{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Estimating Randomized Benchmarking Fidelities #" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction ##" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This Notebook demonstrates how to use QInfer to the fidelity of a gateset using experimental data from randomized benchmarking." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup ##" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, to make sure that this example works in both Python 2 and 3, we tell Python 2 to use 3-style division and printing." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from __future__ import division, print_function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we import QInfer itself, along with NumPy and Matplotlib." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/qinfer/metrics.py:51: UserWarning: Could not import scikit-learn. Some features may not work.\n", " warnings.warn(\"Could not import scikit-learn. Some features may not work.\")\n", "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.\n", " warnings.warn(self.msg_depr % (key, alt_key))\n", "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/IPython/parallel.py:13: ShimWarning: The IPython.parallel package has been deprecated. You should import from ipyparallel instead.\n", " \"You should import from ipyparallel instead.\", ShimWarning)\n", "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/qinfer/parallel.py:53: UserWarning: Could not import IPython parallel. Parallelization support will be disabled.\n", " \"Could not import IPython parallel. \"\n" ] } ], "source": [ "import qinfer as qi\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For pretty-printing later, we'll need to borrow some unicode compatibility from future, so that this notebook also works under Python 2. We'll also import reduce in a 2/3 compatible manner." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from future.utils import python_2_unicode_compatible\n", "from builtins import str\n", "from functools import reduce" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We finish by configuring Matplotlib for plotting in Jupyter Notebook." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "try: plt.style.use('ggplot')\n", "except: pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Randomized Benchmarking ##" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a randomized benchmarking (RB) experiment, one chooses a random sequence of gates from a 2-design (for example, the Clifford group), then inverts the ideal action of the sequence and measures if the inversion was successful.\n", "Magesan *et al.* [10/tfz](https://dx.doi.org/10/tfz) showed that this results in an exponentially decay in the length $m$ of each sequence,\n", "$$\n", " A p^m + B,\n", "$$\n", "where $p$ is related to the the average fidelity $F$ of the 2-design used by $F = 1 - (1 - p) (d - 1) / d$ for a $d$-dimensional system, and where $A$ and $B$ are nuisance parameters. We will give a more precise definition later, and will show a numerical example of how this model arises. For now, though, we will synthesize some data by assuming the correctness of the model." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "p = 0.995\n", "A = 0.5\n", "B = 0.5" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ms = np.linspace(1, 800, 201).astype(int)\n", "signal = A * p ** ms + B" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n_shots = 25\n", "counts = np.random.binomial(p=signal, n=n_shots)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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u35u0eE/qujs/wZK2747OYBmTu3hy7GsRNfdPV+9R0LYNh6J1U+PGjWPlypW8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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ms, signal, label='Signal')\n", "plt.plot(ms, counts / n_shots, 'x', label='Data')\n", "plt.ylim(ymax=1)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analyzing RB Data ##" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now pack our synthetic data up for analysis by **QInfer**." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data = np.column_stack([counts, ms, n_shots * np.ones_like(counts)])" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated p: 0.9925 ± 0.0020\n" ] } ], "source": [ "mean, cov, extra = qi.simple_est_rb(data, return_all=True, n_particles=12000)\n", "print(\"Estimated p: {:0.4f} ± {:0.4f}\".format(mean[0], np.sqrt(cov[0, 0])))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LSvHctMrpOO4ybyH84R2nUzhCxSAyQdlwGPsPP8G+/wfM5+51Oo7rmPkLJ+yI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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "extra['updater'].plot_posterior_marginal(range_max=1)\n", "plt.xlim(xmax=1)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(p, *ylim)\n", "plt.ylim(*ylim);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that in analyzing, we have assumed that the true value of $p$ can be anything in the range $[0, 1]$, such that this will often underestimate the true fidelity. Including even a very modest assumption such as $p\\ge 0.8$ can help dramatically." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated p: 0.9958 ± 0.0010\n" ] } ], "source": [ "mean, cov, extra = qi.simple_est_rb(data, return_all=True, n_particles=12000, p_min=0.8)\n", "print(\"Estimated p: {:0.4f} ± {:0.4f}\".format(mean[0], np.sqrt(cov[0, 0])))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wpt/4K+rq61ExsUaHErDUmGz3ZasjRhkdijhN6a4uLzJIdXW10SH4TDh0ZyW/\nzrSjDtfin2D6zZOoQdZePTc1NZWqqqpePac/jHz/9IG9uH7/CKYFv3Pf+OZlof7ZTElJ8Xqbcuez\nED6i31iHuuaGXheFcKMuHIn6Rh6ux3+BdtYZHY5ACoMQPqHratCffICaMdvoUIKCaepNqOu+geuJ\nX6IbPzc6nLAnhUEIH9D/uxY19UbUwEHdP1gAYLphNurya3A984TRoYQ9KQxCeJk+tB/96ceor80y\nOpSgo26YBft3o9vbjQ4lrElhEMKLdNspXE8/gfr292RepD5QMbFgS4Caw0aHEtakMAjhRfqVFyBl\nGOqKqUaHErRUeib6oEzHbSQpDEJ4id69HV36Hqb/mC/37/TH8ItkPWiDSWEQwgv0yZO4nl2B6Y4f\nyoBzP6nhmeiDMiuzkaQwCOENOzbD0FTUmIlGRxL8hl0IlRVoV4fRkYQtKQxCeIFL1lvwGhU7EAZZ\nocZ/d36LzqQwCNFP+mQr7NyGmnCl0aGEDDU8Ey3jDIaRwiBEP+ntpXDRxTK24E3pI0CuTDKMFAYh\n+kmW7fQ+NXwE+pAMQBtFCoMQ/aBbT8AuOY3kdekXwaF/oV0uoyMJS1IYhOgHvaMURoxCDQjtpSP9\nTQ0cBAMsUHvE6FDCkhQGIfpBTiP50PARMgBtkG5XcFu9ejVbtmwhLi6OZcuWAdDc3Mzy5cupq6sj\nKSmJgoICYmPdK1QVFRVRXFyM2Wxm7ty5jBs3zrcZCGEQ92mkT1F33Gt0KCFJpY9w3wF9+bVGhxJ2\nuu0xTJs2jZ///Oedtq1fv54xY8awYsUK7HY7RUVFAFRWVrJp0yYKCwt58MEHefrppwmgBeKE8K5D\n+yF5mJxG8hE1fAT6oPQYjNBtYRg1ahQDBgzotK20tJQpU6YAMHXqVDZv3uzZnpOTg9lsJikpieTk\nZMrL5coCEZr04QpU2oVGhxG6LrwYKvahT500OpKw06cxhsbGRqxW93KFVquVxsZGAJxOJwkJCZ7H\n2Ww2nE6nF8IUIgBVVcCwDKOjCFlqwED31Ul7dhgdStjpdoyhJ/oyk2RZWRllZWWen/Py8rBYQrdL\nHhUVJfkFsa7ya6o+xAXX5xLho7z9+XoG6vvXOulqXLu2EZszrc9tBGpu3rR27VrP93a7Hbvd3q/2\n+lQYrFYrDQ0Nnq9xcXGAu4dQX1/veZzD4cBms3XZRlfBNzU19SWcoGCxWCS/IHZmftrVgevwAVri\nk1A+ytv1zJlRAAATXElEQVSfr2egvn/64rG43vwf2m/5Xp+nMg/U3LzFYrGQl5fn1TZ7dCpJa91p\nEHnixImUlJQAUFJSQnZ2NgDZ2dls3LiR9vZ2amtrqampITMz06sBCxEQao/AICvqglijIwltQ9PA\nZHafthN+022PYcWKFezcuZOmpibmzZtHXl4es2bNorCwkOLiYhITEykoKAAgLS2NyZMnU1BQQERE\nBPn5+bJgiQhJ+nAFyMCzzymlUGMnobeXykC/HykdQNeTVldXGx2Cz4RDdzac8nMVrQGTCdPMW32y\nv9TUVKqq/DftdCC/f7psK67X/oL5gUf79PxAzs0bUlJSvN6m3PksRB/oygMouSLJP0ZeCtWH0E3H\njI4kbEhhEKIvKisgLcPoKMKCioyEUWPRn31idChhQwqDEL2kjzfD8WZIGGp0KGFDjcmG7ZuNDiNs\nSGEQoreqKiA1HWWS/z7+osZdjt71KdpRa3QoYUE+2UL0kkyF4X9qkBV1XS76r38yOpSwIIVBiN6q\nqpDxBQOoGd9C/2sPes9nRocS8qQwCNFL+rBckWQEFR2Nuvm7uF76I9rVYXQ4IU0KgxC9oF0dUH0I\nUjOMDiUsqeyrIDYW/d7fjQ4lpElhEKI39u2EuHiZCsMgSilM3/4++m8vohscRocTsqQwCNFD+tjn\nuJ4pxPTt7xsdSlhT6Rehpt6I69kVaJfL6HBCkhQGIXpAt7fj+sNjqKumo8ZNMjqcsKe+8W1oPYH+\n52tGhxKSpDAI0QOtf/4DREWhvvkdo0MRgDKbMeXfh/7fdejKA0aHE3K8slCPEKFG79yK6w+PwqmT\n0OFCD03FtPB3KJPZ6NDEaSpxKOqW7+JauRguzELFDoSkZNTX/11mde4nKQxCnEG3teF68Q+Y5v4Y\nLr0MTGYscXE0NzcbHZo4g5p8HSopBRqd6OPN6H++DglDUJOuMTq0oCaFQYgz6H+8CkNSUBOu9GyT\nv0ADk1IKMi9xfw/oISnuQenxV6Aio4wNLojJGIMQX6E/d6DffgXTd/KNDkX0gbp4DKRluHsOos/6\n1WO45557iI2NRSmF2Wzmt7/9Lc3NzSxfvpy6ujqSkpIoKCggNlau+RbBQf/1T6hrv+4+PSGCkunm\nubiWLkTnTEdZ4owOJyj1qzAopVi0aBEDBw70bFu/fj1jxoxh5syZrF+/nqKiIm677bZ+ByqEL+mO\nDvSGV9HlZZjuuMfocEQ/qKFpqMunoF/7C+rWu40OJyj161SS1pozVwYtLS1lypQpAEydOpXNm2UO\ndRHYdMU+XI/ch97xCab/twQVHWN0SKKfVO530Fs+xPVhidGhBKV+9xiWLFmCyWTi+uuvZ/r06TQ2\nNmK1WgGwWq00NjZ6JVAhvE0f2If++3r0nh2om7+LunKqDDKHCGUZhKngN7gKf8mpqEi47CqjQwoq\n/SoMixcvJj4+nmPHjrFkyZIuF6U+13+0srIyysrKPD/n5eVhsVj6E05Ai4qKkvwCRMeRSlqeehTt\nqCX6xm8RPW+B+xr48zAiP3/uL5jevx4bZafjl4Ucf/inRLe3Ez091+iIfGbt2rWe7+12O3a7vV/t\n9aswxMfHAzBo0CAmTZpEeXk5VquVhoYGz9e4uK4Hf7oKvqmpqT/hBDSLxSL5BQCtNa6nHkWNvBT1\njTzazGbaOjR0E7sR+flzf8Hy/vXaoHgGPPQETb/6MSfjBqMuvtToiLzOYrGQl5fn1Tb7PMZw8uRJ\nWltbAWhtbWX79u2kp6czceJESkpKACgpKSE7O9srgQrhFVs2QvMx1DfyUGa5izkcmJPTMN0+H9dz\nK9EnW40OJyj0ucfQ2NjIY489hlKKjo4OrrnmGsaNG8eIESMoLCykuLiYxMRECgoKvBmvEH2mT57E\ntfa/Mf3nT6QohBk17nJU6fvoohdQ35HZcbuj9JmXFRmourra6BB8JmS76qcFQ36uV/8CRw5j+sGC\nXj/X3/mlpqZSVVXlt/0Fw/vXV1/kpo834frVDzF9/6eokaFzSqmrsd3+kjufRVjQ9UfR/3wddfN3\njQ5FGEQNsGD6j/m4/rQS3dpidDgBTQqDCHn65ElcTy1F3XgzanCi0eEIA6lxl6MuHoN+8amz7sES\nX5LCIEKa1hr93ErU0FTUDbOMDkcEAPWdu9AH96M3/tPoUAKWFAYR0vQb69D1R1F33Cs3rwkAVHQ0\nph8sQP/1WfSRw0aHE5Bk2m0RslwfbEC/8xamny1DRUUbHY4IICp1OOpbd+D6/SOoEaPQnzuhqQGV\nnA5Zo1EXj0ElpxkdpmGkMIiQo10d6FdeQG/ZiOknv0JZbUaHJAKQuvprYDZDezum+MEwcBC6sgL2\n7cT1txcxfffHqLHhub63FAYRUvSJFlxPPw4nWzE9uAxlGWR0SCJAKaVQOdM7b7twJFxzA3pHqfue\nl9ETUBHhd5iUMQYRMvTxJlyP/wIVF4/pJ7+WoiD67tKJED8Y/d7/GR2JIaQwiJCgmxpxLfsF6uJL\nUbffE5Z/5QnvUUphyvtP9GsvoVvCb61vKQwi6OmaKlyP/Qw1bpJ7+my5+kh4gUq7EDX+CvQb64wO\nxe/kzyoRlHTVQfRHJehtH8PxJtSM2ZhumG10WCLEqJm34frVveipN6EShhgdjt9IYRBBRZfvwvXm\nX+FgOSpnOqa5P4KMLJRJOr/C+1RcPOrqG9Bvr0fd+gOjw/EbKQwi4GmtYc8OXK+/DPVHUV//FuoH\nC+TeBOEXavo3cS26F/3N76AsXa8vE2qkMIiApst34XrlOWj83L2GwuVTZGBZ+JWy2lATc9D//F/U\nzFuNDscv5H+YCEj61El00Rr05vdQ37oDdcUUWUNBGEbdMBvX0oXoGbNRMRcYHY7P+awwbNu2jT/9\n6U9orZk2bRqzZskEZqJ7ur0Ndm3HtfZp1LCLMP1qJWqg3I8gjKWGpsLIS9Hvv426fqbR4ficTwqD\ny+XimWee4Ze//CXx8fE8+OCDTJo0idTUVF/sTgQB3dEBx49B0zFoaoTmY+jmY9DWBlqDqwNdsQ92\nfgrJaah/uw3TpKuNDlsID9PX/x3XU791X6EUEWl0OD7lk8JQXl5OcnIyiYnuue+vuuoqNm/eLIUh\nhLkanOjPtqKPVkHdUXT9UXcBaGmG483Q2gKxA8ES5/43cBBqoAUio0CZQIEak4269QeoQfFGpyPE\nWdSFWZCRhatwEab/LAjptT18UhicTieDBw/2/Gyz2SgvL/fFroQPaFcHdHTAqZNwtNo9NXFNFZw4\n7v4Lv+0UuFzuq4U62qGygqbWE+iMTFTyMBiaiunSy9wFYIDFXRAGDECZZIxABDfTDxag/68I18P/\nD/XtfNTl14bkDZUy+HwG15v/g95X9uWGL970vq72dPr5zWYzHe3tp9vR4Dr9VX/1n8t9QHa53P+0\n68v9miMgIsL91WQ6/e+MA63WXz7vi5+/eL52fblPcD/uRAu0HHcf8F0dXz4f3LNORkZBYjIqZRgM\nTQNbgntbZBSYzJgU7jhS0rGMuJjm48f79hoJESSUyYy68Wb06Am4nl2O/tNKiB8M8QkQHfOVB/qx\nWPx2tdeb9ElhsNls1NfXe35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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "extra['updater'].plot_posterior_marginal(range_max=1)\n", "plt.xlim(xmax=1)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(p, *ylim)\n", "plt.ylim(*ylim);" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "extra['updater'].plot_covariance()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " SMCUpdater for model of type BinomialModel (based on RandomizedBenchmarkingModel):\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", "\n", "\n", " \n", " \n", "
 $p$ $A$ $B$ $1.00 \\pm 0.00$ $0.5 \\pm 0.0$ $0.5 \\pm 0.0$
\n", " Resample count: 12\n", " " ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "extra['updater']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## [Advanced] RB With Gate-Level Simulation ##" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also synthesize data by simulating gates, instead of assuming the correctness of the Magesan *et al.* model *a priori*. We will do so here using QuTiP. Let's start by modeling each gate $S_i$ as the ideal unitary followed by a gate-independent noise channel, $S_i = \\Lambda U_i$. We will take $\\Lambda = e^{-0.08i \\sigma_x}$ to demonstrate that the RB model arises even when the noise is purely unitary, so long as the noise remains gate- and time-independent." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import qutip as qt\n", "from operator import mul" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = [4, 4], type = super, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.994 & -0.080j & 0.080j & 0.006\\\\-0.080j & 0.994 & 0.006 & 0.080j\\\\0.080j & 0.006 & 0.994 & -0.080j\\\\0.006 & 0.080j & -0.080j & 0.994\\\\\\end{array}\\right)\\end{equation*}" ], "text/plain": [ "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = [4, 4], type = super, isherm = False\n", "Qobj data =\n", "[[ 0.99361364+0.j 0.00000000-0.0796591j 0.00000000+0.0796591j\n", " 0.00638636+0.j ]\n", " [ 0.00000000-0.0796591j 0.99361364+0.j 0.00638636+0.j\n", " 0.00000000+0.0796591j]\n", " [ 0.00000000+0.0796591j 0.00638636+0.j 0.99361364+0.j\n", " 0.00000000-0.0796591j]\n", " [ 0.00638636+0.j 0.00000000+0.0796591j 0.00000000-0.0796591j\n", " 0.99361364+0.j ]]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lambda_ = qt.to_super((-1j * 0.08 * qt.sigmax()).expm())\n", "lambda_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The value of $p$ for this gate then serves as the true value that we are attempting to learn:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.99148485558375188" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qi.rb.p(qt.average_gate_fidelity(lambda_))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For simplicity, we'll take the preparation and measurement to be perfect— because this assumption is represented as a pair of QuTiP Qobj instances, it's easy to change. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rho = qt.ket2dm(qt.basis(2, 0))\n", "meas = rho" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For standard randomized benchmarking, however, we need to do a bit more work, since the ideal action of each sequence must be the identity. In particular, we need to be able to quickly find which gate we need to add to the end of each sequence to invert the previous gates.\n", "\n", "To do so, we will lean heavily on the presentation of the Clifford group used in the [**newsynth**](http://hackage.haskell.org/package/newsynth-0.3.0.2) Haskell package by Ross and Selinger." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Clifford Presentation as $\\mathbb{Z}_3 \\times \\mathbb{Z}_2 \\times \\mathbb{Z}_4 \\times \\mathbb{Z}_8$ ###" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from itertools import product" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Following the **newsynth** approach, we will represent each single-qubit Clifford gate $U$ by a tuple of integers $(i, j, k, l)$ such that\n", "$$\n", " (i, j, k, l) \\mapsto \\omega^l E^i X^j S^k,\n", "$$\n", "where $S = \\operatorname{diag}(1, i)$, $X = \\sigma_x = \\left(\\begin{matrix}0&1\\\\1&0\\end{matrix}\\right)$, $\\omega = e^{2 \\pi i /\n", "8}$, $H = \\left(\\begin{matrix}1&1\\\\1&-1\\end{matrix}\\right) / \\sqrt{2}$ is the Hadamard gate, and where $E = H S^3 \\omega^3$. This is a convienent presentation, as $\\omega^8 = 1$ and $E^3 = X^2 = S^4 = \\mathbb{1}$, such that each element of $\\mathbb{Z}_3 \\times \\mathbb{Z}_2 \\times \\mathbb{Z}_4 \\times \\mathbb{Z}_8$ represents exactly one single-qubit Clifford gate. This in turn makes it very convienent to randomly select Clifford group elements without having to worry that we have double-counted any gates due to our presentation." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "w = np.exp(1j * 2 * np.pi / 8)\n", "H = qt.snot()\n", "\n", "X = qt.sigmax()\n", "S = qt.phasegate(np.pi / 2)\n", "E = H * (S ** 3) * w ** 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll port the **newsynth** presentation to Python by subclassing tuple with methods that implement multiplication and inversion, and that return an ordinary QuTiP Qobj representing each gate. These methods will depend on three lookup tables that represent the commutation relatons between the generators $E$, $X$ and $S$. First, we implement the **newsynth** table $(k, j) \\mapsto (k', l')$ such that $X^j S^k = S^{k'} X^j \\omega^{l'}$. This table will let us commute $X$ past $S$ in products." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "CLIFFORD_SX = {\n", " (0, 0): (0,0),\n", " (0, 1): (0,0),\n", " (1, 0): (1,0),\n", " (1, 1): (3,2),\n", " (2, 0): (2,0),\n", " (2, 1): (2,4),\n", " (3, 0): (3,0),\n", " (3, 1): (1,6),\n", "}" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "for k, j in product(range(4), range(2)):\n", " kp, lp = CLIFFORD_SX[k, j]\n", " assert (\n", " X**j * S**k -\n", " S**kp * X**j * w**lp\n", " ).norm() <= 1e-8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we'll implement the table $(j, k, i) \\mapsto (i', j', k', l')$ such that $X^j S^k E^i = E^{i'} X^{j'} S^{k'} \\omega^{l'}$. This will let us commute $E$ into its proper position." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "CLIFFORD_XSE = {\n", " (0, 0, 0): (0,0,0,0),\n", " (0, 0, 1): (1,0,0,0),\n", " (0, 0, 2): (2,0,0,0),\n", " (0, 1, 0): (0,0,1,0),\n", " (0, 1, 1): (2,0,3,6),\n", " (0, 1, 2): (1,1,3,4),\n", " (0, 2, 0): (0,0,2,0),\n", " (0, 2, 1): (1,1,2,2),\n", " (0, 2, 2): (2,1,0,0),\n", " (0, 3, 0): (0,0,3,0),\n", " (0, 3, 1): (2,1,3,6),\n", " (0, 3, 2): (1,0,1,2),\n", " (1, 0, 0): (0,1,0,0),\n", " (1, 0, 1): (1,0,2,0),\n", " (1, 0, 2): (2,1,2,2),\n", " (1, 1, 0): (0,1,1,0),\n", " (1, 1, 1): (2,1,1,0),\n", " (1, 1, 2): (1,1,1,0),\n", " (1, 2, 0): (0,1,2,0),\n", " (1, 2, 1): (1,1,0,6),\n", " (1, 2, 2): (2,0,2,6),\n", " (1, 3, 0): (0,1,3,0),\n", " (1, 3, 1): (2,0,1,4),\n", " (1, 3, 2): (1,0,3,2),\n", "}" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [], "source": [ "for j, k, i in product(range(2), range(4), range(3)):\n", " ip, jp, kp, lp = CLIFFORD_XSE[j, k, i]\n", " assert (\n", " X**j * S**k * E**i -\n", " E**ip * X**jp * S**kp * w**lp\n", " ).norm() <= 1e-8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The last table we will need is $(i, j, k) \\mapsto (i', j', k', l')$ such that $(E^i S^j X^k)^{-1} = E^{i'} S^{j'} X^{k'} \\omega^{l'}$. That is, the table that stores the inverse of each Clifford gate with phase $l = 0$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "CLIFFORD_INV = {\n", " (0, 0, 0): (0,0,0,0),\n", " (0, 0, 1): (0,0,3,0),\n", " (0, 