jupyter_notebooks/Tutorials/16 Randomized Benchmarking.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Randomized Benchmarking Tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This tutorial demonstrates how to perform randomized benchmarking (RB) using `pygsti`.  While RB is a very distinct protocol from Gate Set Tomography (GST), `pygsti` includes basic support for RB because of its prevalence in the community, its simplicity, and its considerable use of GST-related concepts and data structures.  Much of the implementation draws from ideas in Wallman and Flammia's [\"Randomized benchmarking with confidence\"](http://iopscience.iop.org/article/10.1088/1367-2630/16/10/103032).\n",
    "\n",
    "This tutorial will show the following, all in the context of benchmarking a single qubit:\n",
    "- how to create a list of random RB sequences (experiments).  These are just a list of pyGSTi `GateString` objects.\n",
    "- how to write a template data file from this list.\n",
    "- how to compute RB fit parameters and average fidelity from a pyGSTi `DataSet` filled with RB sequence data.\n",
    "- how to compute error bars on the various RB parameters and derived quantities.\n",
    "\n",
    "We'll begin by importing relevant modules:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function #python 2 & 3 compatibility\n",
    "\n",
    "import pygsti\n",
    "from pygsti.extras import rb\n",
    "from pygsti.construction import std1Q_XYI\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Primitive gates, and how they map to Cliffords\n",
    "First, let's choose a \"target\" gateset.  This is the set of physically-implemented, or \"primitive\" gates.  For this tutorial, we'll just use the standard $I$, $X(\\pi/2)$, $Y(\\pi/2)$ set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Primitive gates =  odict_keys(['Gi', 'Gx', 'Gy'])\n"
     ]
    }
   ],
   "source": [
    "gs_target = std1Q_XYI.gs_target\n",
    "print(\"Primitive gates = \", gs_target.gates.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate appropriately random RB sequences, we'll need to know how the set of all the 1-qubit Clifford gates map onto the primitive set (since RB requires sequences to be random sequences of *Cliffords*, not of primitive gates).  PyGSTi already contains the group of 1-qubit Cliffords, and defines each operator in terms of a set of seven \"canonical\" Clifford gates, $\\{I,X(\\pi/2),X(\\pi),X(-\\pi/2),Y(\\pi/2),Y(\\pi),Y(-\\pi/2)\\}$.\n",
    "\n",
    "Thus, we only need to know how to express each of these canonical gates as our primitive gates; then we can compose the mappings: {all Cliffords} $\\rightarrow$ {canonical Cliffords} and {canonical Cliffords} $\\rightarrow$ {primitive gates} to get our desired {all Cliffords} $\\rightarrow$ {primitive gates} map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# get the 1Q Clifford group, used later\n",
    "clifford_group = rb.std1Q.clifford_group\n",
    "\n",
    "# get the all-Cliffords --> canonical-Cliffords map\n",
    "clifford_to_canonical = rb.std1Q.clifford_to_canonical\n",
    "\n",
    "# define the canonical-Cliffords --> primitive-gates map\n",
    "canonical_to_primitive = { 'Gi':['Gi'],\n",
    "            'Gxp2':['Gx'], 'Gxp':['Gx','Gx'], 'Gxmp2':['Gx','Gx','Gx'],\n",
    "            'Gyp2':['Gy'], 'Gyp':['Gy','Gy'], 'Gymp2':['Gy','Gy','Gy'] }\n",
    "\n",
    "#Compose the two maps above to get the all-Cliffords --> primitive-gates map\n",
    "clifford_to_primitive = pygsti.construction.compose_alias_dicts(\n",
    "                            clifford_to_canonical,canonical_to_primitive)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating RB sequences\n",
    "Now let's decide what random Clifford sequences to generate.  We use $m$ to denote the length of a Clifford sequence (in Clifford gates) and $K_m$ to denote the number of different random sequences of length $m$ to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_min = 1        # minimum Clifford sequence length\n",
    "m_max = 1000     # maximum Clifford sequence length\n",
    "delta_m = 100    # length step size \n",
    "K_m_sched = 10   # K_m == 10 (constant) for all m\n",
    "\n",
    "#Note: K_m_sched need not be m-independent, and can be a dictionary\n",
    "# with (m,K_m) key-value pairs.  We'll demo this in a later tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now generate the list of random RB Clifford sequences to run.  The `write_empty_rb_files` function handles this job, and does a lot. Here's what this one function call does:\n",
    "\n",
