
      "2794: YYZYYX: -0.106%\n",
      "2799: YYZYZY: 0.027%\n",
      "2809: YYZZYI: 0.134%\n",
      "2812: YYZZYZ: 0.207%\n",
      "2817: YZIIII: 0.01%\n",
      "2824: YZIIXZ: -0.06%\n",
      "2826: YZIIYX: -0.122%\n",
      "2831: YZIIZY: -0.041%\n",
      "2881: YZXIII: 0.113%\n",
      "2884: YZXIIZ: 0.124%\n",
      "2909: YZXXZI: 0.131%\n",
      "2912: YZXXZZ: 0.24%\n",
      "2917: YZXYXI: 0.089%\n",
      "2920: YZXYXZ: 0.188%\n",
      "2929: YZXZII: -0.039%\n",
      "2936: YZXZXZ: 0.075%\n",
      "2937: YZXZYI: 0.105%\n",
      "2938: YZXZYX: -0.063%\n",
      "2940: YZXZYZ: 0.127%\n",
      "2943: YZXZZY: 0.004%\n",
      "2961: YZYXII: 0.047%\n",
      "2968: YZYXXZ: 0.068%\n",
      "2970: YZYXYX: -0.041%\n",
      "2975: YZYXZY: 0.027%\n",
      "3041: YZZYII: -0.069%\n",
      "3048: YZZYXZ: -0.005%\n",
      "3050: YZZYYX: -0.111%\n",
      "3055: YZZYZY: 0.011%\n",
      "3073: ZIIIII: 0.001%\n",
      "3074: ZIIIIX: -0.008%\n",
      "3075: ZIIIIY: 0.035%\n",
      "3076: ZIIIIZ: 0.0%\n",
      "3077: ZIIIXI: -0.006%\n",
      "3080: ZIIIXZ: 0.026%\n",
      "3081: ZIIIYI: -0.007%\n",
      "3082: ZIIIYX: 0.027%\n",
      "3084: ZIIIYZ: 0.045%\n",
      "3085: ZIIIZI: 0.001%\n",
      "3087: ZIIIZY: 0.024%\n",
      "3088: ZIIIZZ: 0.033%\n",
      "3089: ZIIXII: -0.003%\n",
      "3092: ZIIXIZ: 0.047%\n",
      "3093: ZIIXXI: -0.005%\n",
      "3096: ZIIXXZ: 0.094%\n",
      "3097: ZIIXYI: 0.001%\n",
      "3100: ZIIXYZ: -0.017%\n",
      "3101: ZIIXZI: -0.001%\n",
      "3102: ZIIXZX: -0.01%\n",
      "3103: ZIIXZY: 0.035%\n",
      "3104: ZIIXZZ: -0.01%\n",
      "3105: ZIIYII: -0.004%\n",
      "3108: ZIIYIZ: 0.066%\n",
      "3109: ZIIYXI: -0.0%\n",
      "3110: ZIIYXX: -0.017%\n",
      "3111: ZIIYXY: 0.028%\n",
      "3112: ZIIYXZ: -0.004%\n",
      "3113: ZIIYYI: 0.003%\n",
      "3116: ZIIYYZ: 0.007%\n",
      "3117: ZIIYZI: 0.003%\n",
      "3120: ZIIYZZ: 0.025%\n",
      "3121: ZIIZII: -0.001%\n",
      "3124: ZIIZIZ: 0.028%\n",
      "3125: ZIIZXI: 0.003%\n",
      "3128: ZIIZXZ: 0.006%\n",
      "3129: ZIIZYI: 0.001%\n",
      "3130: ZIIZYX: -0.008%\n",
      "3131: ZIIZYY: 0.043%\n",
      "3132: ZIIZYZ: -0.005%\n",
      "3133: ZIIZZI: -0.004%\n",
      "3136: ZIIZZZ: 0.064%\n",
      "3137: ZIXIII: 0.001%\n",
      "3140: ZIXIIZ: -0.013%\n",
      "3165: ZIXXZI: -0.007%\n",
      "3168: ZIXXZZ: -0.007%\n",
      "3173: ZIXYXI: -0.002%\n",
      "3176: ZIXYXZ: -0.001%\n",
      "3185: ZIXZII: 0.019%\n",
      "3192: ZIXZXZ: -0.001%\n",
      "3193: ZIXZYI: -0.005%\n",
      "3194: ZIXZYX: 0.079%\n",
      "3196: ZIXZYZ: -0.022%\n",
      "3199: ZIXZZY: 0.016%\n",
      "3201: ZIYIII: -0.001%\n",
      "3204: ZIYIIZ: -0.067%\n",
      "3217: ZIYXII: 0.001%\n",
      "3224: ZIYXXZ: 0.014%\n",
      "3226: ZIYXYX: 0.034%\n",
      "3229: ZIYXZI: 0.005%\n",
      "3231: ZIYXZY: 0.049%\n",
      "3232: ZIYXZZ: -0.097%\n",
      "3237: ZIYYXI: 0.006%\n",
      "3240: ZIYYXZ: -0.059%\n",
      "3257: ZIYZYI: 0.004%\n",
      "3260: ZIYZYZ: -0.073%\n",
      "3265: ZIZIII: -0.001%\n",
      "3268: ZIZIIZ: 0.013%\n",
      "3293: ZIZXZI: -0.005%\n",
      "3296: ZIZXZZ: 0.026%\n",
      "3297: ZIZYII: 0.014%\n",
      "3301: ZIZYXI: -0.005%\n",
      "3304: ZIZYXZ: 0.002%\n",
      "3306: ZIZYYX: 0.054%\n",
      "3311: ZIZYZY: -0.001%\n",
      "3321: ZIZZYI: -0.001%\n",
      "3324: ZIZZYZ: 0.028%\n",
      "3329: ZXIIII: 0.031%\n",
      "3332: ZXIIIZ: 0.023%\n",
      "3336: ZXIIXZ: 0.056%\n",
      "3338: ZXIIYX: 0.024%\n",
      "3343: ZXIIZY: 0.032%\n",
      "3357: ZXIXZI: 0.041%\n",
      "3360: ZXIXZZ: 0.018%\n",
      "3365: ZXIYXI: 0.038%\n",
      "3368: ZXIYXZ: -0.027%\n",
      "3385: ZXIZYI: 0.032%\n",
      "3388: ZXIZYZ: -0.003%\n",
      "3393: ZXXIII: 0.025%\n",
      "3396: ZXXIIZ: -0.012%\n",
      "3421: ZXXXZI: 0.02%\n",
      "3424: ZXXXZZ: -0.03%\n",
      "3429: ZXXYXI: 0.016%\n",
      "3432: ZXXYXZ: -0.061%\n",
      "3441: ZXXZII: 0.047%\n",
      "3448: ZXXZXZ: 0.125%\n",
      "3449: ZXXZYI: 0.014%\n",
      "3450: ZXXZYX: 0.012%\n",
      "3452: ZXXZYZ: -0.038%\n",
      "3455: ZXXZZY: 0.049%\n",
      "3457: ZXYIII: -0.007%\n",
      "3458: ZXYIIX: -0.036%\n",
      "3459: ZXYIIY: -0.024%\n",
      "3460: ZXYIIZ: 0.048%\n",
      "3461: ZXYIXI: 0.011%\n",
      "3464: ZXYIXZ: 0.092%\n",
      "3465: ZXYIYI: -0.005%\n",
      "3468: ZXYIYZ: 0.143%\n",
      "3469: ZXYIZI: 0.01%\n",
      "3472: ZXYIZZ: 0.02%\n",
      "3473: ZXYXII: 0.027%\n",
      "3476: ZXYXIZ: 0.108%\n",
      "3477: ZXYXXI: 0.008%\n",
      "3480: ZXYXXZ: 0.093%\n",
      "3481: ZXYXYI: 0.016%\n",
      "3482: ZXYXYX: 0.032%\n",
      "3484: ZXYXYZ: 0.047%\n",
      "3485: ZXYXZI: -0.017%\n",
      "3486: ZXYXZX: -0.049%\n",
      "3487: ZXYXZY: 0.012%\n",
      "3488: ZXYXZZ: 0.019%\n",
      "3489: ZXYYII: -0.005%\n",
      "3492: ZXYYIZ: 0.168%\n",
      "3493: ZXYYXI: -0.012%\n",
      "3494: ZXYYXX: -0.036%\n",
      "3495: ZXYYXY: -0.025%\n",
      "3496: ZXYYXZ: 0.018%\n",
      "3497: ZXYYYI: 0.004%\n",
      "3500: ZXYYYZ: 0.218%\n",
      "3501: ZXYYZI: 0.015%\n",
      "3504: ZXYYZZ: 0.069%\n",
      "3505: ZXYZII: 0.021%\n",
      "3508: ZXYZIZ: -0.02%\n",
      "3509: ZXYZXI: -0.009%\n",
      "3512: ZXYZXZ: 0.046%\n",
      "3513: ZXYZYI: -0.009%\n",
      "3514: ZXYZYX: -0.027%\n",
      "3515: ZXYZYY: -0.024%\n",
      "3516: ZXYZYZ: 0.009%\n",
      "3517: ZXYZZI: 0.015%\n",
      "3520: ZXYZZZ: 0.008%\n",
      "3521: ZXZIII: 0.044%\n",
      "3524: ZXZIIZ: 0.021%\n",
      "3549: ZXZXZI: 0.03%\n",
      "3552: ZXZXZZ: -0.029%\n",
      "3553: ZXZYII: 0.038%\n",
      "3557: ZXZYXI: 0.037%\n",
      "3560: ZXZYXZ: 0.012%\n",
      "3562: ZXZYYX: 0.018%\n",
      "3567: ZXZYZY: 0.072%\n",
      "3577: ZXZZYI: 0.044%\n",
      "3580: ZXZZYZ: -0.012%\n",
      "3585: ZYIIII: 0.011%\n",
      "3586: ZYIIIX: 0.104%\n",
      "3587: ZYIIIY: 0.007%\n",
      "3588: ZYIIIZ: -0.118%\n",
      "3589: ZYIIXI: 0.041%\n",
      "3590: ZYIIXX: 0.072%\n",
      "3591: ZYIIXY: 0.087%\n",
      "3592: ZYIIXZ: 0.051%\n",
      "3593: ZYIIYI: 0.039%\n",
      "3594: ZYIIYX: 0.038%\n",
      "3595: ZYIIYY: 0.008%\n",
      "3596: ZYIIYZ: 0.108%\n",
      "3597: ZYIIZI: 0.037%\n",
      "3598: ZYIIZX: 0.02%\n",
      "3599: ZYIIZY: 0.018%\n",
      "3600: ZYIIZZ: -0.029%\n",
      "3601: ZYIXII: 0.034%\n",
      "3608: ZYIXXZ: 0.17%\n",
