{
 "metadata": {
  "name": "model_testing.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Accelerated Randomized Benchmarking: Supplemental Material"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Christopher Granade, Christopher Ferrie and D. G. Cory**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[http://www.cgranade.com/research/arb/](http://www.cgranade.com/research/arb/)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Introduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this Supplemental Material, we provide and document the Python-based implementation of our results.\n",
      "All of the figures and tables in the main body of our work are generated from the code provided here."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Preamble"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Before jumping into the code, there's a few housekeeping things to take care of. The main bulk of this notebook continues below.\n",
      "\n",
      "First, we turn on the ``division`` feature, as is recommended for using Python 2.x with scientific code."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we enable plotting support, using ``inline`` to make all of the plots load inside the notebook."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['mean', 'cov']\n",
        "`%pylab --no-import-all` prevents importing * from pylab and numpy\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We'll want to set some sensible defaults for matplotlib, too, that are nice for making printed figures."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "try:\n",
      "    import mpltools.style\n",
      "    mpltools.style.use('ggplot')\n",
      "except ImportError:\n",
      "    print (\n",
      "        \"Not able to load ggplot style--- this won't matter too much, \"\n",
      "        \"but your figures will look a little different.\"\n",
      "    )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Not able to load ggplot style--- this won't matter too much, but your figures will look a little different.\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rcParams['axes.labelsize'] = 20\n",
      "rcParams['axes.titlesize'] = 22\n",
      "rcParams['legend.fontsize'] = 18\n",
      "rcParams['xtick.labelsize'] = 14\n",
      "rcParams['ytick.labelsize'] = 14\n",
      "rcParams['lines.linewidth'] = 1.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "All that's left is to import a few things. First, we import a few tools from SciPy:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.linalg import inv, eig, sqrtm\n",
      "from scipy.stats import chisqprob\n",
      "from scipy.optimize import curve_fit, minimize\n",
      "from scipy.io import loadmat"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we import IPython's rich display support, so that we can generate and display $\\LaTeX$ and Javascript directly in the notebook."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import display, Latex, HTML, Javascript, clear_output"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Later, we'll need access to a few of Python's standard libraries in order manage paths when we load gatesets."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import os\n",
      "import glob\n",
      "import re"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we import from [QInfer](http://python-qinfer.readthedocs.org/en/latest/), our library for working with sequential Monte Carlo."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qinfer.rb import RandomizedBenchmarkingModel, p, F\n",
      "from qinfer.smc import SMCUpdater, SMCUpdaterBCRB\n",
      "from qinfer.resamplers import LiuWestResampler\n",
      "from qinfer.derived_models import BinomialModel, DifferentiableBinomialModel\n",
      "from qinfer.distributions import (\n",
      "    ConstantDistribution, ProductDistribution, UniformDistribution, PostselectedDistribution, MultivariateNormalDistribution\n",
      ")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It will also be useful to have a little function that a dictionary into a NumPy array, so we don't have to work quite so hard at it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def set_fields(arr, ix, fields):\n",
      "    for key, val in fields.iteritems():\n",
      "        if isinstance(val, np.ndarray) and len(val.shape) > 0:\n",
      "            arr[ix][key][:] = val[:]\n",
      "        else:\n",
      "            arr[ix][key] = val"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To consolidate how figures are saved, we define a common folder for figure storage. We wrap ``savefig`` to save to that folder and in multiple formats."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "FIGURES_DIR = os.path.abspath(\"../figures/\")\n",
      "if not os.path.exists(FIGURES_DIR):\n",
      "    os.mkdir(FIGURES_DIR)\n",
      "    \n",
      "print \"Figures will be stored to {}.\".format(FIGURES_DIR)\n",
      "\n",
      "_savefig = savefig\n",
      "def savefig(name):\n",
      "    for fmt in ('pdf', 'svg', 'png'):\n",
      "        _savefig(os.path.join(FIGURES_DIR, \"{}.{}\".format(name, fmt)), format=fmt, bbox_inches='tight')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Figures will be stored to c:\\users\\csferrie\\documents\\github\\accelerated-randomized-benchmarking\\figures.\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since some of the code here takes a while to run, it's helpful to make a small progress bar."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import uuid\n",
      "\n",
      "class ProgressBar(object):\n",
      "    def __init__(self):\n",
      "        self._divid = \"div-{}\".format(uuid.uuid4())\n",
      "        self._value = 0\n",
      "\n",
      "    def __del__(self):\n",
      "        self.hide()\n",
      "        \n",
      "    def hide(self):\n",
      "        display(Javascript('$(\"#{}\").hide()'.format(self._divid)))\n",
      "        \n",
      "    @property\n",
      "    def html(self):\n",
      "        return \"\"\"\n",
      "            <div id=\"{}\"></div>\n",
      "        \"\"\".format(self._divid)\n",
      "        \n",
      "    @property\n",
      "    def value(self):\n",
      "        return self._value\n",
      "    @value.setter\n",
      "    def value(self, newval):\n",
      "        self._value = newval\n",
      "        self.refresh()\n",
      "        \n",
      "    def refresh(self):\n",
      "        display(Javascript('$(\"#{}\").progressbar({{value: {}}})'.format(self._divid, self._value)))\n",
      "        \n",
      "    def show(self):\n",
      "        display(HTML(self.html))\n",
      "        self.refresh()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There's a few non-critical warnings that come up in more recent versions of NumPy, and so we disable those here to prevent excess output from being printed."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import warnings\n",
      "warnings.simplefilter('ignore', DeprecationWarning)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we declare a few LaTeX commands. These don't show up when the notebook is rendered, but you can see them by editing this cell.\n",
      "$\n",
      "    \\newcommand{\\bra}[1]{\\left\\langle#1\\right|}\n",
      "    \\newcommand{\\ket}[1]{\\left|#1\\right\\rangle}\n",