    "- creates lists of random RB gate sequences, one list for each $m$, according to the schedule given by $m_{min}$, $m_{max}$, $\\delta_m$, and $K_m$.  These sequences are expressed as strings of Clifford gate labels and translated using any of the supplied maps (in this case, the string are translated to \"primitive\" labels also).  These lists-of-lists are returned as a dictionary whose keys are \"clifford\" (always present) and \"primitive\" (b/c it's a key of the dict passed as `alias_maps`).\n",
    "- the lists for each set of gate labels (the Cliffords and primitives in this case) is aggregated across all $m$ values (so there's just a single list of all the RB sequences) and saved to a file beginning with the given base filename.\n",
    "- an empty `DataSet` is saved in text format using the RB sequences expressed in terms of Clifford gates.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "filename_base = 'tutorial_files/rb_template'\n",
    "rb_sequences = rb.write_empty_rb_files(filename_base, m_min, m_max, delta_m,\n",
    "                                       clifford_group, K_m_sched,\n",
    "                                       {'primitive': clifford_to_primitive},\n",
    "                                       seed=0)\n",
    "\n",
    "#Note: Because K_m_sched is a constant, we cannot use Wallman and Flammia\n",
    "# error bars; if we try, the code warns us accordingly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "There is now an empty template file [tutorial_files/rb_template.txt](tutorial_files/rb_template.txt). For actual physical experiments, this file should be filled with experimental data and read in using `pygsti.io.load_dataset`.  In this tutorial, we will generate fake data instead and just use the resulting dataset object.\n",
    "\n",
    "The files [tutorial_files/rb_template_clifford.txt](tutorial_files/rb_template_clifford.txt) and [tutorial_files/rb_template_primitive.txt](tutorial_files/rb_template_primitive.txt) are text files listing all the RB sequences, expressed in terms of Cliffords and primitives respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating fake data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#To generate a dataset, we first need to make a gateset.\n",
    "#Here we assume a gate set that is perfect except for some\n",
    "# small amount of depolarizing noise on each gate.\n",
    "depol_strength = 1e-3\n",
    "gs_experimental = std1Q_XYI.gs_target\n",
    "gs_experimental = gs_experimental.depolarize(gate_noise=depol_strength)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Now we choose the number of clicks per experiment and simulate our data.\n",
    "#Note: the time to generate simulated data can be nontrivial, but here it\n",
    "# should only take a few seconds.\n",
    "\n",
    "all_rb_sequences = [] #construct an aggregate list of Clifford sequences\n",
    "for seqs_for_single_cliff_len in rb_sequences['clifford']:\n",
    "    all_rb_sequences.extend(seqs_for_single_cliff_len)\n",
    "    \n",
    "N=100 # number of samples\n",
    "rb_data = pygsti.construction.generate_fake_data(\n",
    "    gs_experimental,all_rb_sequences,N,'binomial',seed=1,\n",
    "    aliasDict=clifford_to_primitive, collisionAction=\"keepseparate\")\n",
    "\n",
    "#Note the use of aliasDict in the line above to generate fake \n",
    "# data for *Clifford-label* sequences using a GateSet  \n",
    "# containing primitive gates, and the collisionAction argument\n",
    "# which is properly handles duplicate Clifford strings (the\n",
    "# default behavior aggregates duplicate strings, but this is\n",
    "# *not* what we want for RB, which relies on *independently*\n",
    "# chosen strings without regard for duplicates)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running the RB analysis\n",
    "Now that we have data, it's time to perform the RB analysis.  The \n",
    "function `do_randomized_benchmarking` returns an `RBResults` object which holds all the relevant (input and output) RB quantities.  This object can (and will!) be used to generate error bars on the computed RB quanties.\n",
    "\n",
    "Some useful arguments are:\n",
    "- success_spamlabel : the spam label corresponding to the *expected* outcome when preparing and immediately measuring.\n",
    "- dim : the Hilbert space dimension.  This defaults to 2 (the 1-qubit case) and so can usually be left out.\n",
    "- pre_avg :  Are we, prior to fitting to the RB decay curve, going to \"pre-average\" the data?  That is, are we using a single survival probability per sequence length or not?  For now we recommend keeping this set to True (the default) for consitency with the literature.\n",