      "3610: ZYIXYX: 0.045%\n",
      "3613: ZYIXZI: -0.093%\n",
      "3615: ZYIXZY: 0.047%\n",
      "3616: ZYIXZZ: -0.238%\n",
      "3617: ZYIYII: -0.046%\n",
      "3621: ZYIYXI: -0.14%\n",
      "3624: ZYIYXZ: -0.114%\n",
      "3626: ZYIYYX: -0.039%\n",
      "3631: ZYIYZY: -0.043%\n",
      "3633: ZYIZII: 0.049%\n",
      "3640: ZYIZXZ: 0.154%\n",
      "3641: ZYIZYI: -0.1%\n",
      "3642: ZYIZYX: 0.129%\n",
      "3644: ZYIZYZ: -0.23%\n",
      "3647: ZYIZZY: 0.026%\n",
      "3649: ZYXIII: 0.03%\n",
      "3652: ZYXIIZ: -0.016%\n",
      "3656: ZYXIXZ: 0.138%\n",
      "3658: ZYXIYX: 0.07%\n",
      "3663: ZYXIZY: 0.054%\n",
      "3665: ZYXXII: 0.018%\n",
      "3672: ZYXXXZ: 0.189%\n",
      "3674: ZYXXYX: 0.092%\n",
      "3677: ZYXXZI: 0.031%\n",
      "3679: ZYXXZY: 0.045%\n",
      "3680: ZYXXZZ: -0.052%\n",
      "3681: ZYXYII: 0.017%\n",
      "3685: ZYXYXI: 0.03%\n",
      "3688: ZYXYXZ: -0.066%\n",
      "3690: ZYXYYX: -0.097%\n",
      "3695: ZYXYZY: -0.111%\n",
      "3697: ZYXZII: -0.009%\n",
      "3698: ZYXZIX: 0.025%\n",
      "3699: ZYXZIY: 0.005%\n",
      "3700: ZYXZIZ: -0.131%\n",
      "3701: ZYXZXI: -0.049%\n",
      "3702: ZYXZXX: 0.096%\n",
      "3703: ZYXZXY: 0.057%\n",
      "3704: ZYXZXZ: 0.12%\n",
      "3705: ZYXZYI: 0.051%\n",
      "3706: ZYXZYX: 0.013%\n",
      "3707: ZYXZYY: -0.038%\n",
      "3708: ZYXZYZ: 0.033%\n",
      "3709: ZYXZZI: -0.06%\n",
      "3710: ZYXZZX: 0.088%\n",
      "3711: ZYXZZY: 0.059%\n",
      "3712: ZYXZZZ: -0.128%\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3713: ZYYIII: -0.058%\n",
      "3716: ZYYIIZ: -0.207%\n",
      "3720: ZYYIXZ: 0.016%\n",
      "3722: ZYYIYX: 0.033%\n",
      "3727: ZYYIZY: -0.056%\n",
      "3729: ZYYXII: 0.006%\n",
      "3730: ZYYXIX: 0.062%\n",
      "3731: ZYYXIY: -0.051%\n",
      "3732: ZYYXIZ: -0.098%\n",
      "3733: ZYYXXI: 0.02%\n",
      "3734: ZYYXXX: 0.034%\n",
      "3735: ZYYXXY: 0.083%\n",
      "3736: ZYYXXZ: 0.08%\n",
      "3737: ZYYXYI: -0.003%\n",
      "3738: ZYYXYX: 0.008%\n",
      "3739: ZYYXYY: -0.016%\n",
      "3740: ZYYXYZ: 0.124%\n",
      "3741: ZYYXZI: -0.053%\n",
      "3742: ZYYXZX: 0.069%\n",
      "3743: ZYYXZY: 0.079%\n",
      "3744: ZYYXZZ: -0.151%\n",
      "3745: ZYYYII: -0.07%\n",
      "3749: ZYYYXI: -0.154%\n",
      "3752: ZYYYXZ: -0.11%\n",
      "3754: ZYYYYX: -0.1%\n",
      "3759: ZYYYZY: -0.068%\n",
      "3761: ZYYZII: 0.017%\n",
      "3768: ZYYZXZ: -0.077%\n",
      "3769: ZYYZYI: -0.109%\n",
      "3770: ZYYZYX: -0.073%\n",
      "3772: ZYYZYZ: -0.22%\n",
      "3775: ZYYZZY: -0.086%\n",
      "3777: ZYZIII: 0.03%\n",
      "3778: ZYZIIX: -0.027%\n",
      "3779: ZYZIIY: 0.031%\n",
      "3780: ZYZIIZ: 0.037%\n",
      "3781: ZYZIXI: 0.096%\n",
      "3784: ZYZIXZ: 0.143%\n",
      "3785: ZYZIYI: -0.038%\n",
      "3786: ZYZIYX: 0.182%\n",
      "3788: ZYZIYZ: -0.036%\n",
      "3789: ZYZIZI: 0.026%\n",
      "3791: ZYZIZY: -0.001%\n",
      "3792: ZYZIZZ: 0.049%\n",
      "3793: ZYZXII: 0.03%\n",
      "3796: ZYZXIZ: 0.117%\n",
      "3797: ZYZXXI: 0.128%\n",
      "3800: ZYZXXZ: 0.009%\n",
      "3801: ZYZXYI: 0.066%\n",
      "3802: ZYZXYX: -0.155%\n",
      "3804: ZYZXYZ: 0.164%\n",
      "3805: ZYZXZI: 0.019%\n",
      "3806: ZYZXZX: -0.075%\n",
      "3807: ZYZXZY: -0.004%\n",
      "3808: ZYZXZZ: -0.062%\n",
      "3809: ZYZYII: 0.008%\n",
      "3810: ZYZYIX: 0.054%\n",
      "3811: ZYZYIY: -0.011%\n",
      "3812: ZYZYIZ: -0.011%\n",
      "3813: ZYZYXI: 0.039%\n",
      "3814: ZYZYXX: 0.056%\n",
      "3815: ZYZYXY: 0.058%\n",
      "3816: ZYZYXZ: 0.009%\n",
      "3817: ZYZYYI: 0.006%\n",
      "3818: ZYZYYX: 0.018%\n",
      "3819: ZYZYYY: -0.027%\n",
      "3820: ZYZYYZ: 0.129%\n",
      "3821: ZYZYZI: 0.041%\n",
      "3822: ZYZYZX: 0.143%\n",
      "3823: ZYZYZY: 0.055%\n",
      "3824: ZYZYZZ: 0.084%\n",
      "3825: ZYZZII: 0.013%\n",
      "3828: ZYZZIZ: 0.038%\n",
      "3829: ZYZZXI: 0.059%\n",
      "3832: ZYZZXZ: 0.161%\n",
      "3833: ZYZZYI: 0.042%\n",
      "3834: ZYZZYX: 0.052%\n",
      "3835: ZYZZYY: 0.079%\n",
      "3836: ZYZZYZ: -0.002%\n",
      "3837: ZYZZZI: 0.024%\n",
      "3839: ZYZZZY: 0.017%\n",
      "3840: ZYZZZZ: 0.056%\n",
      "3841: ZZIIII: 0.061%\n",
      "3844: ZZIIIZ: -0.063%\n",
      "3848: ZZIIXZ: -0.023%\n",
      "3850: ZZIIYX: 0.091%\n",
      "3855: ZZIIZY: 0.024%\n",
      "3869: ZZIXZI: 0.036%\n",
      "3872: ZZIXZZ: -0.016%\n",
      "3877: ZZIYXI: 0.049%\n",
      "3880: ZZIYXZ: -0.017%\n",
      "3897: ZZIZYI: 0.038%\n",
      "3900: ZZIZYZ: -0.024%\n",
      "3905: ZZXIII: 0.027%\n",
      "3906: ZZXIIX: -0.093%\n",
      "3907: ZZXIIY: 0.133%\n",
      "3908: ZZXIIZ: 0.076%\n",
      "3909: ZZXIXI: 0.106%\n",
      "3912: ZZXIXZ: 0.151%\n",
      "3913: ZZXIYI: 0.01%\n",
      "3916: ZZXIYZ: 0.159%\n",
      "3917: ZZXIZI: 0.001%\n",
      "3920: ZZXIZZ: 0.034%\n",
      "3921: ZZXXII: 0.115%\n",
      "3924: ZZXXIZ: 0.18%\n",
      "3925: ZZXXXI: 0.183%\n",
      "3928: ZZXXXZ: 0.238%\n",
      "3929: ZZXXYI: 0.073%\n",
      "3932: ZZXXYZ: 0.186%\n",
      "3933: ZZXXZI: 0.005%\n",
      "3934: ZZXXZX: -0.05%\n",
      "3935: ZZXXZY: 0.14%\n",
      "3936: ZZXXZZ: -0.091%\n",
      "3937: ZZXYII: 0.012%\n",
      "3940: ZZXYIZ: 0.202%\n",
      "3941: ZZXYXI: 0.032%\n",
      "3942: ZZXYXX: -0.056%\n",
      "3943: ZZXYXY: 0.147%\n",
      "3944: ZZXYXZ: -0.069%\n",
      "3945: ZZXYYI: 0.01%\n",
      "3948: ZZXYYZ: 0.205%\n",
      "3949: ZZXYZI: 0.089%\n",
      "3952: ZZXYZZ: 0.238%\n",
      "3953: ZZXZII: -0.01%\n",
      "3956: ZZXZIZ: -0.05%\n",
      "3957: ZZXZXI: 0.132%\n",
      "3960: ZZXZXZ: 0.097%\n",
      "3961: ZZXZYI: 0.04%\n",
      "3962: ZZXZYX: -0.015%\n",
      "3963: ZZXZYY: 0.149%\n",
      "3964: ZZXZYZ: -0.034%\n",
      "3965: ZZXZZI: -0.05%\n",
      "3967: ZZXZZY: -0.0%\n",
      "3968: ZZXZZZ: -0.03%\n",
      "3969: ZZYIII: -0.001%\n",
      "3972: ZZYIIZ: -0.15%\n",
      "3985: ZZYXII: 0.07%\n",
      "3992: ZZYXXZ: 0.032%\n",
      "3994: ZZYXYX: 0.07%\n",
      "3997: ZZYXZI: 0.024%\n",
      "3999: ZZYXZY: 0.001%\n",
      "4000: ZZYXZZ: -0.165%\n",
      "4005: ZZYYXI: 0.022%\n",
      "4008: ZZYYXZ: -0.157%\n",
      "4025: ZZYZYI: 0.007%\n",
      "4028: ZZYZYZ: -0.148%\n",
      "4033: ZZZIII: -0.0%\n",
      "4036: ZZZIIZ: 0.007%\n",
      "4061: ZZZXZI: 0.04%\n",
      "4064: ZZZXZZ: 0.049%\n",
      "4065: ZZZYII: 0.065%\n",
