Source code for qinfer.rb

#!/usr/bin/python
# -*- coding: utf-8 -*-
##
# rb.py: Models for accelerated randomized benchmarking.
##
# © 2017, Chris Ferrie ([email protected]) and
#         Christopher Granade ([email protected]).
#
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# modification, are permitted provided that the following conditions are met:
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##

## FEATURES ###################################################################

from __future__ import absolute_import
from __future__ import division

## ALL ########################################################################

__all__ = [
    'RandomizedBenchmarkingModel'
]

## IMPORTS ####################################################################

from itertools import starmap

import numpy as np
from qinfer._due import due, Doi
from qinfer.abstract_model import FiniteOutcomeModel, DifferentiableModel

from operator import mul

## FUNCTIONS ##################################################################

[docs]def p(F, d=2): """ Given the fidelity of a gate in :math:`d` dimensions, returns the depolarizating probability of the twirled channel. :param float F: Fidelity of a gate. :param int d: Dimensionality of the Hilbert space on which the gate acts. """ return (d * F - 1) / (d - 1)
[docs]def F(p, d=2): """ Given the depolarizating probabilty of a twirled channel in :math:`d` dimensions, returns the fidelity of the original gate. :param float p: Depolarizing parameter for the twirled channel. :param int d: Dimensionality of the Hilbert space on which the gate acts. """ return 1 - (1 - p) * (d - 1) / d
## CLASSES ####################################################################
[docs]class RandomizedBenchmarkingModel(FiniteOutcomeModel, DifferentiableModel): r""" Implements the randomized benchmarking or interleaved randomized benchmarking protocol, such that the depolarizing strength :math:`p` of the twirled channel is a parameter to be estimated, given a sequnce length :math:`m` as an experimental control. In addition, the zeroth-order "fitting"-parameters :math:`A` and :math:`B` are represented as model parameters to be estimated. :param bool interleaved: If `True`, the model implements the interleaved protocol, with :math:`\tilde{p}` being the depolarizing parameter for the interleaved gate and with :math:`p_{\text{ref}}` being the reference parameter. :modelparam p: Fidelity of the twirled error channel :math:`\Lambda`, represented as a decay rate :math:`p = (d F - 1) / (d - 1)`, where :math:`F` is the fidelity and :math:`d` is the dimension of the Hilbert space. :modelparam A: Scale of the randomized benchmarking decay, defined as :math:`\Tr[Q \Lambda(\rho - \ident / d)]`, where :math:`Q` is the final measurement, and where :math:`\ident` is the initial preparation. :modelparam B: Offset of the randomized benchmarking decay, defined as :math:`\Tr[Q \Lambda(\ident / d)]`. :expparam int m: Length of the randomized benchmarking sequence that was measured. """ # TODO: add citations to the above docstring. @due.dcite( Doi("10.1088/1367-2630/17/1/013042"), description="Accelerated randomized benchmarking", tags=["implementation"] ) def __init__(self, interleaved=False, order=0): self._il = interleaved if order != 0: raise NotImplementedError( "Only zeroth-order is currently implemented." ) super(RandomizedBenchmarkingModel, self).__init__() @property def n_modelparams(self): return 3 + (1 if self._il else 0) @property def modelparam_names(self): return ( # We want to know \tilde{p} := p_C / p, and so we make it # a model parameter directly. This means that later, we'll # need to extract p_C = p \tilde{p}. [r'\tilde{p}', 'p', 'A', 'B'] if self._il else ['p', 'A', 'B'] ) @property def is_n_outcomes_constant(self): return True @property def expparams_dtype(self): return [('m', 'uint')] + ( [('reference', bool)] if self._il else [] )
[docs] def n_outcomes(self, expparams): return 2
[docs] def are_models_valid(self, modelparams): if self._il: p_C, p, A, B = modelparams.T return np.all([ 0 <= p, p <= 1, 0 <= p_C, p_C <= 1, 0 <= A, A <= 1, 0 <= B, B <= 1, A + B <= 1, A * p + B <= 1, A * p_C + B <= 1 ], axis=0) else: p, A, B = modelparams.T return np.all([ 0 <= p, p <= 1, 0 <= A, A <= 1, 0 <= B, B <= 1, A + B <= 1, A * p + B <= 1 ], axis=0)
[docs] def likelihood(self, outcomes, modelparams, expparams): super(RandomizedBenchmarkingModel, self).likelihood(outcomes, modelparams, expparams) if self._il: p_tilde, p, A, B = modelparams.T[:, :, np.newaxis] p_C = p_tilde * p p = np.where(expparams['reference'][np.newaxis, :], p, p_C) else: p, A, B = modelparams.T[:, :, np.newaxis] m = expparams['m'][np.newaxis, :] pr0 = np.zeros((modelparams.shape[0], expparams.shape[0])) pr0[:, :] = 1 - (A * (p ** m) + B) return FiniteOutcomeModel.pr0_to_likelihood_array(outcomes, pr0)
[docs] def score(self, outcomes, modelparams, expparams, return_L=False): na = np.newaxis n_m = modelparams.shape[0] n_e = expparams.shape[0] n_o = outcomes.shape[0] n_p = self.n_modelparams m = expparams['m'].reshape((1, 1, 1, n_e)) L = self.likelihood(outcomes, modelparams, expparams)[na, ...] outcomes = outcomes.reshape((1, n_o, 1, 1)) if not self._il: p, A, B = modelparams.T[:, :, np.newaxis] p = p.reshape((1, 1, n_m, 1)) A = A.reshape((1, 1, n_m, 1)) B = B.reshape((1, 1, n_m, 1)) q = (-1)**(1-outcomes) * np.concatenate(np.broadcast_arrays( A * m * (p ** (m-1)), p**m, np.ones_like(p), ), axis=0) / L else: p_tilde, p_ref, A, B = modelparams.T[:, :, np.newaxis] p_C = p_tilde * p_ref mode = expparams['reference'][np.newaxis, :] p = np.where(mode, p_ref, p_C) p = p.reshape((1, 1, n_m, n_e)) A = A.reshape((1, 1, n_m, 1)) B = B.reshape((1, 1, n_m, 1)) q = (-1)**(1-outcomes) * np.concatenate(np.broadcast_arrays( np.where(mode, 0, A * m * (p_tilde ** (m - 1)) * (p_ref ** m)), np.where(mode, A * m * (p_ref ** (m - 1)), A * m * (p_ref ** (m - 1)) * (p_tilde ** m) ), p**m, np.ones_like(p) ), axis=0) / L if return_L: # Need to strip off the extra axis we added for broadcasting to q. return q, L[0, ...] else: return q