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rbfit.py
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""" Functions for analyzing RB data"""
#***************************************************************************************************
# Copyright 2015, 2019 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
# Under the terms of Contract DE-NA0003525 with NTESS, the U.S. Government retains certain rights
# in this software.
# Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
# in compliance with the License. You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0 or in the LICENSE file in the root pyGSTi directory.
#***************************************************************************************************
import numpy as _np
from scipy.optimize import curve_fit as _curve_fit
from ..tools import rbtools as _rbt
# Obsolute function to be deleted.
# def std_practice_analysis(RBSdataset, seed=[0.8, 0.95], bootstrap_samples=200, asymptote='std', rtype='EI',
# datatype='auto'):
# """
# Implements a "standard practice" analysis of RB data. Fits the average success probabilities to the exponential
# decay A + Bp^m, using least-squares fitting, with (1) A fixed (as standard, to 1/2^n where n is the number of
# qubits the data is for), and (2) A, B and p all allowed to varying. Confidence intervals are also estimated using
# a standard non-parameteric boostrap.
# Parameters
# ----------
# RBSdataset : RBSummaryDataset
# An RBSUmmaryDataset containing the data to analyze
# seed : list, optional
# Seeds for the fit of B and p (A is seeded to the asymptote defined by `asympote`).
# bootstrap_samples : int, optional
# The number of samples in the bootstrap.
# asymptote : str or float, optional
# The A value for the fitting to A + Bp^m with A fixed. If a string must be 'std', in
# in which case A is fixed to 1/2^n.
# rtype : {'EI','AGI'}, optional
# The RB error rate rescaling convention. 'EI' results in RB error rates that are associated
# with the entanglement infidelity, which is the error probability with stochastic errors (and
# is equal to the diamond distance). 'AGI' results in RB error rates that are associated with
# average gate infidelity.
# Returns
# -------
# RBResults
# An object encapsulating the RB results (and data).
# """
# assert(datatype == 'raw' or datatype == 'adjusted' or datatype == 'auto'), "Unknown data type!"
# if datatype == 'auto':
# if RBSdataset.datatype == 'hamming_distance_counts':
# datatype = 'adjusted'
# else:
# datatype = 'raw'
# lengths = RBSdataset.lengths
# n = RBSdataset.number_of_qubits
# if isinstance(asymptote, str):
# assert(asymptote == 'std'), "If `asympotote` is a string it must be 'std'!"
# if datatype == 'raw':
# asymptote = 1 / 2**n
# elif datatype == 'adjusted':
# asymptote = 1 / 4**n
# if datatype == 'adjusted':
# ASPs = RBSdataset.adjusted_ASPs
# if datatype == 'raw':
# ASPs = RBSdataset.ASPs
# FF_results, FAF_results = std_least_squares_data_fitting(lengths, ASPs, n, seed=seed, asymptote=asymptote,
# ftype='full+FA', rtype=rtype)
# parameters = ['A', 'B', 'p', 'r']
# bootstraps_FF = {}
# bootstraps_FAF = {}
# if bootstrap_samples > 0:
# bootstraps_FF = {p: [] for p in parameters}
# bootstraps_FAF = {p: [] for p in parameters}
# failcount_FF = 0
# failcount_FAF = 0
# # Add bootstrapped datasets, if neccessary.
# RBSdataset.add_bootstrapped_datasets(samples=bootstrap_samples)
# for i in range(bootstrap_samples):
# if datatype == 'adjusted':
# BS_ASPs = RBSdataset.bootstraps[i].adjusted_ASPs
# if datatype == 'raw':
# BS_ASPs = RBSdataset.bootstraps[i].ASPs
# BS_FF_results, BS_FAF_results = std_least_squares_data_fitting(lengths, BS_ASPs, n, seed=seed,
# asymptote=asymptote, ftype='full+FA',
# rtype=rtype)
# if BS_FF_results['success']:
# for p in parameters:
# bootstraps_FF[p].append(BS_FF_results['estimates'][p])
# else:
# failcount_FF += 1
# if BS_FAF_results['success']:
# for p in parameters:
# bootstraps_FAF[p].append(BS_FAF_results['estimates'][p])
# else:
# failcount_FAF += 1
# failrate_FF = failcount_FF / bootstrap_samples
# failrate_FAF = failcount_FAF / bootstrap_samples
# std_FF = {p: _np.std(_np.array(bootstraps_FF[p])) for p in parameters}
# std_FAF = {p: _np.std(_np.array(bootstraps_FAF[p])) for p in parameters}
# else:
# bootstraps_FF = None
# std_FF = None
# failrate_FF = None
# bootstraps_FAF = None
# std_FAF = None
# failrate_FAF = None
# fits = {}
# fits['full'] = FitResults('LS', FF_results['seed'], rtype, FF_results['success'], FF_results['estimates'],
# FF_results['variable'], stds=std_FF, bootstraps=bootstraps_FF,
# bootstraps_failrate=failrate_FF)
# fits['A-fixed'] = FitResults('LS', FAF_results['seed'], rtype, FAF_results['success'],
# FAF_results['estimates'], FAF_results['variable'], stds=std_FAF,
# bootstraps=bootstraps_FAF, bootstraps_failrate=failrate_FAF)
# results = SimpleRBResults(RBSdataset, rtype, fits)
# return results
def std_least_squares_data_fitting(lengths, ASPs, n, seed=None, asymptote=None, ftype='full', rtype='EI'):
"""
Implements a "standard" least-squares fit of RB data. Fits the average success probabilities to
the exponential decay A + Bp^m, using least-squares fitting.
Parameters
----------
lengths : list
The RB lengths to fit to (the 'm' values in A + Bp^m).