      "4069: ZZZYXI: 0.05%\n",
      "4072: ZZZYXZ: 0.056%\n",
      "4074: ZZZYYX: 0.131%\n",
      "4079: ZZZYZY: 0.079%\n",
      "4089: ZZZZYI: 0.025%\n",
      "4092: ZZZZYZ: 0.039%\n",
      "Mean error = 0.0116%, std = 0.07076(%)\n"
     ]
    }
   ],
   "source": [
    "# Just out of intereset we can now work out the error in the oracle using this number of shots and our\n",
    "# fitting algorithm:\n",
    "print(\"Actual error in the eigenvalues estimated\\n\")\n",
    "avE =[]\n",
    "for (ix,i) in enumerate(oracleToUse)\n",
    "    if i !=0\n",
    "        percentError = round((i-actualOracle[ix])/actualOracle[ix]*100,digits=6)\n",
    "        push!(avE,percentError)\n",
    "        print(\"$(string(ix,pad=4)): $(fidelityLabels(ix-1,qubits=6)): $(round(percentError,digits=3))%\\n\")\n",
    "    end\n",
    "end\n",
    "print(\"Mean error = $(round(mean(avE),digits=4))%, std = $(round(std(avE),digits=5))(%)\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Running the peeling decoder \n",
    "\n",
    "- we don't have all the values in the oracle, but we have enough"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Any,1}:\n",
       " Any[[[\"0000\", \"0110\", \"1101\", \"1011\"], [\"1100\", \"1010\", \"0001\", \"0111\"], [\"1000\", \"1110\", \"0101\", \"0011\"], [\"0100\", \"0010\", \"1001\", \"1111\"]], [[\"0000\", \"0110\", \"1101\", \"1011\"], [\"1100\", \"1010\", \"0001\", \"0111\"], [\"1000\", \"1110\", \"0101\", \"0011\"], [\"0100\", \"0010\", \"1001\", \"1111\"]], [[\"0000\", \"0110\", \"1101\", \"1011\"], [\"1100\", \"1010\", \"0001\", \"0111\"], [\"1000\", \"1110\", \"0101\", \"0011\"], [\"0100\", \"0010\", \"1001\", \"1111\"]]]\n",
       " Any[[[\"00\", \"11\"], [\"10\", \"01\"]], [[\"0000\", \"1110\", \"1001\", \"0111\"], [\"1100\", \"0010\", \"0101\", \"1011\"], [\"0100\", \"1010\", \"1101\", \"0011\"], [\"1000\", \"0110\", \"0001\", \"1111\"]], [[\"0000\", \"0110\", \"1101\", \"1011\"], [\"1100\", \"1010\", \"0001\", \"0111\"], [\"1000\", \"1110\", \"0101\", \"0011\"], [\"0100\", \"0010\", \"1001\", \"1111\"]], [[\"00\", \"11\"], [\"10\", \"01\"]]]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use the patterns to create the listOfPs\n",
    "\n",
    "# What is this?? Well basically it tells us which Pauli error fell into which bin, given our choice of experiment\n",
    "# So the first vector (listOfPs[1][1])\n",
    "listOfPs=[]\n",
    "for p in paulisAll\n",
    "    hMap = []\n",
    "    # Because here we use right hand least significant - we just reverse the order we stored the experiments.\n",
    "    for i in reverse(p)\n",
    "       #print(\"Length $(length(i))\\n\")\n",
    "       if length(i) == 2\n",
    "            push!(hMap,twoPattern(i))\n",
    "        elseif length(i) == 4\n",
    "            push!(hMap,fourPattern([i])[1])\n",
    "        else # Assume a binary bit pattern\n",
    "            push!(hMap,[length(i)])\n",
    "        end\n",
    "    end\n",
    "    push!(listOfPs,hMap)\n",
    "end\n",
    "listOfPs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Any,1}:\n",
       " [[0, 14, 7, 9, 224, 238, 231, 233, 112, 126  …  2535, 2537, 2416, 2430, 2423, 2425, 2448, 2462, 2455, 2457], [2048, 2062, 2055, 2057, 2272, 2286, 2279, 2281, 2160, 2174  …  487, 489, 368, 382, 375, 377, 400, 414, 407, 409], [1024, 1038, 1031, 1033, 1248, 1262, 1255, 1257, 1136, 1150  …  3559, 3561, 3440, 3454, 3447, 3449, 3472, 3486, 3479, 3481], [512, 526, 519, 521, 736, 750, 743, 745, 624, 638  …  3047, 3049, 2928, 2942, 2935, 2937, 2960, 2974, 2967, 2969], [256, 270, 263, 265, 480, 494, 487, 489, 368, 382  …  2279, 2281, 2160, 2174, 2167, 2169, 2192, 2206, 2199, 2201], [128, 142, 135, 137, 96, 110, 103, 105, 240, 254  …  2407, 2409, 2544, 2558, 2551, 2553, 2320, 2334, 2327, 2329], [64, 78, 71, 73, 160, 174, 167, 169, 48, 62  …  2471, 2473, 2352, 2366, 2359, 2361, 2512, 2526, 2519, 2521], [32, 46, 39, 41, 192, 206, 199, 201, 80, 94  …  2503, 2505, 2384, 2398, 2391, 2393, 2480, 2494, 2487, 2489], [16, 30, 23, 25, 240, 254, 247, 249, 96, 110  …  2551, 2553, 2400, 2414, 2407, 2409, 2432, 2446, 2439, 2441], [8, 6, 15, 1, 232, 230, 239, 225, 120, 118  …  2543, 2529, 2424, 2422, 2431, 2417, 2456, 2454, 2463, 2449], [4, 10, 3, 13, 228, 234, 227, 237, 116, 122  …  2531, 2541, 2420, 2426, 2419, 2429, 2452, 2458, 2451, 2461], [2, 12, 5, 11, 226, 236, 229, 235, 114, 124  …  2533, 2539, 2418, 2428, 2421, 2427, 2450, 2460, 2453, 2459], [1, 15, 6, 8, 225, 239, 230, 232, 113, 127  …  2534, 2536, 2417, 2431, 2422, 2424, 2449, 2463, 2454, 2456]]\n",
       " [[0, 3, 56, 59, 28, 31, 36, 39, 832, 835  …  3812, 3815, 3456, 3459, 3512, 3515, 3484, 3487, 3492, 3495], [2048, 2051, 2104, 2107, 2076, 2079, 2084, 2087, 2880, 2883  …  1764, 1767, 1408, 1411, 1464, 1467, 1436, 1439, 1444, 1447], [1024, 1027, 1080, 1083, 1052, 1055, 1060, 1063, 1856, 1859  …  2788, 2791, 2432, 2435, 2488, 2491, 2460, 2463, 2468, 2471], [512, 515, 568, 571, 540, 543, 548, 551, 320, 323  …  3300, 3303, 3968, 3971, 4024, 4027, 3996, 3999, 4004, 4007], [256, 259, 312, 315, 284, 287, 292, 295, 576, 579  …  4068, 4071, 3200, 3203, 3256, 3259, 3228, 3231, 3236, 3239], [128, 131, 184, 187, 156, 159, 164, 167, 960, 963  …  3684, 3687, 3328, 3331, 3384, 3387, 3356, 3359, 3364, 3367], [64, 67, 120, 123, 92, 95, 100, 103, 768, 771  …  3748, 3751, 3520, 3523, 3576, 3579, 3548, 3551, 3556, 3559], [32, 35, 24, 27, 60, 63, 4, 7, 864, 867  …  3780, 3783, 3488, 3491, 3480, 3483, 3516, 3519, 3460, 3463], [16, 19, 40, 43, 12, 15, 52, 55, 848, 851  …  3828, 3831, 3472, 3475, 3496, 3499, 3468, 3471, 3508, 3511], [8, 11, 48, 51, 20, 23, 44, 47, 840, 843  …  3820, 3823, 3464, 3467, 3504, 3507, 3476, 3479, 3500, 3503], [4, 7, 60, 63, 24, 27, 32, 35, 836, 839  …  3808, 3811, 3460, 3463, 3516, 3519, 3480, 3483, 3488, 3491], [2, 1, 58, 57, 30, 29, 38, 37, 834, 833  …  3814, 3813, 3458, 3457, 3514, 3513, 3486, 3485, 3494, 3493], [1, 2, 57, 58, 29, 30, 37, 38, 833, 834  …  3813, 3814, 3457, 3458, 3513, 3514, 3485, 3486, 3493, 3494]]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples = []\n",
    "for (ix,x) in enumerate(paulisAll)\n",
    "    # Similarly if we reverse above (right hand least significant, then we reverse here)\n",
    "   push!(samples,[[y for y in generateFromPVecSamples4N(reverse(x),d)] for d in ds])\n",
    "end\n",