    "- clifford_to_primitive : specifying this map causes per-primitive values to be computed in addition to the usual per-Clifford values (of the average fidelity, for instance) NOTE, however, that RB IS NOT GUARANTEED TO GIVE RELIABLE A PRIMITIVE ANALYSIS (and in general will not!)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rb_results = rb.do_randomized_benchmarking(rb_data, all_rb_sequences,\n",
    "                                           success_spamlabel='minus', dim=2, pre_avg=True,\n",
    "                                           clifford_to_primitive = clifford_to_primitive)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examining the output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, so we've done RB!  Now let's examine how we can use the returned `RBResults` object to visualize and inspect the results.  First let's plot the decay curves."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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ZjRs3JiUlhRtuuIFly5bF1B08eDD33HMPL7/8MscffzxPPPEE7dq1o1OnTgV1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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a1515c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KkiVLwq7fqVMnGjVqlK5doXGw+/fvZ9++fbRv3z6sTR9//DEiwi233BJWdtiw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mAAAT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\n18c4f/2/QwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a1514a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Note: because we pre-averaged, each data blue data point is simply an \n",
    "# average of multiple success rates. However, for the primitives plot,\n",
    "# many sequences have a unique primitive sequence length, so this effect\n",
    "# is not nearly as pronounced.\n",
    "rb_results.plot('clifford')\n",
    "rb_results.plot('primitive')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the RB fit results.  The parameters are defined as follows,\n",
    "following the Wallman and Flammia article cited above.\n",
    "- `A`,`B`,`f` are fit parameters to the function $F(m) = A+B\\,f^m$, where $F(m)$ is the survival probability for sequences of length $m$.\n",
    "- `F_avg` $= ((d-1)\\,f+1)/d$, where for 1 qubit, $d=2$.  $F_{avg}$ is the average (Clifford or primitive) gate fidelity.\n",
    "- `r` $= 1-F_{avg}$.  For Cliffords, $r$ is the \"RB number.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "clifford results \n",
      "  - Using zeroth order fitting function: A + B*f^m  \n",
      "A = 0.509876520858\n",
      "B = 0.490123479142\n",
      "f = 0.996421673104\n",
      "F_avg = 0.998210836552\n",
      "r = 0.0017891634481\n",
      "\n",
      "primitive results \n",
      "  - Using zeroth order fitting function: A + B*f^m  \n",
      "A = 0.509072311819\n",
      "B = 0.490927688181\n",
      "f = 0.998995358684\n",
      "F_avg = 0.999497679342\n",
      "r = 0.000502320657821\n",
      "\n"
     ]
    }
   ],
   "source": [
    "rb_results.print_clifford()\n",
    "print\n",
    "rb_results.print_primitive()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determining error rate\n",
    "Because we generated our data from a known Markovian gate set, we can analytically compute the Clifford RB error rate r."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analytic RB error rate: 0.00176791958146\n",
      "Experimental RB error rate: 0.0017891634481\n"
     ]
    }
   ],
   "source": [
    "#First we make map our experimental gate set of primitive operations\n",
    "#into a dictionary of Cliffords:\n",
    "gs_cliff_experimental = pygsti.construction.build_alias_gateset(\n",
    "                                gs_experimental,clifford_to_primitive)\n",
    "\n",
    "#Then we directly compute the average twirled Clifford error rate:\n",
    "analytic_rb_error_rate = rb.analytic_rb_clifford_gateset_error_rate(\n",
    "                                            gs_cliff_experimental,\n",
    "                                            rb.std1Q.gs_clifford_target,\n",
    "                                            rb.std1Q.clifford_group)\n",
    "\n",
    "print(\"Analytic RB error rate:\", analytic_rb_error_rate)\n",
    "print(\"Experimental RB error rate:\", rb_results.dicts['clifford']['r'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error Bars\n",
    "Lastly, let's put some error bars on the estimates. Because we used a constant K_m_sched, we can't compute analytic error bars using the Wallman and Flammia method. We can instead, however, compute bootstrapped error bars. Error bars here are 1-sigma confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Generating non-parametric dataset.\n",
