Practical Bayesian Tomography: Supplementary Material

Animations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Bayesian Tomography: Supplemental Material<br/>Animations #\n",
    "\n",
    "[Christopher Granade](http://www.cgranade.com), Joshua Combes and D. G. Cory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preamble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import qutip as qt\n",
    "import qinfer as qi\n",
    "import matplotlib\n",
    "matplotlib.style.use('ggplot')\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tempfile as tf\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pallette = plt.rcParams['axes.color_cycle']\n",
    "plt.rcParams['legend.fontsize'] = 18\n",
    "plt.rcParams['axes.labelsize'] = 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from qinfer.tomography.plotting_tools import (\n",
    "    plot_cov_ellipse, plot_decorate_rebits, plot_rebit_modelparams, plot_rebit_prior, plot_rebit_posterior\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "I, X, Y, Z = qt.qeye(2), qt.sigmax(), qt.sigmay(), qt.sigmaz()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Diffusive Qubit Tomography ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def diffusion_movie(n_steps=1000, save_stills=()):\n",
    "    tempdir = tf.mkdtemp()\n",
    "    print \"Saving to {}.\".format(tempdir)\n",
    "    pbar = qt.ui.TextProgressBar()\n",
    "    pbar.start(n_steps, chunk_size=1)\n",
    "    \n",
    "    basis = qi.tomography.pauli_basis(1)\n",
    "    \n",
    "    diffusive_model = qi.BinomialModel(qi.tomography.DiffusiveTomographyModel(basis, False))\n",
    "    \n",
    "    true_states = []\n",
    "    est_states = []\n",
    "    \n",
    "    true_state = np.array([[1, 0.99, 0, 0, 0]]) / np.sqrt(2)\n",
    "    true_state[0, -1] = 0.0045\n",
    "    diffusive_prior = qi.ProductDistribution(\n",
    "        qi.tomography.GADFLIDistribution(\n",
    "            qi.tomography.GinibreReditDistribution(basis),\n",
    "            I / 2 - 0.02 * Z / 2 + 0.88 * X / 2\n",
    "        ),\n",
    "        qi.LogNormalDistribution(0.0, 0.006)\n",
    "    )\n",
    "    \n",
    "    updater = qi.smc.SMCUpdater(diffusive_model, 3000, diffusive_prior)\n",
    "    heuristic = qi.tomography.RandomPauliHeuristic(updater, other_fields={'n_meas': 25, 't': 1})\n",
    "    \n",
    "    fig, (ax_rebit, ax_cov) = plt.subplots(1, 2, figsize=(1920 * 12 / 1080, 12))\n",
    "    \n",
    "    for idx_exp in xrange(n_steps):\n",
    "        expparams = heuristic()\n",
    "        outcome = diffusive_model.simulate_experiment(true_state, expparams)\n",
    "        updater.update(outcome, expparams)\n",
    "        \n",
    "        est_states.append(basis.modelparams_to_state(updater.est_mean()[:-1]))\n",
    "        true_states.append(basis.modelparams_to_state(true_state[0, :-1]))\n",
    "        err = np.linalg.norm(true_state[0] - updater.est_mean(), 2)\n",
    "        \n",
    "        true_state = diffusive_model.update_timestep(true_state, expparams)[:, :, 0]\n",
    "        \n",
    "        plt.sca(ax_rebit)\n",
    "        plot_rebit_posterior(updater, prior=None, true_state=true_state, rebit_axes=[1, 3], true_size=600)\n",
    "        plt.xticks([-1, 0, 1], size=14)\n",
    "        plt.yticks([-1, 0, 1], size=14)\n",
    "        \n",
    "        plt.sca(ax_cov)\n",
    "        updater.plot_covariance(param_slice=np.s_[1:4], tick_params={'size': 20})\n",
    "        \n",
    "        plt.savefig(os.path.join(tempdir, '{:05}.png'.format(idx_exp)), dpi=1080 * 100 / 1200)\n",
    "        if idx_exp in save_stills:\n",
    "            plt.savefig(os.path.join(tempdir, '{:05}.pdf'.format(idx_exp)), dpi=1080 * 100 / 1200)\n",
    "        ax_rebit.clear()\n",
    "        ax_cov.clear()\n",
    "        pbar.update(idx_exp)\n",
    "        \n",
    "    return true_states, est_states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    {
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     "text": [
      "/home/cgranade/anaconda/lib/python2.7/site-packages/qinfer/utils.py:109: ApproximationWarning: Numerical error in covariance estimation causing positive semidefinite violation.\n",
      "  warnings.warn('Numerical error in covariance estimation causing positive semidefinite violation.', ApproximationWarning)\n"
     ]
    },
    {
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2AADSvfrqqzd8ftOmTbFp06YazQYAoDbcOgoAAAAACYQ2AAAAAEggtAEAAABA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\naIG/Afb3GOFv24hgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffb8b622e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "true_states, est_states = diffusion_movie(10000, save_stills=[1000 * idx for idx in xrange(1, 10)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compile these frames into a video, use ``ffmpeg``:\n",
    "```\n",
    "$ ffmpeg -framerate 30 -i %05d.png -c:v libx264 -r 30 -pix_fmt yuv420p out.mp4\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}

Paper Figures.ipynb

QInfer Tomography Tutorial.ipynb