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "000000000000: 1 0.9566049496644947\n",
      "000000000001: 2 0.009742443708564856\n",
      "000000000010: 3 0.0038969774834259428\n",
      "000000000100: 5 0.0002882968036207967\n",
      "000000010000: 17 0.00019223633173193815\n",
      "000000110000: 49 0.0002883544975979071\n",
      "000010000000: 129 0.0002882968036207967\n",
      "000100000000: 257 0.003936905531411864\n",
      "001000000000: 513 0.01968452765705932\n",
      "001000000001: 514 0.0001996402399296077\n",
      "001100101111: 816 0.004\n",
      "100000000000: 2049 0.0002882968036207967\n"
     ]
    }
   ],
   "source": [
    "## This is just to remind ourselves these are the Paulis we might hope to recover\n",
    "## In particular we hid a high weight Pauli with an error of 0.004, it appears below as 'number' 816\n",
    "for i = 1:4096\n",
    "    if (dist[i]>0.0001)\n",
    "        print(\"$(string(i-1,base=2,pad=12)): $i $(dist[i])\\n\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64-element Array{Float64,1}:\n",
       " 1.0\n",
       " 0.9720291467193548\n",
       " 0.9991998946835859\n",
       " 0.9711926086643352\n",
       " 0.9981857588412699\n",
       " 0.9702571630197817\n",
       " 0.9986028494533448\n",
       " 0.9705848390270296\n",
       " 0.9520673532412371\n",
       " 0.925736192005811\n",
       " 0.9514365391411761\n",
       " 0.9245680352867948\n",
       " 0.9502737041497508\n",
       " ⋮\n",
       " 0.9489201111745996\n",
       " 0.9213777820094172\n",
       " 0.9494913862208747\n",
       " 0.9224038681901503\n",
       " 0.9825468776014576\n",
       " 0.9553338422655632\n",
       " 0.981732052552941\n",
       " 0.9541915237156421\n",
       " 0.9806621081060998\n",
       " 0.9533235904595504\n",
       " 0.9811036366343943\n",
       " 0.953703278609339"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "([oracleToUse[x+1] for x in samples[2][1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass 1, 8 0.9988247398205602\n",
      "Pass 2, 8 0.9988247398205602\n",
      "Pass 3, 8 0.9988247398205602\n",
      "Pass 4, 8 0.9988247398205602\n",
      "Pass 5, 8 0.9988247398205602\n",
      "Pass 6, 9 0.9992720461601559\n",
      "Pass 7, 9 0.9992720461601559\n",
      "Pass 8, 10 0.9995543017770276\n",
      "Pass 9, 10 0.9995543017770276\n",
      "Pass 10, 10 0.9995543017770276\n",
      "Pass 11, 10 0.9995543017770276\n",
      "Pass 12, 10 0.9995543017770276\n",
      "Pass 13, 10 0.9995543017770276\n",
      "Pass 14, 10 0.9995543017770276\n",
      "Pass 15, 10 0.9995543017770276\n",
      "Pass 16, 10 0.9995543017770276\n",
      "Pass 17, 10 0.9995543017770276\n",
      "Pass 18, 10 0.9995543017770276\n",
      "Pass 19, 10 0.9995543017770276\n",
      "Pass 20, 11 0.999854001381265\n",
      "Pass 21, 11 0.999854001381265\n",
      "Pass 22, 11 0.999854001381265\n",
      "Pass 23, 11 0.999854001381265\n",
      "Pass 24, 11 0.999854001381265\n",
      "Pass 25, 11 0.999854001381265\n",
      "Pass 26, 11 0.999854001381265\n",
      "Pass 27, 11 0.999854001381265\n",
      "Pass 28, 11 0.999854001381265\n",
      "Pass 29, 11 0.999854001381265\n",
      "Pass 30, 11 0.999854001381265\n",
      "Pass 31, 12 1.000093606020884\n"
     ]
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "maxPass = 200\n",
    "# singletons is when 'noise' threshold below which we declare we have found a singletons\n",
    "# It will be related to the measurment accuracy and the number of bins\n",
    "# Here we base it off the shotsToDo variance, on the basis of our hoped for recovery\n",
    "\n",
    "# We start that one low and then slowly increase it, meaning we are more likely to accept\n",
    "# If you have a certain probability distribution and this ansatz is not working, set it\n",
    "# so that you get a reasonable number of hits in the first round.\n",
    "singletons = (0.001*.999)/30000\n",
    "singletonsInc = singletons/2\n",
    "\n",
    "# Zeros is set high - we don't want to accept bins with very low numbers as they are probably just noise\n",
    "# If the (sum(mean - value)^2) for all the offsets is below this number we ignore it.\n",
    "# But then we lower it, meaning we are less likely to think a bin has no value in it.\n",
    "# Obviously it should never be negative.\n",
    "zerosC = (0.001*.999)/20000*2*1.1\n",
    "zerosDec = (zerosC*0.99)/maxPass\n",
    "\n",
    "\n",
    "prevFound = 0\n",
    "qubitSize = 6\n",
    "j6=diagm(1 => vec(hcat([[1 0] for i = 1:6]...)[1:end-1]),-1 => vec(hcat([[1 0] for i = 1:6]...)[1:end-1]))\n",
    "\n",
    "listOfX = [[fwht_natural([oracleToUse[x+1] for x in y]) for y in s] for s in samples]\n",
    "found = Dict()\n",
    "rmappings = []\n",
    "for x in mappings\n",
    "    if length(x) == 0\n",
    "        push!(rmappings,x)\n",
    "    else\n",
    "        ralt = Dict()\n",
    "        for i in keys(x)\n",
    "            ralt[x[i]]= i\n",
    "        end\n",
    "        push!(rmappings,ralt)\n",
    "    end\n",
    "end    \n",
    "prevFound = 0\n",
    "\n",
    "\n",
    "for i in 1:maxPass\n",
    "\n",
    "\n",
    "\n",
    "    for co = 1:length(listOfX)\n",
    "        bucketSize = length(listOfX[co][1])\n",
    "        for extractValue = 1:bucketSize\n",
    "            extracted = [x[extractValue] for x in listOfX[co]]\n",
    "            if !(PEEL.closeToZero(extracted,qubitSize*2,cutoff= zerosC))\n",
    "               (isit,bits,val) = PEEL.checkAndExtractSingleton([extracted],qubitSize*2,cutoff=singletons)\n",
    "               if isit\n",
    "                  #print(\"$bits\\n\")\n",
    "                  #pval = binaryArrayToNumber(j6*[x == '0' ?  0 : 1 for x in bits])\n",
    "                  vval = parse(Int,bits,base=2)\n",
    "                  #print(\"$bits, $vval $(round(dist[vval+1],digits=5)) and $(round(val,digits=5))\\n\")\n",
    "                  PEEL.peelBack(listOfX,listOfPs,bits,val,found,ds,rmappings)\n",
    "               end\n",
    "            end\n",
    "        end   \n",
    "    end\n",
    "    if length(found) > prevFound\n",
    "                prevFound = length(found)\n",
    "    else\n",
    "        singletons += singletonsInc\n",
    "        zerosC -=zerosDec \n",
    "        if (zerosC <= 0)\n",
    "                break\n",
    "        end\n",
    "     end\n",