      "Bootstrapped error bars computed.  Use print methods to access.\n"
     ]
    }
   ],
   "source": [
    "rb_results.compute_bootstrap_error_bars(('clifford','primitive'),seed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've generated (bootstrapped) error bars, we can print them using the same print methods as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "clifford results \n",
      "  - Using zeroth order fitting function: A + B*f^m  \n",
      "  - with boostrapped-derived error bars (1 sigma):\n",
      "A = 0.509876520858 +/- 0.0134861508781\n",
      "B = 0.490123479142 +/- 0.0130413013227\n",
      "f = 0.996421673104 +/- 0.000273118697027\n",
      "F_avg = 0.998210836552 +/- 0.000136559348514\n",
      "r = 0.0017891634481 +/- 0.000136559348514\n",
      "\n",
      "primitive results \n",
      "  - Using zeroth order fitting function: A + B*f^m  \n",
      "  - with boostrapped-derived error bars (1 sigma):\n",
      "A = 0.509072311819 +/- 0.0143410627104\n",
      "B = 0.490927688181 +/- 0.0132980931108\n",
      "f = 0.998995358684 +/- 8.4152745885e-05\n",
      "F_avg = 0.999497679342 +/- 4.20763729425e-05\n",
      "r = 0.000502320657821 +/- 4.20763729425e-05\n",
      "\n"
     ]
    }
   ],
   "source": [
    "rb_results.print_clifford()\n",
    "print\n",
    "rb_results.print_primitive()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000136559348514\n"
     ]
    }
   ],
   "source": [
    "#We can also manually extract the error bars now; for example:\n",
    "print(rb_results.dicts['clifford']['r_error_BS'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First order fitting model\n",
    "\n",
    "As well as fitting to the standard \"zeroth order\" RB decay model, $F(m) = A+B\\,f^m$, the data is also fit to the \"first order\" decay model, as defined by Magesan et al [\"Scalable and Robust Benchmarking of Quantum Processes\"](http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.180504). This is the fit model $F(m) = A_1 + B_1 f^m + C_1(D_1 - f^2)f^{m-2}$. The average gate fidilety and the \"RB number\" are then calculated from $f$ as with the \"zeroth order\" decay model.\n",
    "\n",
    "The fit parameters can be extracted by specifying the optional parameter order='zeroth','first' or 'all' in the print and plot commands introduced above. E.g: \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "clifford results \n",
      "  - Using zeroth order fitting function: A + B*f^m  \n",
      "  - with boostrapped-derived error bars (1 sigma):\n",
      "A = 0.509876520858 +/- 0.0134861508781\n",
      "B = 0.490123479142 +/- 0.0130413013227\n",
      "f = 0.996421673104 +/- 0.000273118697027\n",
      "F_avg = 0.998210836552 +/- 0.000136559348514\n",
      "r = 0.0017891634481 +/- 0.000136559348514\n",
      "\n",
      "clifford results \n",
      "   - Using first order fitting function: A1 + (B1+C1m)*f^m \n",
      "   - with boostrapped-derived error bars (1 sigma):\n",
      "A1 = 0.509876520858 +/- 0.0488702629878\n",
      "B1 = 0.490123479142 +/- 0.0486464643206\n",
      "C1 = -3.39065966103e-15 +/- 0.00017159433693\n",
      "f1 = 0.996421673104 +/- 0.000342794307896\n",
      "F_avg1 = 0.998210836552 +/- 0.000171397153948\n",
      "r1 = 0.0017891634481 +/- 0.000171397153948\n",
      "\n"
     ]
    }
   ],
   "source": [
    "rb_results.print_clifford(order='all')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first order fitting model is claimed to be preferable when there is small but non-negligable gate-dependency in the error map associated with each Clifford.\n",
    "\n",
    "`gdep` = $D_1 - f^2$ and this is claimed by Magesan et al to be a measure of the gate-dependence of the noise, in that significantly non-zero values are associated with gate-dependence. Note that the $C_1$ value is meaningless in isolation (hence non-zero values are not important on their own) as there are only four indepedent parameters in the first order fit (rather than five) -- the decay parameter and constant factors in front of: a constant term, pure exponential decay and an $m f^m$ term."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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SpQtvvvkmX3zxBTfffDMzZ86kdu3a1K9f31MnOTmZ+vXr8/LLL/sNMCtXruzz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t0lXSfpxeI8T0i6QNKWNXlXknSapMeKvJMkXS5pw2bHb5ekhSUdJOkOSZMlTZV0n6RDJC1ck//t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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3ab518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rb_results.plot('clifford',order='all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}