0, 2): (0,0,2,0),\n", " (0, 0, 3): (0,0,1,0),\n", " (0, 1, 0): (0,1,0,0),\n", " (0, 1, 1): (0,1,1,6),\n", " (0, 1, 2): (0,1,2,4),\n", " (0, 1, 3): (0,1,3,2),\n", " (1, 0, 0): (2,0,0,0),\n", " (1, 0, 1): (1,0,1,2),\n", " (1, 0, 2): (2,1,0,0),\n", " (1, 0, 3): (1,1,3,4),\n", " (1, 1, 0): (2,1,2,2),\n", " (1, 1, 1): (1,1,1,6),\n", " (1, 1, 2): (2,0,2,2),\n", " (1, 1, 3): (1,0,3,4),\n", " (2, 0, 0): (1,0,0,0),\n", " (2, 0, 1): (2,1,3,6),\n", " (2, 0, 2): (1,1,2,2),\n", " (2, 0, 3): (2,0,3,6),\n", " (2, 1, 0): (1,0,2,0),\n", " (2, 1, 1): (2,1,1,6),\n", " (2, 1, 2): (1,1,0,2),\n", " (2, 1, 3): (2,0,1,6),\n", "}" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [], "source": [ "for i, j, k in product(range(3), range(2), range(4)):\n", " ip, jp, kp, lp = CLIFFORD_INV[i, j, k]\n", " assert (\n", " (E**i * X**j * S**k).dag() -\n", " E**ip * X**jp * S**kp * w**lp\n", " ).norm() <= 1e-8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now equipped to represent each element of the Ross and Selinger presentation as an instance of a new class Clifford. By overriding Clifford.__new__, we can ensure that exactly one instance is created for each combination of $i$, $j$, $k$ and $l$. This will effectively let us lazily compute the different properties of each gate, making it much faster to sample each sequence." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sup_numerals = u\"⁰¹²³⁴⁵⁶⁷⁸⁹\"" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "@python_2_unicode_compatible\n", "class Clifford(tuple):\n", " \n", " # Maintain a dictionary of which Clifford instances already\n", " # exist, so that __new__ can return such existing instances.\n", " __instances = {} \n", " \n", " def __new__ (cls, i=0, j=0, k=0, l=0):\n", " if (i, j, k, l) in cls.__instances:\n", " return cls.__instances[i, j, k, l]\n", " else:\n", " new = super(Clifford, cls).__new__(cls, (i % 3, j % 2, k % 4, l % 8))\n", " cls.__instances[i, j, k, l] = new\n", " return new\n", " \n", " # Lazily store the QuTiP representation of each gate.\n", " _Q = None \n", " \n", " def __mul__(self, other):\n", " \"\"\"\n", " Returns the product of this Clifford gate with another one.\n", " \"\"\"\n", " \n", " # Unpack the powers of E, S, X and omega for each gate.\n", " i1, j1, k1, l1 = self\n", " i2, j2, k2, l2 = other\n", " \n", " # Commute E^i₂ past X^j₁ S^k₁.\n", " i3, j3, k3, l3 = CLIFFORD_XSE[j1, k1, i2]\n", " \n", " # Commute S past X.\n", " k4, l4 = CLIFFORD_SX[k3, j2]\n", " \n", " return Clifford(\n", " i1 + i3,\n", " j3 + j2,\n", " k4 + k2,\n", " # Accumulate the phases we picked up at each step.\n", " l4 + l3 + l1 + l2\n", " )\n", " @property\n", " def inv(self):\n", " (i2, j2, k2, l2) = CLIFFORD_INV[self[0], self[1], self[2]]\n", " return Clifford(\n", " i2, j2, k2, l2 - self[3]\n", " )\n", " \n", " def qobj(self):\n", " if not self._Q:\n", " self._Q = E**self[0] * X**self[1] * S**self[2] * w**self[3]\n", " return self._Q\n", " \n", " # Finally, we'll add some support for pretty-printing.\n", " \n", " def __repr__(self):\n", " return u\"Clifford({0[0]}, {0[1]}, {0[2]}, {0[3]})\".format(self)\n", " \n", " def __str__(self):\n", " if self[3] >= 4:\n", " return u\"-\" + str(Clifford(self[0], self[1], self[2], self[3] % 4))\n", " elif self[3] >= 2:\n", " return u\"i\" + str(Clifford(self[0], self[1], self[2], self[3] % 2))\n", " elif self[3] == 1:\n", " return u\"ω\" + str(Clifford(self[0], self[1], self[2]))\n", " elif self == Clifford(0, 0, 0, 0):\n", " return u\"𝟙\"\n", " else:\n", " return u\"\".join([\n", " u\"{}{}\".format(U, sup_numerals[power] if power > 1 else u\"\")\n", " for U, power in zip(u\"EXS\", self[:3])\n", " if power\n", " ])\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clifford_group = [\n", " Clifford(i, j, k, l)\n", " for i, j, k, l in\n", " product(range(3), range(2), range(4), range(8))\n", "]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "𝟙, ω𝟙, i𝟙, iω𝟙, -𝟙, -ω𝟙, -i𝟙, -iω𝟙, S, ωS, iS, iωS, -S, -ωS, -iS, -iωS, S², ωS², iS², iωS², -S², -ωS², -iS², -iωS², S³, ωS³, iS³, iωS³, -S³, -ωS³, -iS³, -iωS³, X, ωX, iX, iωX, -X, -ωX, -iX, -iωX, XS, ωXS, iXS, iωXS, -XS, -ωXS, -iXS, -iωXS, XS², ωXS², iXS², iωXS², -XS², -ωXS², -iXS², -iωXS², XS³, ωXS³, iXS³, iωXS³, -XS³, -ωXS³, -iXS³, -iωXS³, E, ωE, iE, iωE, -E, -ωE, -iE, -iωE, ES, ωES, iES, iωES, -ES, -ωES, -iES, -iωES, ES², ωES², iES², iωES², -ES², -ωES², -iES², -iωES², ES³, ωES³, iES³, iωES³, -ES³, -ωES³, -iES³, -iωES³, EX, ωEX, iEX, iωEX, -EX, -ωEX, -iEX, -iωEX, EXS, ωEXS, iEXS, iωEXS, -EXS, -ωEXS, -iEXS, -iωEXS, EXS², ωEXS², iEXS², iωEXS², -EXS², -ωEXS², -iEXS², -iωEXS², EXS³, ωEXS³, iEXS³, iωEXS³, -EXS³, -ωEXS³, -iEXS³, -iωEXS³, E², ωE², iE², iωE², -E², -ωE², -iE², -iωE², E²S, ωE²S, iE²S, iωE²S, -E²S, -ωE²S, -iE²S, -iωE²S, E²S², ωE²S², iE²S², iωE²S², -E²S², -ωE²S², -iE²S², -iωE²S², E²S³, ωE²S³, iE²S³, iωE²S³, -E²S³, -ωE²S³, -iE²S³, -iωE²S³, E²X, ωE²X, iE²X, iωE²X, -E²X, -ωE²X, -iE²X, -iωE²X, E²XS, ωE²XS, iE²XS, iωE²XS, -E²XS, -ωE²XS, -iE²XS, -iωE²XS, E²XS², ωE²XS², iE²XS², iωE²XS², -E²XS², -ωE²XS², -iE²XS², -iωE²XS², E²XS³, ωE²XS³, iE²XS³, iωE²XS³, -E²XS³, -ωE²XS³, -iE²XS³, -iωE²XS³\n" ] } ], "source": [ "print(\", \".join(map(str, clifford_group)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we can sample, multiply and invert Clifford gates efficiently, we have everything we need to define *sequences* of Cliffords. We will do so in terms of a gateset that defines the noisy implementation of each Clifford gate. For this example, we will hold to the traditional RB assumptions and the same noise channel $\\Lambda$ after the ideal action of each gate." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "gateset = {\n", " gate: lambda_ * qt.to_super(gate.qobj())\n", " for gate in clifford_group\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To form a sequence, we pick gates at random from the Clifford group, then append the inverse gate to the end." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def seq(m, gateset):\n", " gates = [clifford_group[idx] for idx in np.random.randint(len(clifford_group), size=m)]\n", " inv_gate = reduce(mul, reversed(gates)).inv\n", " gates = [inv_gate] + list(gates)\n", " return reduce(mul, [\n", " gateset[gate] for gate in reversed(gates)\n", " ])" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/latex": [ "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = [4, 4], type = super, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.756 & (-0.305-0.302j) & (-0.305+0.302j) & 0.244\\\\(0.352-0.246j) & (0.745+0.129j) & (-0.043+0.240j) & (-0.352+0.246j)\\\\(0.352+0.246j) & (-0.043-0.240j) & (0.745-0.129j) & (-0.352-0.246j)\\\\0.244 & (0.305+0.302j) & (0.305-0.302j) & 0.756\\\\\\end{array}\\right)\\end{equation*}" ], "text/plain": [ "Quantum object: dims = [[[2], [2]], [[2], [2]]], shape = [4, 4], type = super, isherm = False\n", "Qobj data =\n", "[[ 0.75637527+0.j -0.30459068-0.30248345j -0.30459068+0.30248345j\n", " 0.24362473+0.j ]\n", " [ 0.35180016-0.24598449j 0.74524982+0.12925265j -0.04329705+0.23974649j\n", " -0.35180016+0.24598449j]\n", " [ 0.35180016+0.24598449j -0.04329705-0.23974649j 0.74524982-0.12925265j\n", " -0.35180016-0.24598449j]\n", " [ 0.24362473+0.j 0.30459068+0.30248345j 0.30459068-0.30248345j\n", " 0.75637527+0.j ]]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "seq(100, gateset)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def sample_rb_datum(m, gateset, rho, meas):\n", " S = seq(m, gateset)\n", " pr = (\n", " qt.operator_to_vector(meas).dag() * S * qt.operator_to_vector(rho)\n", " )[0, 0]\n", " return 1 if np.random.random() < pr else 0" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [], "source": [ "counts = np.empty_like(ms)\n", "progbar = qi.IPythonProgressBar()\n", "progbar.start(ms.sum())\n", "progress = 0\n", "\n", "for idx, m in enumerate(ms):\n", " progbar.description = u'𝑚 = {}...'.format(m)\n", " counts[idx] = sum([\n", " sample_rb_datum(m, gateset, rho, meas)\n", " for _ in range(n_shots)\n", " ])\n", " progress += m\n", " progbar.update(progress)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated p: 0.9911 ± 0.0017\n", "Estimated A: 0.4432 ± 0.0261\n", "Estimated B: 0.5063 ± 0.0118\n" ] } ], "source": [ "data = np.column_stack([counts, ms, n_shots * np.ones_like(counts)])\n", "mean, cov, extra = qi.simple_est_rb(data, return_all=True, n_particles=12000, p_min=0.8)\n", "print(\"Estimated p: {:0.4f} ± {:0.4f}\".format(mean[0], np.sqrt(cov[0, 0])))\n", "print(\"Estimated A: {:0.4f} ± {:0.4f}\".format(mean[1], np.sqrt(cov[1, 1])))\n", "print(\"Estimated B: {:0.4f} ± {:0.4f}\".format(mean[2], np.sqrt(cov[2, 2])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the Magesan *et al.* model, $A$ and $B$ are defined as\n", "\\begin{align*}\n", " A & \\mathrel{:=} \\operatorname{Tr}(E \\Lambda(\\rho - \\mathbb{1} / d)) \\textrm{ and} \\\\\n", " B & \\mathrel{:=} \\operatorname{Tr}(E \\Lambda(\\mathbb{1} / d)),\n", "\\end{align*}\n", "where $d$ is the dimension of the system (in this case, 2). By using our description of $\\Lambda$, $\\rho$ and $E$, we can calculate these parameters and plot the \"true\" model for our data, along side the data and our reconstruction from the estimated values of $p$, $A$ and $B$." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true }, "outputs": [], "source": [ "A = (qt.operator_to_vector(meas).dag() * lambda_ * qt.operator_to_vector(rho - qt.qeye(2) / 2))[0, 0]\n", "B = (qt.operator_to_vector(meas).dag() * lambda_ * qt.operator_to_vector(qt.qeye(2) / 2))[0, 0]" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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P9W49asNlSp43nTajHEzMIFd5AH7l21/a0xd0Ol2PhjFWq9VBRcJ1xGyRqTJ2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\nuvWEzp6IpdQrhr+wsJBXX30VWZaZM2c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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ms, A + B * qi.rb.p(qt.average_gate_fidelity(lambda_)) ** ms, label='True Model')\n", "plt.plot(ms, counts / n_shots, 'x', label='Data')\n", "plt.plot(ms, mean[2] + mean[1] * mean[0] ** ms, label='Estimated Model')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9mWw8mk3f6wIY0sqKt3vF03WqzHRcvl1O0aa1aDfegtZ3CJqvfx0nvjJ5z+1L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\nVEqxLSWX+bsycNE1RrcNon2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(ms, B * qi.rb.p(qt.average_gate_fidelity(lambda_)) ** ms, label='True Model')\n", "# plt.plot(ms, (counts / n_shots) - mean[1], 'x', label='Data')\n", "plt.semilogy(ms, mean[1] * mean[0] ** ms, label='Estimated Model')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "extra['updater'].plot_posterior_marginal(range_max=1)\n", "plt.xlim(xmax=1)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(qi.rb.p(qt.average_gate_fidelity(lambda_)), *ylim)\n", "plt.ylim(*ylim);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also look at the posterior marginal distributions over each of $A$ and $B$." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "image/png": 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NtRx3fbZh9GXt2rVcfvnlTmQZuqr3xq1fGTjRhqH/mUQSVTgc5utf/zqHDh3i+uuv5/zz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\nIn5nrT3lE79LLrmEdevWMW/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 4))\n", "plt.subplot(1, 2, 1)\n", "extra['updater'].plot_posterior_marginal(idx_param=1)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(A, *ylim)\n", "plt.ylim(*ylim);\n", "\n", "plt.subplot(1, 2, 2)\n", "extra['updater'].plot_posterior_marginal(idx_param=2)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(B, *ylim)\n", "plt.ylim(*ylim);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plot the covariance matrix for all three parameters, showing how our uncertianty about each of the parameters $p$, $A$ and $B$ are correlated. We do so as a [Hinton diagram](http://tonysyu.github.io/mpltools/auto_examples/special/plot_hinton.html), in which each positive element is plotted as a white square while each negative element is plotted as a black square. The respective sizes of each element show their magnitudes. That we see a large black square in the $(A, B)$ and $(B, A)$ matrix elements tells us that the estimates of $A$ and $B$ are strongly anti-correlated, such that learning about one tells us a lot about the other." ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "extra['updater'].plot_covariance()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This becomes more obvious if we plot the correlation matrix instead, where each matrix element is rescaled as $\\operatorname{Corr}(X, Y) = \\operatorname{Cov}(X, Y) / \\sqrt{\\operatorname{Cov}(X, X) \\operatorname{Cov}(Y, Y)}$." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "extra['updater'].plot_covariance(corr=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This shows that improving our knowledge of $B$ can have a large impact on our uncertianty in $p$." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Custom Priors and Updater Loop ##" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can exploit this by providing a prior distribution that is relatively certain about the values of $A$ and $B$. Such a prior can be justified, for instance, by other experiments that demonstrate high-fidelity measurements. In this example, we will assume a prior distribution over $A$ and $B$ that is narrowly centered around the true values to demonstrate the utility of prior information.\n", "\n", "Instead of using simple_est_rb, we'll use RandomizedBenchmarkingModel directly, and then wrapping this model with a BinomialModel to describe multiple shots." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = qi.BinomialModel(qi.RandomizedBenchmarkingModel())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then use PostselectedDistribution to ensure that our prior is always valid for randomized benchmarking." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [], "source": [ "prior = qi.PostselectedDistribution(\n", " qi.ProductDistribution(\n", " qi.UniformDistribution([0.8, 1]),\n", " qi.MultivariateNormalDistribution(\n", " np.array([0.498, 0.499]),\n", " np.diag([0.004, 0.002]) ** 2\n", " )\n", " ),\n", " model\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we'll set up an updater to consume the data we simulated in the previous section." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true }, "outputs": [], "source": [ "updater = qi.smc.SMCUpdater(model, 12000, prior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then setup arrays to hold our outcomes and our experiment parameters." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [], "source": [ "outcomes = np.array(counts, dtype='uint')[:, np.newaxis]\n", "expparams = np.empty(outcomes.shape, dtype=model.expparams_dtype)\n", "expparams['n_meas'] = n_shots\n", "expparams['m'][:, 0] = ms" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can update our prior with the data to find the posterior distribution." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [], "source": [ "for outcome, experiment in zip(outcomes, expparams):\n", " updater.update(outcome, experiment)" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": true }, "outputs": [], "source": [ "mean = updater.est_mean()\n", "cov = updater.est_covariance_mtx()" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimated p: 0.9916 ± 0.0006\n", "Estimated A: 0.4950 ± 0.0031\n", "Estimated B: 0.4987 ± 0.0019\n" ] } ], "source": [ "print(\"Estimated p: {:0.4f} ± {:0.4f}\".format(mean[0], np.sqrt(cov[0, 0])))\n", "print(\"Estimated A: {:0.4f} ± {:0.4f}\".format(mean[1], np.sqrt(cov[1, 1])))\n", "print(\"Estimated B: {:0.4f} ± {:0.4f}\".format(mean[2], np.sqrt(cov[2, 2])))" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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r3ENXdZyQ7P+qZ4LeRYmQGn1Bg6Bn6HOG3z4NreOaut2FEHA+pvqXt/CpLYYx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\nWZYwm62Y22QkG9hkUKtBlmh/ytBItFh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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ms, A + B * qi.rb.p(qt.average_gate_fidelity(lambda_)) ** ms, label='True Model')\n", "plt.plot(ms, counts / n_shots, 'x', label='Data')\n", "plt.plot(ms, mean[2] + mean[1] * mean[0] ** ms, label='Estimated Model')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/cgranade/anaconda/envs/qinfer-binder/lib/python3.5/site-packages/numpy/core/numeric.py:482: ComplexWarning: Casting complex values to real discards the imaginary part\n", " return array(a, dtype, copy=False, order=order)\n" ] }, { "data": { "image/png": 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+Da1NMN3tyjmBO7+I/Yf/jT0edZpDREQkLXV10HpyYEwfUJpgGKtlOpNCRQjx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\nzGeTCh0wXbpDxy7QshUcP72h+hgcqwo+fnYOpHYJTlrs3oa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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(18, 4))\n", "plt.subplot(1, 3, 1)\n", "extra['updater'].plot_posterior_marginal(idx_param=0)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(qi.rb.p(qt.average_gate_fidelity(lambda_)), *ylim)\n", "plt.ylim(*ylim);\n", "\n", "\n", "plt.subplot(1, 3, 2)\n", "extra['updater'].plot_posterior_marginal(idx_param=1)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(A, *ylim)\n", "plt.ylim(*ylim);\n", "\n", "plt.subplot(1, 3, 3)\n", "extra['updater'].plot_posterior_marginal(idx_param=2)\n", "ylim = plt.ylim(ymin=0)\n", "plt.vlines(B, *ylim)\n", "plt.ylim(*ylim);" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.subplot(1, 2, 1)\n", "updater.plot_covariance()\n", "\n", "plt.subplot(1, 2, 2)\n", "updater.plot_covariance(corr=True)" ] }, { "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": "3.5.1" }, "widgets": { "state": { "2653fdeffff44239a6f4d648d760a848": { "views": [] }, "2aa33dc93c1f4d45a70b06d26f8e90c9": { "views": [] }, "32a674f47af142aeb8dcb958f60a56df": { "views": [] }, "51aaf408951149f9b28a82874c30832c": { "views": [] }, "56ef519037cb4465bdadda75831cd233": { "views": [ { "cell_index": 61 } ] }, 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