    "     if length(found) > 0\n",
    "                print(\"Pass $i, $(length(found)) $(sum([mean(found[x]) for x in keys(found)]))\\n\")\n",
    "            if sum([mean(found[x]) for x in keys(found)]) >= 0.999995\n",
    "                break\n",
    "            end\n",
    "     end\n",
    "\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimate  <===>   Actual\n",
      "------------------------\n",
      "IIXIII: 128 : 0.00035 <===>  0.00029\n",
      "ZIIZZI: 3132 : 0.00024 <===>  0.0\n",
      "IZIXZZ: 815 : 0.00401 <===>  0.004\n",
      "ZIIZZY: 3133 : 0.00028 <===>  0.0\n",
      "IIIIIX: 2 : 0.00404 <===>  0.0039\n",
      "IYIIII: 256 : 0.00391 <===>  0.00394\n",
      "IIIZII: 48 : 0.0003 <===>  0.00029\n",
      "IXIIII: 512 : 0.01978 <===>  0.01968\n",
      "IIIIYI: 4 : 0.00045 <===>  0.00029\n",
      "YIIIII: 1024 : 0.00039 <===>  0.0001\n",
      "IIIIII: 0 : 0.95671 <===>  0.9566\n",
      "IIIIIY: 1 : 0.00963 <===>  0.00974\n"
     ]
    }
   ],
   "source": [
    "foundV = []\n",
    "print(\"Estimate  <===>   Actual\\n\")\n",
    "print(\"------------------------\\n\")\n",
    "\n",
    "\n",
    "for x in keys(found)\n",
    "    vval = parse(Int,x,base=2)\n",
    "    push!(foundV,vval+1)\n",
    "    print(\"$(probabilityLabels(vval,qubits=6)): $vval : $(round(mean(found[x]),digits=5)) <===>  $(round(dist[vval+1],digits=5))\\n\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "title(\"Distribution of Pauli error rates\")\n",
    "yscale(\"log\")\n",
    "ylabel(\"Error Rate\")\n",
    "xlabel(\"Paulis indexed and sorted by error rate\")\n",
    "indices = reverse(sortperm(dist))[1:15]\n",
    "scatter(1:15,[dist[x] for x in indices])\n",
    "loc = [findfirst(x->x==y,indices) for y in foundV]\n",
    "scatter(loc,[found[string(x-1,base=2,pad=12)] for x in foundV])\n",
    "xticks(1:15,[probabilityLabels(x-1,qubits=6) for x in indices],rotation=90);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How will things improve if we up the shot count?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### What we will see is that the accuracy of the recovery increases, but not necessarily the number recovered.\n",
    "\n",
    "The recovery number after a $\\delta$ of 0.25 requires we up the sub-sampling groups. This is described in the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# So we kept the actual probabilities of each of the experiments\n",
    "# And now we can increase the shot statistics to see how things improve:\n",
    "\n",
    "# 1,000 sequences of 1,000 shots\n",
    "manyMoreShots = 1000000\n",
    "\n",
    "# We need culmlative probability matrixes\n",
    "cumMatrix = map(cumsum,experiment1_allProbs)\n",
    "experiment1_observed = shotSimulator(64,manyMoreShots,cumMatrix);\n",
    "(params,l, failed) = fitTheFidelities(lengths,experiment1_observed)\n",
    "experiment1_fidelities = vcat(1,[p[2] for p in params]) # We don't fit the first one, it is always 1 for CPTP maps\n",
    "#Turn those into a number...\n",
    "fidelitiesExtracted = []\n",
    "\n",
    "for x0 in paulisAll[1][3]\n",
    "    p56 = binaryArrayToNumber(x0)\n",
    "    for x1 in paulisAll[1][2]\n",
    "        p34 = binaryArrayToNumber(x1)\n",
    "        for x2 in paulisAll[1][1]\n",
    "            p12= binaryArrayToNumber(x2)\n",
    "            push!(fidelitiesExtracted,p56*4^4+p34*16+p12+1) # + 1 cause we index of 1 in Julia\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "estimateOracle = [[] for _ in 1:4096]\n",
    "\n",
    "for i in 1:64\n",
    "    push!(estimateOracle[fidelitiesExtracted[i]],experiment1_fidelities[i])\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "# So I am going to just do all of the above for each of the 5 (other than the one already done) for each of the qubits\n",
    "e1_all_additional_fidelities = []\n",
    "e1_fidelity_extracted = []\n",
    "# Note we don't actually need to save the actual probabilities - but I am going to use them later\n",
    "# To demonstrate some different recovery regimes.\n",
    "exp_count = 1\n",
    "for qubitPairOn = 1:3 # qubit pairs here are 1&2, 3&4 and 5&6\n",
    "    for experimentType = 1:5\n",
    "        if experiments[1][qubitPairOn][2] != experimentType\n",
    "            # Its one we haven't done\n",
    "            expOnFirstPair  = experiments[1][1][2]\n",
    "            expOnSecondPair = experiments[1][2][2]\n",
    "            expOnThirdPair  = experiments[1][3][2]\n",
    "\n",
    "            \n",
    "            if qubitPairOn == 1\n",
    "                expOnFirstPair = experimentType\n",
    "            elseif qubitPairOn == 2\n",
    "                expOnSecondPair = experimentType\n",
    "            else\n",
    "                expOnThirdPair = experimentType\n",
    "            end\n",
    "            \n",
    "            # Get the actual probabilities previously saved.\n",
    "            additionalExperiment = e1_all_actualProbabilities[exp_count]\n",
    "            exp_count +=1\n",
    "            # Generate the measurement statistics\n",
    "            cumMatrix = map(cumsum,additionalExperiment)\n",
    "            experiment1_additional_observed = shotSimulator(64,manyMoreShots,cumMatrix);\n",
    "            # Fit and extract the fidelities\n",
    "            (params,l, failed) = fitTheFidelities(lengths,experiment1_additional_observed)\n",
    "            experiment1_additional_fidelities = vcat(1,[p[2] for p in params])\n",
    "            push!(e1_all_additional_fidelities,experiment1_additional_fidelities)\n",
    "            fidelitiesExtracted=[]\n",
    "            for x0 in all2QlMuBs[expOnThirdPair]\n",
    "                p56 = binaryArrayToNumber(x0)\n",
    "                for x1 in all2QlMuBs[expOnSecondPair]\n",
    "                    p34 = binaryArrayToNumber(x1)\n",
    "                    for x2 in all2QlMuBs[expOnFirstPair]\n",
    "                        p12= binaryArrayToNumber(x2)\n",
    "                        push!(fidelitiesExtracted,p56*4^4+p34*16+p12+1) # + 1 cause we index of 1 in Julia\n",
    "                    end\n",
    "                end\n",
    "            end\n",
    "            push!(e1_fidelity_extracted,fidelitiesExtracted)\n",
    "        end\n",
    "    end\n",
    "end\n",
    "# So we just need to fill in the oracle\n",
    "\n",