      "$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Model Setup"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To generate and analyze benchmarking data, we'll need the likelihood model defined in ``benchmarking_models.py``. Since we'll be considering batches over the underlying two-outcome experiment described in the main text, we'll wrap the randomized benchmarking models in ``DifferentiableBinomialModel`` instances, representing binomial samples over Bernoulli data in a way that allows us to take derivatives\n",
      "of the likelihood function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import benchmarking_models as bm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = DifferentiableBinomialModel(RandomizedBenchmarkingModel(order=0))\n",
      "il_model = DifferentiableBinomialModel(RandomizedBenchmarkingModel(interleaved=True, order=0))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's plot a \"real\" signal to test that our models are at least somewhat reasonable. For our test signals, we will plot $\\hat{F}_g(m)$ for $m$ ranging in steps of 10 up to 400. For each sequence length, we simulate $K = 10\\,000$ data points."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ms = np.arange(0, 400, 10)\n",
      "\n",
      "expparams = np.empty(ms.shape, dtype=model.expparams_dtype)\n",
      "expparams['m'] = ms\n",
      "expparams['n_meas'] = 10000\n",
      "\n",
      "true_model = np.array([[0.9994, 0.5, 0.5], [0.9998, 0.5, 0.5]])\n",
      "\n",
      "example_signal = model.simulate_experiment(true_model, expparams) / expparams['n_meas']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(ms, example_signal[0, 0], 'k:', label=r'$p = {}$'.format(true_model[0, 0]))\n",
      "plot(ms, example_signal[0, 1], 'k-', label=r'$p = {}$'.format(true_model[1, 0]))\n",
      "xlabel('$m$')\n",
      "ylabel(r'$\\hat{F}_g(m)$')\n",
      "legend(loc='best')\n",
      "\n",
      "savefig('ex-signal-noninterleaved')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YM2dOsx4PaXlDhw7FqFGjALyec2zx4sXvHHeOkNbMwMAAgwYNknYYDdYmhvd2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\ndIkDjIiIdIkDjIiIdOlfpCpL4CG6/uMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xabc5240>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will also want to test that the interleaved model gives reasonable signals."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ms = np.arange(0, 400, 10)\n",
      "expparams = np.empty(ms.shape, dtype=il_model.expparams_dtype)\n",
      "expparams['m'] = ms\n",
      "expparams['n_meas'] = 10000\n",
      "expparams = np.repeat(expparams, 2)\n",
      "\n",
      "# Make the first half of the data the reference.\n",
      "expparams['reference'][:len(expparams)//2] = True\n",
      "\n",
      "# For the interleaved signals, m is doubled.\n",
      "expparams['reference'][len(expparams)//2:] = False\n",
      "expparams['m'][len(expparams)//2:] *= 2\n",
      "\n",
      "true_model = np.array([[0.99994, 0.99999, 0.5, 0.5], [0.9999, 0.99999, 0.5, 0.5]])\n",
      "example_il_signal = il_model.simulate_experiment(true_model, expparams) / expparams['n_meas']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ylim((0.965, 1.001))\n",
      "plot(ms, example_il_signal[0, 0, :len(expparams)/2], 'k:', label='Reference')\n",
      "plot(ms, example_il_signal[0, 0, len(expparams)/2:], 'k-', label='Interleaved')\n",
      "legend(loc='lower left')\n",
      "\n",
      "xlabel('$m$')\n",
      "ylabel(r'$\\hat{F}_g(m)$')\n",
      "\n",
      "savefig('ex-signal-interleaved')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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k9OnTBdrnjRs36N27N6mpqURFReHk5MSmTZvIysoqdPyCIAjFQWUJr2LFirn2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\nEp4QQohGQRKeEEKIRkESnhBCiEbh/wBZn4qlBZs99wAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4c1cb10>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fisher Information Calculations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For a given set of parameters, these functions numerically compute the Fisher information matrix, invert it and take the square root and finally return the element which corresponds to a lower bound on $p$ and $\\tilde p$ for the non-interleaved and interleaved models, respectively."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def achievable_non_interleaved(m_max, K, p, A, B):\n",
      "    ms = np.arange(m_max)\n",
      "    model = DifferentiableBinomialModel(RandomizedBenchmarkingModel())\n",
      "    \n",
      "    expparams = np.empty(ms.shape, dtype=model.expparams_dtype)\n",
      "    expparams['m'] = ms\n",
      "    expparams['n_meas'] = K\n",
      "    \n",
      "    true_model = np.array([[p, A, B]])\n",
      "    \n",
      "    fi = np.sum(model.fisher_information(true_model, expparams), axis=-1)[:, :, 0]\n",
      "    \n",
      "    return sqrtm(inv(fi))[0, 0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def achievable_interleaved(m_max_ref, m_max_C, K, p_tilde, p_ref, A, B, m_step_ref=1, m_step_C=1):\n",
      "    ms_ref = np.arange(0, m_max_ref, m_step_ref)\n",
      "    ms_C   = np.arange(0, m_max_C,   m_step_C)\n",
      "    \n",
      "    model = DifferentiableBinomialModel(RandomizedBenchmarkingModel(interleaved=True))\n",
      "    \n",
      "    true_model = np.array([[p_tilde, p_ref, A, B]])\n",
      "    \n",
      "    # Calculate the FI for the reference and p_C measurements separately,\n",
      "    # then add them.\n",
      "    fi = np.zeros((4, 4))\n",
      "    \n",
      "    for ms, reference in [(ms_ref, True), (ms_C, False)]:\n",
      "        expparams = np.empty(ms.shape, dtype=model.expparams_dtype)\n",
      "        expparams['m'] = ms\n",
      "        expparams['n_meas'] = K       \n",
      "        expparams['reference'] = reference\n",
      "        \n",
      "        fi += np.sum(model.fisher_information(true_model, expparams), axis=-1)[:, :, 0]\n",
      "    \n",
      "    return sqrtm(inv(fi))[0, 0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "achievable_non_interleaved(40, 40, p(0.9994), 1.5, -.6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "0.00033446613060621893"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can also consider the optimization of the Fisher information over $m$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def best_m(p_tilde, p_ref, A, B):\n",
      "    objective = lambda m: (A**2 *m**2 *p_tilde**(-2 + 2*m)*p_ref**(2*m))/((-1 + B + A* p_tilde**m *p_ref**m)* (B + A*p_tilde**m *p_ref**m))\n",
      "    result = minimize(objective,\n",
      "                      100, method='nelder-mead'\n",
      "                      )\n",
      "    return result.x   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the optimal $m$ depends strongly on the value of $B$. For large $B$, the benefits of longer sequences is correspondingly reduced."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(4,3))\n",
      "As = linspace(0, 0.5, 100)\n",
      "\n",
      "best_ms = []\n",
      "for A in As:\n",
      "    best_ms.append(np.ceil(best_m(p(0.9994), p(1 - 0.0011), A, 0.5)))\n",
      "\n",
      "xlabel('$A$')\n",
      "ylabel(r'$m_{\\mathrm{opt}}(A)$')\n",
      "plot(As, best_ms, 'k-')\n",
      "\n",
