Source code for qinfer.rb

#!/usr/bin/python
# -*- coding: utf-8 -*-
##
# rb.py: Models for accelerated randomized benchmarking.
##
# © 2017, Chris Ferrie (csferrie@gmail.com) and
#
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#        notice, this list of conditions and the following disclaimer.
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#        contributors may be used to endorse or promote products derived from
#        this software without specific prior written permission.
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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))

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))

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