    "for (expNo,x) in enumerate(e1_fidelity_extracted)\n",
    "    for (fidelityIndex,fidelity)  in enumerate(x)\n",
    "        push!(estimateOracle[fidelity],e1_all_additional_fidelities[expNo][fidelityIndex])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate shot limited stats\n",
    "\n",
    "cumMatrix = map(cumsum,experiment2)\n",
    "experiment2_observed = shotSimulator(64,manyMoreShots,cumMatrix);\n",
    "# Fit and extract the fidelities\n",
    "(params,l, failed) = fitTheFidelities(lengths,experiment2_observed)\n",
    "experiment2_fidelities = vcat(1,[p[2] for p in params])\n",
    "fidelitiesExtracted = []\n",
    "for x1b in potentialSingles[experiments[2][4][2]] # Experiment 2, qubit division 3 (q1, q2&3, q4) the second part = exp number\n",
    "    p6 = binaryArrayToNumber(x1b)\n",
    "    for x2b in all2QlMuBs[experiments[2][3][2]]\n",
    "        p45 = binaryArrayToNumber(x2b)\n",
    "        for x2a in all2QlMuBs[experiments[2][2][2]]\n",
    "            p23 = binaryArrayToNumber(x2a)\n",
    "            for x1a in potentialSingles[experiments[2][1][2]]\n",
    "                p1 = binaryArrayToNumber(x1a)\n",
    "                push!(fidelitiesExtracted,p6*4^5+p45*4^3+p23*4^1+p1+1) # + 1 cause we index of 1 in Julia\n",
    "             end\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "\n",
    "for (fidelityIndex,fidelity)  in enumerate(fidelitiesExtracted)\n",
    "    push!(estimateOracle[fidelity],experiment2_fidelities[fidelityIndex])\n",
    "end\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "e2_all_additional_fidelities = []\n",
    "e2_fidelity_extracted = []\n",
    "# Note here I am hard coding that we have single qubit twirls on 1 and 4.\n",
    "e_count = 0\n",
    "exp_count = 1\n",
    "for qubitOn in 1:4 # qubits we can be \"On\" here are 1, 2&3 4&5 and 6\n",
    "    \n",
    "    if qubitOn == 2 || qubitOn == 3\n",
    "        noOfExperiments = 5\n",
    "    else \n",
    "        noOfExperiments = 3 # Only 3 if its a single qubit.\n",
    "    end\n",
    "    for experimentType = 1:noOfExperiments\n",
    "        if experiments[2][qubitOn][2] != experimentType\n",
    "            # Its one we haven't done\n",
    "            expOnFirstSet = experiments[2][1][2]\n",
    "            expOnSecondSet = experiments[2][2][2]\n",
    "            expOnThirdSet = experiments[2][3][2]\n",
    "            expOnFourthSet = experiments[2][4][2]\n",
    "\n",
    "\n",
    "            if qubitOn == 1\n",
    "                expOnFirstSet = experimentType\n",
    "            elseif qubitOn == 2\n",
    "                expOnSecondSet = experimentType\n",
    "            elseif qubitOn ==3 \n",
    "                expOnThirdSet = experimentType\n",
    "            else \n",
    "                expOnFourthSet = experimentType\n",
    "            end\n",
    "                \n",
    "            additionalExperiment = e2_all_actualProbabilities[exp_count]\n",
    "            exp_count+=1\n",
    "            \n",
    "            # Generate the measurement statistics\n",
    "            cumMatrix = map(cumsum,additionalExperiment)\n",
    "            experiment2_additional_observed =  shotSimulator(64,manyMoreShots,cumMatrix);\n",
    "            # Fit and extract the fidelities\n",
    "            (params,l, failed) = fitTheFidelities(lengths,experiment2_additional_observed)\n",
    "            experiment2_additional_fidelities = vcat(1,[p[2] for p in params])\n",
    "            push!(e2_all_additional_fidelities,experiment2_additional_fidelities)\n",
    "            fidelitiesExtracted=[]\n",
    "            for x1 in potentialSingles[expOnFourthSet] # Experiment 2, qubit division 3 (q1, q2&3, q4&5 q6) the second part = exp number\n",
    "                p6 = binaryArrayToNumber(x1)\n",
    "                for x2b in all2QlMuBs[expOnThirdSet]\n",
    "                    p45 = binaryArrayToNumber(x2b)\n",
    "                    for x2 in all2QlMuBs[expOnSecondSet]\n",
    "                        p23 = binaryArrayToNumber(x2)\n",
    "                        for x3 in potentialSingles[expOnFirstSet]\n",
    "                            p1 = binaryArrayToNumber(x3)\n",
    "                            push!(fidelitiesExtracted,p6*4^5+p45*4^3+p23*4+p1+1) # + 1 cause we index of 1 in Julia\n",
    "                        end\n",
    "                     end\n",
    "                end\n",
    "            end\n",
    "            push!(e2_fidelity_extracted,fidelitiesExtracted)\n",
    "        end\n",
    "    end\n",
    "end\n",
    "\n",
    "# So we just need to fill in the oracle\n",
    "\n",
    "for (expNo,x) in enumerate(e2_fidelity_extracted)\n",
    "    for (fidelityIndex,fidelity)  in enumerate(x)\n",
    "        push!(estimateOracle[fidelity],e2_all_additional_fidelities[expNo][fidelityIndex])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4096-element Array{Real,1}:\n",
       " 1.0\n",
       " 0.9719885180800645\n",
       " 0.983979552464777\n",
       " 0.9719979638905242\n",
       " 0.991397670766155\n",
       " 0.9794047891968238\n",
       " 0.9913805110959736\n",
       " 0.963418819353371\n",
       " 0.9917692042639024\n",
       " 0.9797838796499244\n",
       " 0.9918044072561205\n",
       " 0.9637864067913748\n",
       " 0.9991981128146965\n",
       " ⋮\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0.9497286952423499\n",
       " 0\n",
       " 0\n",
       " 0.9231080136842243\n",
       " 0\n",
       " 0\n",
       " 0\n",
       " 0"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "millionShotOracle = [length(x) > 0 ? mean(x) : 0 for x in estimateOracle]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pass 1, 6 0.9979370870188927\n",
      "Pass 2, 6 0.9979370870188927\n",
      "Pass 3, 6 0.9979370870188927\n",
      "Pass 4, 6 0.9979370870188927\n",
      "Pass 5, 6 0.9979370870188927\n",
      "Pass 6, 6 0.9979370870188927\n",
      "Pass 7, 6 0.9979370870188927\n",
      "Pass 8, 6 0.9979370870188927\n",
      "Pass 9, 6 0.9979370870188927\n",
      "Pass 10, 6 0.9979370870188927\n",
      "Pass 11, 6 0.9979370870188927\n",
      "Pass 12, 6 0.9979370870188927\n",
      "Pass 13, 6 0.9979370870188927\n",
      "Pass 14, 6 0.9979370870188927\n",
      "Pass 15, 6 0.9979370870188927\n",
      "Pass 16, 6 0.9979370870188927\n",
      "Pass 17, 6 0.9979370870188927\n",