      "savefig('best-m-vs-A')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UXOXxxx/n/vvvx2g0YjQaGTduHL/97W+ZNWsWvr6+d7XtgIAAkpKS7rrGOn+6+nPLly/n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\no/0/Qf/of97VX0AAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4d74c10>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(4, 3))\n",
      "\n",
      "Bs = linspace(.25, .75, 100)\n",
      "best_ms = [] \n",
      "\n",
      "for B in Bs:\n",
      "    best_ms.append(np.ceil(best_m(p(0.9994), p(1 - 0.0011), 0.25, B)))\n",
      "\n",
      "xlabel('$B$')\n",
      "ylabel(r'$m_{\\mathrm{opt}}(B)$')\n",
      "plot(Bs, best_ms, 'k-')\n",
      "\n",
      "savefig('best-m-vs-B')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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zM8v1oG7cuDFqtVrflBYfviAYlkKh4N133yU8PJz9+/ezefNmqSPJQo215IYN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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4d74ed0>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As discussed in the main body, as $d \\to \\infty$ then $B \\to 0$ and $A\\to 1$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ps = 1 - np.logspace(-4, -0.5, 100)\n",
      "m_opts = []\n",
      "\n",
      "for p_val in ps:\n",
      "    m_opts.append(best_m(p_val, p_val, 1, 0))\n",
      "    \n",
      "loglog((1 - ps), np.ceil(m_opts), 'k-')\n",
      "gca().invert_xaxis()\n",
      "xlabel('$1 - F$')\n",
      "ylabel(r'$m_{\\mathrm{opt}}(F)$')\n",
      "\n",
      "savefig('limit-best-m')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:2: RuntimeWarning: invalid value encountered in true_divide\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YyKBFBAtOFebm5nZ48Ky1tRU7duyw2H6FltB+jav9sFqv13daV2j/Wcwxc86Z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\nmFWoHFvIgjO3jJhySl8rtQ5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       "text": [
        "<matplotlib.figure.Figure at 0x4c0bfd0>"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Risk"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We want to find the risk in $p$ as a function of $A$, $B$, $m_\\max$ and the number of shots $K$ per sequence length. We will assume linear sampling ($m = 0, 1, 2, \\dots$) for now. Recall that the Bayes risk is defined as the expected loss that an estimator will incur, taken over a prior $\\pi$ for the true parameters and all possible datasets:\n",
      "\\begin{equation}\n",
      "    r(\\hat{p}, \\pi) := \\mathbb{E}_{\\vec{x}\\sim\\pi, D} [(\\hat{p}(D) - p)^2].\n",
      "\\end{equation}\n",
      "We let $r_{\\text{SMC}}$ and $r_{\\text{LSF}}$ be the risks for $\\hat{p}$ being the sequential Monte Carlo and least-squares fit estimators, respectively, and shall let the choice of prior $\\pi$ be fixed."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Model and Prior"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We choose as the prior a normal distribution with mean $\ud835\udf41 = (0.95, 0.05, 0.3, 0.5)$ and covariance $\ud835\udf2e = \\mathrm{diag}(0.01, 0.01, 0.01, 0.01)^2$, postselected to lie within the region of valid parameter vectors $\\boldsymbol{x} = (\\tilde{p}, p_{\\text{ref}}, A, B)$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "risk_model = DifferentiableBinomialModel(RandomizedBenchmarkingModel(interleaved=True))\n",
      "risk_prior = MultivariateNormalDistribution(\n",
      "        mean=np.array([0.95, 0.95, 0.3, 0.5]),\n",
      "        cov=np.diag([0.01, 0.01, 0.01, 0.01])**2\n",
      "    )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "SMC"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First, we find the risk achieved by sequential Monte Carlo processing. In doing so, we will also calculate the relevant Bayesian Cramer-Rao Bounds (BCRBs) and posterior variances. Ideally, the SMC algorithm should achieve a risk close to that given by the BCRB, and that estimated by the posterior variance.\n",
      "\n",
      "Note that because this function also calculates the BCRBs, it is significantly slower than updating alone."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def risk(refms, Cms, K, n_trials=100, n_particles = 1000):\n",
      "    \"\"\"\n",
      "    Evaluates the risk incurred by using sequential Monte Carlo (SMC)\n",
      "    to estimate benchmarking models.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    refms : list\n",
      "        List of values of $m$ to sample the reference curve at.\n",
      "    Cms : list\n",
      "        List of values of $m$ to sample the interleaved curve at.\n",
      "    K : int\n",
      "        Number of shots to take per sequence length.\n",
      "    n_trials : int\n",
      "        Number of times to run the SMC estimation procedure in\n",
      "        estimating the risk.\n",
      "    n_particles : int\n",
      "        Number of SMC particles to use in estimating the benchmarking model.\n",
      "    \"\"\"\n",
      "    \n",
      "    # Allocate arrays to hold results.\n",
      "    loss     = np.empty((n_trials,))\n",
      "    postvar  = np.empty((n_trials,))\n",
      "    bcrb_pps = np.empty((n_trials,))\n",
      "    \n",
      "    # TODO: fill these arrays!\n",
      "    loss_trs = np.empty((n_trials,))\n",
      "    bcrb_trs = np.empty((n_trials,))\n",
      "    postvar_trs  = np.empty((n_trials,))\n",
      "    \n",
      "    # Make and show a progress bar.\n",
      "    prog = ProgressBar()\n",
      "    prog.show()\n",
      "    \n",
      "    for idx_trial in xrange(n_trials):\n",
      "        true_model = risk_prior.sample()\n",
      "        updater = SMCUpdaterBCRB(risk_model, n_particles, risk_prior, resampler=LiuWestResampler(0.95),\n",
      "                                 initial_bim=None, adaptive=False)\n",
      "         \n",
      "        eps = np.array((\n",
      "            [(m, True, K) for m in refms] +\n",
      "            [(m, False, K) for m in Cms]\n",
      "        ), dtype=risk_model.expparams_dtype)\n",
      "        # Randomizing the order we perform experiments in may help?\n",
      "        # np.random.shuffle(eps)\n",
      "        data = risk_model.simulate_experiment(true_model, eps)[0, 0, :]\n",
      "        \n",
      "        for epvec, datum in zip(eps, data):\n",
      "            updater.update(datum, epvec.reshape((1,)))\n",
      "            \n",
      "        mu = updater.est_mean()\n",
      "        loss[idx_trial] = np.real(mu[0] - true_model[0, 0])**2\n",
      "        loss_trs[idx_trial] = np.real(np.sum((mu - true_model[0])**2))\n",
      "        \n",
      "        prog.value = 100 * ((idx_trial + 1) / n_trials)\n",
      "        \n",
      "        inv_bim = inv(updater.current_bim)\n",
      "        bcrb_pps[idx_trial] = inv_bim[0, 0]\n",
      "        bcrb_trs[idx_trial] = np.trace(inv_bim)\n",
      "        cov = updater.est_covariance_mtx()\n",
      "        postvar[idx_trial] = cov[0, 0]\n",
      "        postvar_trs[idx_trial] = np.trace(cov)\n",
      "        \n",
      "    return {\n",
      "        'smc_risk_p': np.array([np.mean(loss), np.std(loss)]),\n",
      "        'smc_risk_tr': np.array([np.mean(loss_trs), np.std(loss_trs)]),\n",
      "        'smc_median_tr': np.median(loss_trs),\n",
      "        'bcrb_p': np.mean(bcrb_pps),\n",
      "        'postvar_p': np.mean(postvar),\n",
      "        'bcrb_tr': np.mean(bcrb_trs),\n",
      "        'postvar_tr': np.mean(postvar_trs)\n",
      "    }"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Least Squares Fitting"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to do least squares fitting, we must have a trial function. This could in principle be provided by the SMC model above (by way of the likelihood method), but we want to make a comparison to how least squares fitting is used in practice. Thus, we use as a trial function $F_g(m; p, A, B) = A p^m + B$, where $p$ is either $p_{\\text{ref}}$ or $p_{\\bar{\\mathcal{C}}}$ depending on whether we are analyzing referenced data or not.\n",
      "\n",
      "In addition, we will let $F_g = 10^{10}$ for invalid choices of $p$, $A$ and $B$ such that the residuals from actual data are very large, hence constraining the fit to an appropriate region. Note that if we do not do this, it's fairly common to obtain $\\hat{p}_\\text{LSF} \\ge 10^{7}$, as the estimator is the ratio between two fit parameters, and is hence sensitive to cases where the unconstrained fit finds small denominators."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def exp_trial_fn(m, p, A, B):\n",
      "    F_g = A * p**m + B\n",
      "    return np.where(\n",
      "        np.all([\n",
      "            p >= 0, p <= 1,\n",
      "            A >= -1, A <= 1,\n",
      "            B >= 0, B <= 1\n",
      "        ], axis=0),\n",
      "        F_g,\n",
      "        1e10 # Something far from actual data.\n",
      "    )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Once we have a trial function, we now repeatedly generate test data for the LSF estimator, then run the fit on this test data. Since LSFs require an initial test point, we will chose such from our prior, using the same informative prior as was used for the SMC risk evaluation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def risk_lsf(refms, Cms, K, n_trials=100):\n",
      "    \"\"\"\n",
      "    Evaluates the risk incurred by using least squares fitting (LSF)\n",
      "    to estimate benchmarking models.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    refms : list\n",
      "        List of values of $m$ to sample the reference curve at.\n",
      "    Cms : list\n",
      "        List of values of $m$ to sample the interleaved curve at.\n",
      "    K : int\n",
      "        Number of shots to take per sequence length.\n",
      "    n_trials : int\n",
      "        Number of times to run the SMC estimation procedure in\n",
      "        estimating the risk.\n",
      "    \"\"\"\n",
      "    \n",
      "    loss = np.empty((n_trials,))\n",
      "    loss_tr = np.empty((n_trials,))\n",
      "    \n",
      "    prog = ProgressBar()\n",
      "    prog.show()\n",
      "    \n",
      "    for idx_trial in xrange(n_trials):\n",
      "        true_model = risk_prior.sample()\n",
      "        \n",
      "        # Generate simulated data, using the same model as was used in the SMC risk\n",
      "        # evaluation.\n",
      "        ref_eps = np.array([\n",
      "            (m, True, K) for m in refms\n",
      "        ], dtype=risk_model.expparams_dtype)\n",
      "        C_eps = np.array([\n",
      "            (m, False, K) for m in Cms\n",
      "        ], dtype=risk_model.expparams_dtype)\n",
      "        \n",
      "        ref_data = risk_model.simulate_experiment(true_model, ref_eps)[0, 0, :] / K\n",
      "        C_data = risk_model.simulate_experiment(true_model, C_eps)[0, 0, :] / K\n",
      "        \n",
      "        # Obtain least squares fits to each of the two curves.\n",
      "        p0 = np.real(risk_prior.sample()[0, 1:]) # Another hack...\n",
      "        res = curve_fit(exp_trial_fn, xdata=refms, ydata=ref_data, p0=p0, maxfev=10000)\n",
      "        p_ref, A_ref, B_ref = res[0]\n",
      "        \n",
      "        res = curve_fit(exp_trial_fn, xdata=Cms, ydata=C_data, p0=p0, maxfev=10000)\n",
      "        p_C, A_C, B_C = res[0]\n",
      "        \n",
      "        mu = p_C / p_ref\n",
      "        \n",
      "        prog.value = 100 * ((idx_trial + 1) / n_trials)\n",
      "        \n",
      "        loss[idx_trial] = (mu - true_model[0, 0])**2\n",
      "        loss_tr[idx_trial] = np.sum((np.array([mu, p_ref, (A_ref + A_C) / 2, (B_ref + B_C) / 2]) - true_model[0])**2)\n",
      "        \n",
      "    return {\n",
      "        'lsf_risk_p': np.array([np.mean(loss), np.std(loss)]),\n",
      "        'lsf_risk_tr': np.array([np.mean(loss_tr), np.std(loss_tr)])\n",
      "    }"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Performance vs $K$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "refms = np.arange(1,100,1).astype(int)\n",
      "Cms = np.arange(1,50,1).astype(int)\n",
      "\n",
      "n_trials = 100\n",
      "\n",
      "Ks = np.logspace(0, 5, 4).astype(int)\n",
      "\n",
      "performance = np.zeros(\n",
      "    (Ks.shape[0],),\n",
      "    dtype=[\n",
      "        ('smc_risk_p', '2float'),\n",
      "        ('smc_risk_tr', '2float'),\n",
      "        ('lsf_risk_p', '2float'),\n",
      "        ('lsf_risk_tr', '2float'),\n",
      "        ('smc_median_tr', float),\n",
      "        \n",
      "        ('bcrb_p', float),\n",
      "        ('postvar_p', float),\n",
      "        ('bcrb_tr', float),\n",
      "        ('postvar_tr', float),\n",
      "    ]\n",
      ").view(np.recarray)\n",
      "\n",
      "with warnings.catch_warnings():\n",
      "    warnings.simplefilter('ignore')\n",
      "    for idx_K, K in enumerate(Ks):\n",
      "        print \"K = {}, SMC:\".format(K)\n",
      "        set_fields(performance, idx_K, risk(refms, Cms, K, n_trials=n_trials, n_particles=10000))\n",
      "        clear_output()\n",
      "        \n",
      "        print \"K = {}, LSF:\".format(K)\n",
      "        set_fields(performance, idx_K, risk_lsf(refms, Cms, K, n_trials=n_trials))\n",
      "        clear_output()\n",
      "        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(9, 5))\n",
      "\n",
      "loglog(Ks, performance.bcrb_p, 'k-', linewidth=2, label='BCRB')\n",
      "\n",
      "\n",
      "plot(Ks, performance.smc_risk_p[:, 0], 'bx-', label='SMC Risk')\n",
      "plot(Ks, performance.lsf_risk_p[:, 0], 'rx--', label='LSF Risk')\n",
      "loglog(Ks, performance.postvar_p, 'mx:', label='Posterior Variance')\n",
      "\n",
      "ylabel('Mean squared error')\n",
      "xlabel('Number of Shots per Sequence')\n",
      "\n",
      "# We'll make the legend in the next cell.\n",
      "ax = gca()\n",
      "ax.yaxis.grid(color='gray', linestyle='dotted')\n",
      "\n",
      "savefig('risk-comparison')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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efPFFNmzYQFlZWaDDEqJ+UVFcevRRzufmUjF7Ng6tFt3SpahOnXJOmi6/AyWE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\niESUOBFCCCGESESJEyGEEEKIRP8AWbMJmjkBE0cAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x535b1d0>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(9, 5))\n",
      "\n",
      "loglog(Ks, performance.bcrb_tr, 'k-', linewidth=2, label='BCRB')\n",
      "\n",
      "plot(Ks, performance.smc_risk_tr[:, 0], 'bx-', label='SMC Risk')\n",
      "plot(Ks, performance.lsf_risk_tr[:, 0], 'rx--', label='LSF Risk')\n",
      "loglog(Ks, performance.postvar_tr, 'mx:', linewidth= 5, label='Posterior Variance')\n",
      "\n",
      "ylabel('Risk')\n",
      "xlabel('Number of Shots per Sequence')\n",