      "Pass 18, 6 0.9979370870188927\n",
      "Pass 19, 6 0.9979370870188927\n",
      "Pass 20, 6 0.9979370870188927\n",
      "Pass 21, 6 0.9979370870188927\n",
      "Pass 22, 6 0.9979370870188927\n",
      "Pass 23, 6 0.9979370870188927\n",
      "Pass 24, 6 0.9979370870188927\n",
      "Pass 25, 6 0.9979370870188927\n",
      "Pass 26, 6 0.9979370870188927\n",
      "Pass 27, 6 0.9979370870188927\n",
      "Pass 28, 6 0.9979370870188927\n",
      "Pass 29, 6 0.9979370870188927\n",
      "Pass 30, 6 0.9979370870188927\n",
      "Pass 31, 6 0.9979370870188927\n",
      "Pass 32, 6 0.9979370870188927\n",
      "Pass 33, 6 0.9979370870188927\n",
      "Pass 34, 6 0.9979370870188927\n",
      "Pass 35, 6 0.9979370870188927\n",
      "Pass 36, 6 0.9979370870188927\n",
      "Pass 37, 6 0.9979370870188927\n",
      "Pass 38, 6 0.9979370870188927\n",
      "Pass 39, 6 0.9979370870188927\n",
      "Pass 40, 6 0.9979370870188927\n",
      "Pass 41, 6 0.9979370870188927\n",
      "Pass 42, 6 0.9979370870188927\n",
      "Pass 43, 6 0.9979370870188927\n",
      "Pass 44, 6 0.9979370870188927\n",
      "Pass 45, 6 0.9979370870188927\n",
      "Pass 46, 6 0.9979370870188927\n",
      "Pass 47, 6 0.9979370870188927\n",
      "Pass 48, 6 0.9979370870188927\n",
      "Pass 49, 6 0.9979370870188927\n",
      "Pass 50, 6 0.9979370870188927\n",
      "Pass 51, 6 0.9979370870188927\n",
      "Pass 52, 6 0.9979370870188927\n",
      "Pass 53, 6 0.9979370870188927\n",
      "Pass 54, 6 0.9979370870188927\n",
      "Pass 55, 6 0.9979370870188927\n",
      "Pass 56, 6 0.9979370870188927\n",
      "Pass 57, 6 0.9979370870188927\n",
      "Pass 58, 6 0.9979370870188927\n",
      "Pass 59, 6 0.9979370870188927\n",
      "Pass 60, 6 0.9979370870188927\n",
      "Pass 61, 6 0.9979370870188927\n",
      "Pass 62, 6 0.9979370870188927\n",
      "Pass 63, 6 0.9979370870188927\n",
      "Pass 64, 6 0.9979370870188927\n",
      "Pass 65, 6 0.9979370870188927\n",
      "Pass 66, 6 0.9979370870188927\n",
      "Pass 67, 6 0.9979370870188927\n",
      "Pass 68, 6 0.9979370870188927\n",
      "Pass 69, 6 0.9979370870188927\n",
      "Pass 70, 6 0.9979370870188927\n",
      "Pass 71, 6 0.9979370870188927\n",
      "Pass 72, 6 0.9979370870188927\n",
      "Pass 73, 6 0.9979370870188927\n",
      "Pass 74, 6 0.9979370870188927\n",
      "Pass 75, 6 0.9979370870188927\n",
      "Pass 76, 6 0.9979370870188927\n",
      "Pass 77, 6 0.9979370870188927\n",
      "Pass 78, 6 0.9979370870188927\n",
      "Pass 79, 6 0.9979370870188927\n",
      "Pass 80, 6 0.9979370870188927\n",
      "Pass 81, 6 0.9979370870188927\n",
      "Pass 82, 6 0.9979370870188927\n",
      "Pass 83, 6 0.9979370870188927\n",
      "Pass 84, 6 0.9979370870188927\n",
      "Pass 85, 6 0.9979370870188927\n",
      "Pass 86, 6 0.9979370870188927\n",
      "Pass 87, 6 0.9979370870188927\n",
      "Pass 88, 6 0.9979370870188927\n",
      "Pass 89, 6 0.9979370870188927\n",
      "Pass 90, 6 0.9979370870188927\n",
      "Pass 91, 6 0.9979370870188927\n",
      "Pass 92, 6 0.9979370870188927\n",
      "Pass 93, 6 0.9979370870188927\n",
      "Pass 94, 6 0.9979370870188927\n",
      "Pass 95, 6 0.9979370870188927\n",
      "Pass 96, 6 0.9979370870188927\n",
      "Pass 97, 6 0.9979370870188927\n",
      "Pass 98, 6 0.9979370870188927\n",
      "Pass 99, 6 0.9979370870188927\n",
      "Pass 100, 6 0.9979370870188927\n",
      "Pass 101, 6 0.9979370870188927\n",
      "Pass 102, 6 0.9979370870188927\n",
      "Pass 103, 6 0.9979370870188927\n",
      "Pass 104, 6 0.9979370870188927\n",
      "Pass 105, 6 0.9979370870188927\n",
      "Pass 106, 6 0.9979370870188927\n",
      "Pass 107, 6 0.9979370870188927\n",
      "Pass 108, 6 0.9979370870188927\n",
      "Pass 109, 6 0.9979370870188927\n",
      "Pass 110, 6 0.9979370870188927\n",
      "Pass 111, 6 0.9979370870188927\n",
      "Pass 112, 6 0.9979370870188927\n",
      "Pass 113, 6 0.9979370870188927\n",
      "Pass 114, 6 0.9979370870188927\n",
      "Pass 115, 6 0.9979370870188927\n",
      "Pass 116, 6 0.9979370870188927\n",
      "Pass 117, 6 0.9979370870188927\n",
      "Pass 118, 6 0.9979370870188927\n",
      "Pass 119, 6 0.9979370870188927\n",
      "Pass 120, 6 0.9979370870188927\n",
      "Pass 121, 6 0.9979370870188927\n",
      "Pass 122, 6 0.9979370870188927\n",
      "Pass 123, 6 0.9979370870188927\n",
      "Pass 124, 6 0.9979370870188927\n",
      "Pass 125, 6 0.9979370870188927\n",
      "Pass 126, 6 0.9979370870188927\n",
      "Pass 127, 6 0.9979370870188927\n",
      "Pass 128, 6 0.9979370870188927\n",
      "Pass 129, 6 0.9979370870188927\n",
      "Pass 130, 6 0.9979370870188927\n",
      "Pass 131, 6 0.9979370870188927\n",
      "Pass 132, 6 0.9979370870188927\n",
      "Pass 133, 6 0.9979370870188927\n",
      "Pass 134, 6 0.9979370870188927\n",
      "Pass 135, 6 0.9979370870188927\n",
      "Pass 136, 6 0.9979370870188927\n",
      "Pass 137, 6 0.9979370870188927\n",
      "Pass 138, 6 0.9979370870188927\n",
      "Pass 139, 6 0.9979370870188927\n",
      "Pass 140, 6 0.9979370870188927\n",
      "Pass 141, 6 0.9979370870188927\n",
      "Pass 142, 6 0.9979370870188927\n",
      "Pass 143, 6 0.9979370870188927\n",
      "Pass 144, 6 0.9979370870188927\n",
      "Pass 145, 6 0.9979370870188927\n",
      "Pass 146, 6 0.9979370870188927\n",
      "Pass 147, 6 0.9979370870188927\n",
      "Pass 148, 6 0.9979370870188927\n",
      "Pass 149, 6 0.9979370870188927\n",
      "Pass 150, 6 0.9979370870188927\n",
      "Pass 151, 6 0.9979370870188927\n",
      "Pass 152, 6 0.9979370870188927\n",
      "Pass 153, 6 0.9979370870188927\n",
      "Pass 154, 6 0.9979370870188927\n",
      "Pass 155, 6 0.9979370870188927\n",
      "Pass 156, 7 0.9983899128189936\n",
      "Pass 157, 7 0.9983899128189936\n",
      "Pass 158, 7 0.9983899128189936\n",
      "Pass 159, 7 0.9983899128189936\n",
      "Pass 160, 7 0.9983899128189936\n",
      "Pass 161, 7 0.9983899128189936\n",
      "Pass 162, 7 0.9983899128189936\n",
      "Pass 163, 7 0.9983899128189936\n",
      "Pass 164, 7 0.9983899128189936\n",
      "Pass 165, 7 0.9983899128189936\n",
      "Pass 166, 7 0.9983899128189936\n",
      "Pass 167, 7 0.9983899128189936\n",
      "Pass 168, 7 0.9983899128189936\n",
      "Pass 169, 7 0.9983899128189936\n",
      "Pass 170, 7 0.9983899128189936\n",
      "Pass 171, 7 0.9983899128189936\n",