      "\n",
      "#legend()\n",
      "\n",
      "savefig('risk-tr-comparison')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VlZWVLwj56KOPcvXVV9OlSxcsFgvJycmsWbOGOXPmcMstt9C2bVtWrFjBqlWr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\nYPAKM5TjW/2MHaIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4f80310>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Performance vs $m_\\max$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ms = np.logspace(1.5, 3, 4).astype(int)\n",
      "K = 1000\n",
      "n_trials = 100\n",
      "\n",
      "performance_v_m = np.zeros(\n",
      "    (ms.shape[0],),\n",
      "    dtype=[\n",
      "        ('smc_risk_p', '2float'),\n",
      "        ('smc_risk_tr', '2float'),\n",
      "        ('lsf_risk_p', '2float'),\n",
      "        ('lsf_risk_tr', '2float'),\n",
      "        ('smc_median_tr', float),\n",
      "        \n",
      "        ('bcrb_p', float),\n",
      "        ('postvar_p', float),\n",
      "        ('bcrb_tr', float),\n",
      "        ('postvar_tr', float),\n",
      "    ]\n",
      ").view(np.recarray)\n",
      "\n",
      "with warnings.catch_warnings():\n",
      "    warnings.simplefilter('ignore')\n",
      "    for idx_m, m_max in enumerate(ms):\n",
      "        marr = np.arange(1, m_max, 10).astype(int)\n",
      "        \n",
      "        print \"m_max = {}, SMC:\".format(m_max)\n",
      "        set_fields(performance_v_m, idx_m, risk(marr, marr, K, n_trials=n_trials,n_particles=10000))\n",
      "        clear_output()\n",
      "        \n",
      "        print \"m_max = {}, SMC:\".format(m_max)\n",
      "        set_fields(performance_v_m, idx_m, risk_lsf(marr, marr, K, n_trials=n_trials))\n",
      "        clear_output()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(9, 5))\n",
      "xlim(10.0**1.5, 10**3)\n",
      "\n",
      "#loglog(Ks, crbs, label='Cramer-Rao Bound')\n",
      "loglog(ms, performance_v_m.bcrb_tr, 'k-', linewidth=2, label='BCRB')\n",
      "\n",
      "#errorbar(Ks, risks_smc[:, 0], yerr=risks_smc[:, 1], label='SMC Risk')\n",
      "#errorbar(Ks, risks_lsf[:, 0], yerr=risks_lsf[:, 1], label='LSF Risk')\n",
      "\n",
      "# Error bars don't seem to be working, so switching to ordinary plots for now.\n",
      "#plot(ms, performance_v_m.smc_median_tr[:], 'x-.', color='cyan', label='SMC Median Loss')\n",
      "plot(ms, performance_v_m.smc_risk_tr[:, 0], 'bx-', label='SMC Risk')\n",
      "plot(ms, performance_v_m.lsf_risk_tr[:, 0], 'rx--', label='LSF Risk')\n",
      "loglog(ms, performance_v_m.postvar_tr, 'mx:', linewidth = 5, label='Posterior Variance')\n",
      "\n",
      "\n",
      "ylabel('Risk')\n",
      "xlabel('Maximum Sequence Length Considered')\n",
      "\n",
      "legend()\n",
      "\n",
      "# We use the same legend as above, so no additional legend here.\n",
      "\n",
      "savefig('risk-tr-comparison-vs-m-max')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0SbZBJgiCIHUQNZWSkoIVK1YgKysLCoUCISEhVc76LWGVVbVajQcPHuhtkycn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\ngRIhhBBCSAT/AJPt2URR1RS2AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x62dccd0>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exploring prior knowledge"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_sigs = 3\n",
      "sigs = 1/logspace(2,n_sigs+1,n_sigs)\n",
      "\n",
      "ms_ref = xrange(1, 101,10) #np.logspace(0, 10, num=20, base=2).astype(int)\n",
      "ms_C   = xrange(1, 202,10) #np.logspace(0, 10, num=20, base=2).astype(int)\n",
      "K = 10000\n",
      "\n",
      "phys_model = BinomialModel(RandomizedBenchmarkingModel(interleaved=True))\n",
      "mean=np.array([0.99, 0.99, 0.32, 0.5])\n",
      "\n",
      "err = np.zeros(n_sigs)\n",
      "\n",
      "for idx_sig in xrange(n_sigs):\n",
      "    \n",
      "    cov=np.diag(sigs[idx_sig]*ones((4,)))**2\n",
      "\n",
      "    phys_prior =  PostselectedDistribution(MultivariateNormalDistribution(\n",
      "            mean=mean,\n",
      "            cov=cov\n",
      "        ), phys_model)\n",
      "    \n",
      "    updater = SMCUpdater(\n",
      "        phys_model, 10000, phys_prior,\n",
      "        resampler=LiuWestResampler(0.9)\n",
      "    )\n",
      "     \n",
      "    eps = np.array((\n",
      "        [(m, True, K) for m in ms_ref] +\n",
      "        [(m, False, K) for m in ms_C]\n",
      "    ), dtype=phys_model.expparams_dtype)\n",
      "    \n",
      "    data = phys_model.simulate_experiment(mean[np.newaxis], eps)\n",
      "        \n",
      "    for epvec, datum in zip(eps, data):\n",
      "        updater.update(datum, epvec.reshape((1,)))\n",
      "            \n",
      "    mu = updater.est_mean()\n",
      "    err[idx_sig] = np.real(mu[1] - mean[1])**2\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print err"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[  1.23039305e-05   3.19167963e-09   3.07232847e-12]\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Testing with Physically-Simulated Gates"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We start by making an initial state and a measurement that both look like $\\eta \\ket{0}\\bra{0} + (1-\\eta)\\ket{1}\\bra{1}$. Note that the ``flatten`` argument ``order='F'`` corresponds to the column-stacking convention."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rho_psi = np.diag(np.array([0.9, 0.1], dtype=complex)).flatten(order='F')\n",
      "E_psi = rho_psi.conj().transpose()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we need to load the gates produced by Holger Haas. These are stored as one MAT-file per gate, so we'll use ``loadmat`` to import them."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gateset_dir = os.path.abspath('../gates/Sim_03_12_1742/')\n",
      "gateset_files = glob.glob(os.path.join(gateset_dir, '*.mat'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# QuaEC uses slightly different names from QuantumUtils`, so we define a mapping here.\n",
      "gateset_namemap = {\n",
      "    'Had': 'H',\n",
      "    'Z90': 'R_pi4',\n",
      "    'Z45': 'T',\n",
      "    'X180': 'X',\n",
      "    'Y180': 'Y',\n",
      "    'Z180': 'Z'\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gateset = {\n",
      "    # Extract the name of the gate from strings like \"pulseHad.mat\".\n",
      "    gateset_namemap[re.match('pulse(.*)\\.mat', os.path.split(gateset_file)[1]).groups()[0]]:\n",
      "    # Load the actual file, and grab the supermatrix representation of the actual gate.\n",
      "    loadmat(gateset_file)['S']\n",
      "    for gateset_file in gateset_files\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We add to the gateset a *perfect* identity, since we can implement this gate by simply doing nothing. That is, since everything is single-qubit, we don't have to wait relative to another qubit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gateset['I'] = np.eye(4, dtype=complex)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ideal_simulator = bm.RBPhysicalSimulator(paranoid=True)\n",
      "simulator = bm.RBPhysicalSimulator(gateset, E_psi, rho_psi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.set_printoptions(precision=4, linewidth=100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gs_true = simulator.interleaved_model_parameters((0, 1))\n",
      "print gs_true\n",
      "best_m(*gs_true)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "NameError",
       "evalue": "name 'best_m' is not defined",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-29-32e7e8f14944>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mgs_true\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msimulator\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minterleaved_model_parameters\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[0mgs_true\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mbest_m\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mgs_true\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;31mNameError\u001b[0m: name 'best_m' is not defined"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(0.99833448374511424, 0.99570506108502421, 0.3184575405086596, 0.50120763151836933)\n"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The optimal $m$ found by ``best_m`` agrees roughly with the heuristic that $A p^m + B \\approx 0.5$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "log2(0.5) / log2(gs_true[0] * gs_true[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "116.08379417858944"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we get a simple \"signal\" out and plot it to make sure everything works. We do so by taking the limit $K \\to \\infty$, such that we get out the exact survival probability for each sequence, then average over sequences. In actual estimation, we will use something much less demanding."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ms = np.arange(2, 100, 20)\n",
      "target = (0, 1) # (identity, X)\n",
      "n_seq_per_m = 20\n",
      "ref_ps = np.array([\n",
      "    np.mean([simulator.p_survival(simulator.random_sequence(m)) for idx in xrange(n_seq_per_m)])\n",
      "    for m in ms\n",
      "])\n",
      "interleaved_ps = np.array([\n",
      "    np.mean([simulator.p_survival(simulator.random_interleaved_sequence(m, target)) for idx in xrange(n_seq_per_m)])\n",
      "    for m in ms\n",
      "])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "C:\\Users\\csferrie\\Documents\\GitHub\\python-quaec\\src\\qecc\\utils.py:71: UserWarning: Deprecated; see method from_clifford in PauliClass.\n",
        "  warnings.warn(explanation)\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(11,7))\n",
      "\n",
      "p_til, p_ref, A, B = gs_true\n",
      "p_C = p_til * p_ref\n",
      "\n",
      "plot(ms, ref_ps, 'xk', label='Reference Signal', markersize=10)\n",
      "plot(ms, A * p_ref**ms + B, '--k', label='Reference Model')\n",
      "plot(ms, interleaved_ps, '.k', label='Interleaved Signal for $U = X$',  markersize=10)\n",
      "plot(ms, A * p_C**(ms/2) + B, '-k', label='Interleaved Model')\n",
      "legend()\n",
      "xlabel('$m$')\n",
      "ylabel(r'$\\hat{p}(m)$')\n",
      "\n",
      "savefig('example-phys-signal')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "C:\\Users\\csferrie\\AppData\\Local\\Enthought\\Canopy\\User\\lib\\site-packages\\numpy\\core\\numeric.py:460: ComplexWarning: Casting complex values to real discards the imaginary part\n",
        "  return array(a, dtype, copy=False, order=order)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VFZW67VizZs2wdu1aXLx4EQMHDsT8+fNhZmaGhQsX4t9//63BSBljtUleXh4WL16MnJwc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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x808bac8>"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@np.vectorize\n",
      "def phys_simulate_experiment(expparam_vec):\n",
      "    print '.', \n",
      "    m, ref, n_meas = expparam_vec\n",
      "    if ref:\n",
      "        return np.sum([\n",
      "            simulator.sample_interleaved_sequence(int(m), (0, 1))\n",
      "            for idx in xrange(n_meas)\n",
      "        ])\n",
      "    \n",
      "    else:        \n",
      "        return np.sum([\n",
      "            # Note that the sequence length is defined differently\n",
      "            # for the interleaved and reference cases by a factor of 2.\n",
      "            simulator.sample_random_sequence(2 * int(m))\n",
      "            for idx in xrange(n_meas)\n",
      "        ])\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Lots of data with a \"bad\" prior"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ms_ref = xrange(1, 201,10) #np.logspace(0, 10, num=20, base=2).astype(int)\n",
      "ms_C   = xrange(2, 202,10) #np.logspace(0, 10, num=20, base=2).astype(int)\n",
      "K = 1000\n",
      "\n",
      "mean=np.array([0.95, 0.95, 0.3, 0.5])\n",
      "cov=np.diag([0.01, 0.01, 0.01, 0.01])**2\n",
      "\n",
      "phys_model = BinomialModel(RandomizedBenchmarkingModel(interleaved=True))\n",
      "phys_prior =  PostselectedDistribution(MultivariateNormalDistribution(\n",
      "        mean=mean,\n",
      "        cov=cov\n",
      "    ), phys_model)\n",
      "print \"The true state is \", np.sqrt(np.dot(mean - gs_true, np.dot(inv(cov),mean - gs_true))),\"sigma from the prior mean.\"\n",
      "\n",
      "print \"The true state is outside of a\", 100*(1 - chisqprob(np.dot(mean - gs_true, np.dot(inv(cov),mean - gs_true)),4)),\"% credible region.\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The true state is  6.90457392111 sigma from the prior mean.\n",
        "The true state is outside of a 99.9999998896 % credible region.\n"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "updater = SMCUpdater(\n",
      "    phys_model, 20000, phys_prior,\n",
      "    resampler=LiuWestResampler(0.9)\n",
      ")\n",
      " \n",
      "eps = np.array((\n",
      "    [(m, True, K) for m in ms_ref] +\n",
      "    [(m, False, K) for m in ms_C]\n",
      "), dtype=phys_model.expparams_dtype)\n",
      "\n",
      "print 'Simulating data...\\r',\n",
      "data = phys_simulate_experiment(eps)\n",
      "\n",
      "print 'Performing SMC updates...\\r',\n",
      "for epvec, datum in zip(eps, data):\n",
      "    updater.update(datum, epvec.reshape((1,)))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Simulating data...\r",
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
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        ". "
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       "text": [
        ". "
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        ". "
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       "output_type": "stream",
       "stream": "stdout",
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        ". "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
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      },
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
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      {
       "output_type": "stream",
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        ". "
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        ". "
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        ". "
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        ". "
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        ". "
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        ". "
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        ". "
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        ". "
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        ". "