      "Pass 172, 7 0.9983899128189936\n",
      "Pass 173, 7 0.9983899128189936\n",
      "Pass 174, 7 0.9983899128189936\n",
      "Pass 175, 7 0.9983899128189936\n",
      "Pass 176, 7 0.9983899128189936\n",
      "Pass 177, 7 0.9983899128189936\n",
      "Pass 178, 7 0.9983899128189936\n",
      "Pass 179, 7 0.9983899128189936\n",
      "Pass 180, 7 0.9983899128189936\n",
      "Pass 181, 7 0.9983899128189936\n",
      "Pass 182, 8 0.998744776853889\n",
      "Pass 183, 8 0.998744776853889\n",
      "Pass 184, 8 0.998744776853889\n",
      "Pass 185, 8 0.998744776853889\n",
      "Pass 186, 8 0.998744776853889\n",
      "Pass 187, 8 0.998744776853889\n",
      "Pass 188, 8 0.998744776853889\n",
      "Pass 189, 8 0.998744776853889\n",
      "Pass 190, 8 0.998744776853889\n",
      "Pass 191, 9 0.9990320240533556\n",
      "Pass 192, 9 0.9990320240533556\n",
      "Pass 193, 10 0.9993160693653758\n",
      "Pass 194, 10 0.9993160693653758\n",
      "Pass 195, 11 0.9995875209269763\n",
      "Pass 196, 11 0.9995875209269763\n",
      "Pass 197, 12 0.9998371797056896\n",
      "Pass 198, 12 0.9998371797056896\n",
      "Pass 199, 12 0.9998371797056896\n",
      "Pass 200, 12 0.9998371797056896\n",
      "Terminated finding 12 Paulis, total of 0.9998371797056896 worth of probability!\n"
     ]
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "maxPass = 200\n",
    "# singletons is when 'noise' threshold below which we declare we have found a singletons\n",
    "# It will be related to the measurment accuracy and the number of bins\n",
    "# Here we base it off the shotsToDo variance, on the basis of our hoped for recovery\n",
    "\n",
    "# We start that one low and then slowly increase it, meaning we are more likely to accept\n",
    "# If you have a certain probability distribution and this ansatz is not working, set it\n",
    "# so that you get a reasonable number of hits in the first round.\n",
    "singletons = (0.001*.999)/30000\n",
    "singletonsInc = singletons/2\n",
    "\n",
    "# Zeros is set high - we don't want to accept bins with very low numbers as they are probably just noise\n",
    "# If the (sum(mean - value)^2) for all the offsets is below this number we ignore it.\n",
    "# But then we lower it, meaning we are less likely to think a bin has no value in it.\n",
    "# Obviously it should never be negative.\n",
    "zerosC = (0.01*.999)/20000*2*1.1\n",
    "zerosDec = (zerosC*0.99)/maxPass\n",
    "\n",
    "\n",
    "\n",
    "prevFound = 0\n",
    "qubitSize = 6\n",
    "j6=diagm(1 => vec(hcat([[1 0] for i = 1:6]...)[1:end-1]),-1 => vec(hcat([[1 0] for i = 1:6]...)[1:end-1]))\n",
    "\n",
    "listOfX = [[fwht_natural([millionShotOracle[x+1] for x in y]) for y in s] for s in samples]\n",
    "found = Dict()\n",
    "rmappings = []\n",
    "for x in mappings\n",
    "    if length(x) == 0\n",
    "        push!(rmappings,x)\n",
    "    else\n",
    "        ralt = Dict()\n",
    "        for i in keys(x)\n",
    "            ralt[x[i]]= i\n",
    "        end\n",
    "        push!(rmappings,ralt)\n",
    "    end\n",
    "end    \n",
    "prevFound = 0\n",
    "\n",
    "\n",
    "for i in 1:maxPass\n",
    "\n",
    "\n",
    "\n",
    "    for co = 1:length(listOfX)\n",
    "        bucketSize = length(listOfX[co][1])\n",
    "        for extractValue = 1:bucketSize\n",
    "            extracted = [x[extractValue] for x in listOfX[co]]\n",
    "            if !(PEEL.closeToZero(extracted,qubitSize*2,cutoff= zerosC))\n",
    "               (isit,bits,val) = PEEL.checkAndExtractSingleton([extracted],qubitSize*2,cutoff=singletons)\n",
    "               if isit\n",
    "                  #print(\"$bits\\n\")\n",
    "                  #pval = binaryArrayToNumber(j6*[x == '0' ?  0 : 1 for x in bits])\n",
    "                  vval = parse(Int,bits,base=2)\n",
    "                  #print(\"$bits, $vval $(round(dist[vval+1],digits=5)) and $(round(val,digits=5))\\n\")\n",
    "                  PEEL.peelBack(listOfX,listOfPs,bits,val,found,ds,rmappings)\n",
    "               end\n",
    "            end\n",
    "        end   \n",
    "    end\n",
    "    if length(found) > prevFound\n",
    "                prevFound = length(found)\n",
    "    else\n",
    "        singletons += singletonsInc\n",
    "        zerosC -=zerosDec \n",
    "        if (zerosC <= 0)\n",
    "                break\n",
    "        end\n",
    "     end\n",
    "     if length(found) > 0\n",
    "            print(\"Pass $i, $(length(found)) $(sum([mean(found[x]) for x in keys(found)]))\\n\")\n",
    "            if sum([mean(found[x]) for x in keys(found)]) >= 0.999995\n",
    "                break\n",
    "            end\n",
    "     end\n",
    "\n",
    "\n",
    "end\n",
    "print(\"Terminated finding $(length(found)) Paulis, total of $(sum([mean(found[x]) for x in keys(found)]) ) worth of probability!\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00025 <===> 0.000192\n",
      "0.000284 <===> 0.000288\n",
      "0.003997 <===> 0.004\n",
      "0.003898 <===> 0.003897\n",
      "0.003929 <===> 0.003937\n",
      "0.000355 <===> 0.000288\n",
      "0.000453 <===> 0.000288\n",
      "0.019743 <===> 0.019685\n",
      "0.000287 <===> 0.000288\n",
      "0.956614 <===> 0.956605\n",
      "0.000271 <===> 0.0002\n",
      "0.009757 <===> 0.009742\n"
     ]
    }
   ],
   "source": [
    "foundV = []\n",
    "for x in keys(found)\n",
    "    vval = parse(Int,x,base=2)\n",
    "    push!(foundV,vval+1)\n",
    "    print(\"$(round(mean(found[x]),digits=6)) <===> $(round(dist[vval+1],digits=6))\\n\")\n",
    "end\n",
    "title(\"Distribution of Pauli error rates\")\n",
    "yscale(\"log\")\n",
    "ylabel(\"Error Rate\")\n",
    "xlabel(\"Paulis indexed and sorted by error rate\")\n",
    "indices = reverse(sortperm(dist))[2:15]\n",
    "scatter(1:14,[dist[x] for x in indices])\n",
    "loc = [findfirst(x->x==y,indices) for y in foundV]\n",
    "scatter(loc,[found[string(x-1,base=2,pad=12)] for x in foundV])\n",
    "xticks(1:15,[probabilityLabels(x-1,qubits=6) for x in indices],rotation=90);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "kernelspec": {
   "display_name": "Julia 1.4.1",
   "language": "julia",
   "name": "julia-1.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.4.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}