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        ". "
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        ". "
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      },
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        ". "
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      },
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        ". "
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      },
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       "output_type": "stream",
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        ". "
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      },
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        ". "
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      },
      {
       "output_type": "stream",
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        ". "
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
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        ". "
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
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        ". "
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      },
      {
       "output_type": "stream",
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        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
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        ". "
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Performing SMC updates...\r"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Performing LSF...\\t',\n",
      "ref_data = data[:len(ms_ref)] / K\n",
      "C_data = data[len(ms_ref):] / K\n",
      "\n",
      "p0 = np.real(phys_prior.sample()[0, 1:]) # Another hack...\n",
      "res = curve_fit(exp_trial_fn, xdata=ms_ref, ydata=ref_data, p0=p0, maxfev=10000)\n",
      "p_ref, A_ref, B_ref = res[0]\n",
      "\n",
      "res = curve_fit(exp_trial_fn, xdata=ms_C, ydata=C_data, p0=p0, maxfev=10000)\n",
      "p_C, A_C, B_C = res[0]\n",
      "\n",
      "lsf_estimate = np.array([p_C / p_ref, p_ref, (A_ref + A_C) / 2.0, (B_ref + B_C) / 2.0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Performing LSF...\t"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phys_table = r\"\"\"\n",
      "    \\begin{{array}}{{l|cccc}}\n",
      "        & \\tilde{{p}} & p_{{\\text{{ref}}}} & A_0 & B_0 \\\\\n",
      "        \\hline\n",
      "        \\text{{True}} & {true[0]:.4f} & {true[1]:.4f} & {true[2]:.4f} & {true[3]:.4f} \\\\\n",
      "        \\text{{SMC Estimate}} & {smc_mean[0]:.4f} & {smc_mean[1]:.4f} & {smc_mean[2]:.4f} & {smc_mean[3]:.4f} \\\\\n",
      "        \\text{{LSF Estimate}} & {lsf_est[0]:.4f} & {lsf_est[1]:.4f} & {lsf_est[2]:.4f} & {lsf_est[3]:.4f} \\\\\n",
      "        \\hline\n",
      "        \\text{{SMC Error}}    & {smc_error[0]:.4f} & {smc_error[1]:.4f} & {smc_error[2]:.4f} & {smc_error[3]:.4f} \\\\\n",
      "        \\text{{LSF Error}} & {lsf_error[0]:.4f} & {lsf_error[1]:.4f} & {lsf_error[2]:.4f} & {lsf_error[3]:.4f}\n",
      "    \\end{{array}}\n",
      "\"\"\".format(\n",
      "    true=gs_true,\n",
      "    smc_mean=updater.est_mean(),\n",
      "    smc_stddev=np.real(np.diag(sqrtm(updater.est_covariance_mtx()))),\n",
      "    smc_error=np.abs(updater.est_mean() - gs_true),\n",
      "    lsf_est=lsf_estimate,\n",
      "    lsf_error=np.abs(lsf_estimate - gs_true)\n",
      ")\n",
      "\n",
      "print \"The true state is inside of a\", 100*(1- chisqprob(np.dot(updater.est_mean() - gs_true, np.dot(inv(updater.est_covariance_mtx()),updater.est_mean() - gs_true)),4)),\"% credible region.\"\n",
      "\n",
      "display(Latex(phys_table))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The true state is inside of a 100.0 % credible region.\n"
       ]
      },
      {
       "latex": [
        "\n",
        "    \\begin{array}{l|cccc}\n",
        "        & \\tilde{p} & p_{\\text{ref}} & A_0 & B_0 \\\\\n",
        "        \\hline\n",
        "        \\text{True} & 0.9983 & 0.9957 & 0.3185 & 0.5012 \\\\\n",
        "        \\text{SMC Estimate} & 0.9715 & 0.9969 & 0.3468 & 0.4834 \\\\\n",
        "        \\text{LSF Estimate} & 0.9952 & 0.9990 & 0.5980 & 0.2189 \\\\\n",
        "        \\hline\n",
        "        \\text{SMC Error}    & 0.0269 & 0.0012 & 0.0284 & 0.0178 \\\\\n",
        "        \\text{LSF Error} & 0.0031 & 0.0033 & 0.2795 & 0.2823\n",
        "    \\end{array}\n"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.Latex at 0xabd59b0>"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(9, 6))\n",
      "plot(ms_ref, K * data[:len(ms_ref)] / K, 'k--', label='Reference')\n",
      "plot(ms_C, K * data[len(ms_ref):] / K, label='Interleaved')\n",
      "legend(loc='lower left')\n",
      "\n",
      "xlabel('$m$')\n",
      "ylabel('Number of survivals')\n",
      "savefig('phys-gate-final-data-bad')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bsxUWFpb+z8HBwQQHB2epfndQtCiEhpoPw4CDB81wtG4dhIfDhx+ax4E0bPhH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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xccce668>"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print phys_table"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "    \\begin{array}{l|cccc}\n",
        "        & \\tilde{p} & p_{\\text{ref}} & A_0 & B_0 \\\\\n",
        "        \\hline\n",
        "        \\text{True} & 0.9983 & 0.9957 & 0.3185 & 0.5012 \\\\\n",
        "        \\text{SMC Estimate} & 0.9715 & 0.9969 & 0.3468 & 0.4834 \\\\\n",
        "        \\text{LSF Estimate} & 0.9952 & 0.9990 & 0.5980 & 0.2189 \\\\\n",
        "        \\hline\n",
        "        \\text{SMC Error}    & 0.0269 & 0.0012 & 0.0284 & 0.0178 \\\\\n",
        "        \\text{LSF Error} & 0.0031 & 0.0033 & 0.2795 & 0.2823\n",
        "    \\end{array}\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Make another updater and use it for plotting below.\n",
      "prior_updater = SMCUpdater(\n",
      "    phys_model, 10000, phys_prior,\n",
      "    resampler=LiuWestResampler(0.9)\n",
      ")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(12,6))\n",
      "updater.plot_posterior_marginal(0, res=200)\n",
      "prior_updater.plot_posterior_marginal(0, res=200)\n",
      "\n",
      "ymin, ymax = ylim()\n",
      "vlines(lsf_estimate[0], ymin, ymax * 2, linestyles=':')\n",
      "vlines(gs_true[0], ymin, ymax * 2)\n",
      "ylim(ymin, ymax)\n",
      "\n",
      "xlabel(r'$\\tilde{p}$')\n",
      "ylabel(r'$\\Pr(\\tilde{p})$')\n",
      "legend(['SMC Posterior', 'Bad Prior', 'LSF Estimate', 'True'], loc='upper left')\n",
      "\n",
      "savefig('bad-prior-distns')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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yrYJ0xx13WNxZ2SQkJMSqmHLbX5LN12ocPHhQU6ZMUefOnVW7dm2LbeHh4UpJ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\nMz3ZO+/c/DZ4pJ/o1sB3YyKi61RUU4Ss0izsPr0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WZCy4qW30ZFKO6b+VePWY/srKSkRE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\ndtaYNraY0lIAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8094550>"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Less data with a \"good\" prior"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ms_ref = xrange(1, 101,10) #np.logspace(0, 10, num=20, base=2).astype(int)\n",
      "ms_C   = xrange(2, 202,10) #np.logspace(0, 10, num=20, base=2).astype(int)\n",
      "K = 100\n",
      "\n",
      "mean=np.array([0.99, 0.99, 0.3, 0.5])\n",
      "cov=np.diag([0.01, 0.01, 0.01, 0.01])**2\n",
      "\n",
      "phys_model = BinomialModel(RandomizedBenchmarkingModel(interleaved=True))\n",
      "phys_prior =  PostselectedDistribution(MultivariateNormalDistribution(\n",
      "        mean=mean,\n",
      "        cov=cov\n",
      "    ), phys_model)\n",
      "print \"The true state is \", np.sqrt(np.dot(mean - gs_true, np.dot(inv(cov),mean - gs_true))),\"sigma from the prior mean.\"\n",
      "print \"The true state is outside of a\", 100*(1 - chisqprob(np.dot(mean - gs_true, np.dot(inv(cov),mean - gs_true)),4)),\"% credible region.\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The true state is  2.10748788085 sigma from the prior mean.\n",
        "The true state is outside of a 65.0460089255 % credible region.\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "updater = SMCUpdater(\n",
      "    phys_model, 10000, phys_prior,\n",
      "    resampler=LiuWestResampler(0.9)\n",
      ")\n",
      " \n",
      "eps = np.array((\n",
      "    [(m, True, K) for m in ms_ref] +\n",
      "    [(m, False, K) for m in ms_C]\n",
      "), dtype=phys_model.expparams_dtype)\n",
      "\n",
      "print 'Simulating data...\\r',\n",
      "data = phys_simulate_experiment(eps)\n",
      "\n",
      "print 'Performing SMC updates...\\r',\n",
      "for epvec, datum in zip(eps, data):\n",
      "    updater.update(datum, epvec.reshape((1,)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Simulating data...\r",
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        ". "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Performing SMC updates...\r"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print 'Performing LSF...\\t',\n",
      "ref_data = data[:len(ms_ref)] / K\n",
      "C_data = data[len(ms_ref):] / K\n",
      "\n",
      "p0 = np.real(phys_prior.sample()[0, 1:]) # Another hack...\n",
      "res = curve_fit(exp_trial_fn, xdata=ms_ref, ydata=ref_data, p0=p0, maxfev=10000)\n",
      "p_ref, A_ref, B_ref = res[0]\n",
      "\n",
      "res = curve_fit(exp_trial_fn, xdata=ms_C, ydata=C_data, p0=p0, maxfev=10000)\n",
      "p_C, A_C, B_C = res[0]\n",
      "\n",
      "lsf_estimate = np.array([p_C / p_ref, p_ref, (A_ref + A_C) / 2.0, (B_ref + B_C) / 2.0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Performing LSF...\t"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phys_table = r\"\"\"\n",
      "    \\begin{{array}}{{l|cccc}}\n",
      "        & \\tilde{{p}} & p_{{\\text{{ref}}}} & A_0 & B_0 \\\\\n",
      "        \\hline\n",
      "        \\text{{True}} & {true[0]:.4f} & {true[1]:.4f} & {true[2]:.4f} & {true[3]:.4f} \\\\\n",
      "        \\text{{SMC Estimate}} & {smc_mean[0]:.4f} & {smc_mean[1]:.4f} & {smc_mean[2]:.4f} & {smc_mean[3]:.4f} \\\\\n",
      "        \\text{{LSF Estimate}} & {lsf_est[0]:.4f} & {lsf_est[1]:.4f} & {lsf_est[2]:.4f} & {lsf_est[3]:.4f} \\\\\n",
      "        \\hline\n",
      "        \\text{{SMC Error}}    & {smc_error[0]:.4f} & {smc_error[1]:.4f} & {smc_error[2]:.4f} & {smc_error[3]:.4f} \\\\\n",
      "        \\text{{LSF Error}} & {lsf_error[0]:.4f} & {lsf_error[1]:.4f} & {lsf_error[2]:.4f} & {lsf_error[3]:.4f}\n",
      "    \\end{{array}}\n",
      "\"\"\".format(\n",
      "    true=gs_true,\n",
      "    smc_mean=updater.est_mean(),\n",
      "    smc_stddev=np.real(np.diag(sqrtm(updater.est_covariance_mtx()))),\n",
      "    smc_error=np.abs(updater.est_mean() - gs_true),\n",
      "    lsf_est=lsf_estimate,\n",
      "    lsf_error=np.abs(lsf_estimate - gs_true)\n",
      ")\n",
      "\n",
      "print \"The true state is inside of a\", 100*(1- chisqprob(np.dot(updater.est_mean() - gs_true, np.dot(inv(updater.est_covariance_mtx()),updater.est_mean() - gs_true)),4)),\"% credible region.\"\n",
      "\n",
      "display(Latex(phys_table))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The true state is inside of a 98.9699212839 % credible region.\n"
       ]
      },
      {
       "latex": [
        "\n",
        "    \\begin{array}{l|cccc}\n",
        "        & \\tilde{p} & p_{\\text{ref}} & A_0 & B_0 \\\\\n",
        "        \\hline\n",
        "        \\text{True} & 0.9983 & 0.9957 & 0.3185 & 0.5012 \\\\\n",
        "        \\text{SMC Estimate} & 0.9946 & 0.9982 & 0.3054 & 0.5057 \\\\\n",
        "        \\text{LSF Estimate} & 1.0687 & 0.9249 & 0.1661 & 0.6747 \\\\\n",
        "        \\hline\n",
        "        \\text{SMC Error}    & 0.0037 & 0.0025 & 0.0131 & 0.0045 \\\\\n",
        "        \\text{LSF Error} & 0.0703 & 0.0708 & 0.1523 & 0.1735\n",
        "    \\end{array}\n"
       ],
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<IPython.core.display.Latex at 0xaa6b2b0>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(9, 6))\n",
      "plot(ms_ref, data[:len(ms_ref)] / K, 'k--', label='Reference')\n",
      "plot(ms_C, data[len(ms_ref):] / K, label='Interleaved')\n",
      "legend(loc='lower left')\n",
      "\n",
      "xlabel('$m$')\n",
      "ylabel('Number of survivals')\n",
      "savefig('phys-gate-final-data-good')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0tBTnz5/H0KEVN4sNDg7G6dOn9Zo7ISEBzs7O6NatW6XP3n77bZSWlqJFixZ4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\nhBBCCBOkUBJCCCGEMOH/ABdt8lFEQ09GAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6a96110>"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print phys_table"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "    \\begin{array}{l|cccc}\n",
        "        & \\tilde{p} & p_{\\text{ref}} & A_0 & B_0 \\\\\n",
        "        \\hline\n",
        "        \\text{True} & 0.9983 & 0.9957 & 0.3185 & 0.5012 \\\\\n",
        "        \\text{SMC Estimate} & 0.9957 & 0.9969 & 0.2973 & 0.5010 \\\\\n",
        "        \\text{LSF Estimate} & 0.9925 & 0.9986 & 0.5153 & 0.2782 \\\\\n",
        "        \\hline\n",
        "        \\text{SMC Error}    & 0.0026 & 0.0011 & 0.0212 & 0.0003 \\\\\n",
        "        \\text{LSF Error} & 0.0058 & 0.0029 & 0.1968 & 0.2230\n",
        "    \\end{array}\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Make another updater and use it for plotting below.\n",
      "prior_updater = SMCUpdater(\n",
      "    phys_model, 40000, phys_prior,\n",
      "    resampler=LiuWestResampler(0.9)\n",
      ")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(12,6))\n",
      "updater.plot_posterior_marginal(0, res=200)\n",
      "prior_updater.plot_posterior_marginal(0, res=200)\n",
      "\n",
      "ymin, ymax = ylim()\n",
      "vlines(lsf_estimate[0], ymin, ymax * 2, linestyles=':')\n",
      "vlines(gs_true[0], ymin, ymax * 2)\n",
      "ylim(ymin, ymax)\n",
      "\n",
      "xlabel(r'$\\tilde{p}$')\n",
      "ylabel(r'$\\Pr(\\tilde{p})$')\n",
      "legend(['SMC Posterior', 'Prior', 'LSF Estimate', 'True'], loc='upper left')\n",
      "\n",
      "savefig('good-prior-distns')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3bt3CuHHjoFQq8dFHH2HKlCn429/+hjlz5uCpp57CY489hv379+Ojjz5CcHAw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\n9RPQsAfrnH/JbkC5oHzEoQK/PYBJJQ+N8A8CFfgiIpJXjDHsaovSEI4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       "text": [
        "<matplotlib.figure.Figure at 0x712d790>"
       ]
      }
     ],
     "prompt_number": 90
    }
   ],
   "metadata": {}
  }
 ]
}