ASPs : list
The average survival probabilities to fit (the observed P_m values to fit
to P_m = A + Bp^m).
seed : list, optional
Seeds for the fit of B and p (A, if a variable, is seeded to the asymptote defined by `asympote`).
asymptote : float, optional
If not None, the A value for the fitting to A + Bp^m with A fixed. Defaults to 1/2^n.
Note that this value is used even when fitting A; in that case B and p are estimated
with A fixed to this value, and then this A and the estimated B and p are seed for the
full fit.
ftype : {'full','FA','full+FA'}, optional
The fit type to implement. 'full' corresponds to fitting all of A, B and p. 'FA' corresponds
to fixing 'A' to the value specified by `asymptote`. 'full+FA' returns the results of both
fits.
rtype : {'EI','AGI'}, optional
The RB error rate rescaling convention. 'EI' results in RB error rates that are associated
with the entanglement infidelity, which is the error probability with stochastic errors (and
is equal to the diamond distance). 'AGI' results in RB error rates that are associated with
average gate infidelity.
Returns
-------
Dict or Dicts
If `ftype` = 'full' or `ftype` = 'FA' then a dict containing the results of the relevant fit.
If `ftype` = 'full+FA' then two dicts are returned. The first dict corresponds to the full fit
and the second to the fixed-asymptote fit.
"""
if asymptote is not None: A = asymptote
else: A = 1 / 2**n
# First perform a fit with a fixed asymptotic value
FAF_results = custom_least_squares_data_fitting(lengths, ASPs, n, A=A, seed=seed)
# Full fit is seeded by the fixed asymptote fit.
seed_full = [FAF_results['estimates']['A'], FAF_results['estimates']['B'], FAF_results['estimates']['p']]
FF_results = custom_least_squares_data_fitting(lengths, ASPs, n, seed=seed_full)
# Returns the requested fit type.
if ftype == 'full': return FF_results
elif ftype == 'FA': return FAF_results
elif ftype == 'full+FA': return FF_results, FAF_results
else: raise ValueError("The `ftype` value is invalid!")
def custom_least_squares_data_fitting(lengths, ASPs, n, A=None, B=None, seed=None, rtype='EI'):
"""
Fits RB average success probabilities to the exponential decay A + Bp^m using least-squares fitting.
Parameters
----------
lengths : list
The RB lengths to fit to (the 'm' values in A + Bp^m).
ASPs : list
The average survival probabilities to fit (the observed P_m values to fit
to P_m = A + Bp^m).
n : int
The number of qubits the data is on..
A : float, optional
If not None, a value to fix A to.
B : float, optional
If not None, a value to fix B to.
seed : list, optional
Seeds for variables in the fit, in the order [A,B,p] (with A and/or B dropped if it is set
to a fixed value).
rtype : {'EI','AGI'}, optional
The RB error rate rescaling convention. 'EI' results in RB error rates that are associated
with the entanglement infidelity, which is the error probability with stochastic errors (and
is equal to the diamond distance). 'AGI' results in RB error rates that are associated with
average gate infidelity.
Returns
-------
Dict
The fit results. If item with the key 'success' is False, the fit has failed.
"""
seed_dict = {}
variable = {}
variable['A'] = True
variable['B'] = True
variable['p'] = True
lengths = _np.array(lengths, int)
ASPs = _np.array(ASPs, 'd')
# The fit to do if a fixed value for A is given
if A is not None:
variable['A'] = False
if B is not None:
variable['B'] = False
def curve_to_fit(m, p):
return A + B * p**m
if seed is None:
seed = 0.9
seed_dict['A'] = None
seed_dict['B'] = None
seed_dict['p'] = seed
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed, bounds=([0.], [1.]))
p = fitout
success = True
except:
success = False
else:
def curve_to_fit(m, B, p):
return A + B * p**m
if seed is None:
seed = [1. - A, 0.9]
seed_dict['A'] = None
seed_dict['B'] = 1. - A
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed, bounds=([-_np.inf, 0.], [+_np.inf, 1.]))
B = fitout[0]
p = fitout[1]
success = True
except:
success = False
# The fit to do if a fixed value for A is not given
else:
if B is not None:
variable['B'] = False
def curve_to_fit(m, A, p):
return A + B * p**m
if seed is None:
seed = [1 / 2**n, 0.9]
seed_dict['A'] = 1 / 2**n
seed_dict['B'] = None
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed, bounds=([0., 0.], [1., 1.]))
A = fitout[0]
p = fitout[1]
success = True
except:
success = False
else:
def curve_to_fit(m, A, B, p):
return A + B * p**m
if seed is None:
seed = [1 / 2**n, 1 - 1 / 2**n, 0.9]
seed_dict['A'] = 1 / 2**n
seed_dict['B'] = 1 - 1 / 2**n
seed_dict['p'] = 0.9
try:
fitout, junk = _curve_fit(curve_to_fit, lengths, ASPs, p0=seed,
bounds=([0., -_np.inf, 0.], [1., +_np.inf, 1.]))
A = fitout[0]
B = fitout[1]
p = fitout[2]
success = True
except:
success = False
estimates = {}
if success:
estimates['A'] = A
estimates['B'] = B
estimates['p'] = p
estimates['r'] = _rbt.p_to_r(p, 2**n)
results = {}
results['estimates'] = estimates
results['variable'] = variable
results['seed'] = seed_dict
# Todo : fix this.
results['success'] = success
return results
class FitResults(object):
"""
An object to contain the results from fitting RB data. Currently just a
container for the results, and does not include any methods.
"""
def __init__(self, fittype, seed, rtype, success, estimates, variable, stds=None,
bootstraps=None, bootstraps_failrate=None):
"""
Initialize a FitResults object.
Parameters
----------
fittype : str
A string to identity the type of fit.
seed : list
The seed used in the fitting.
rtype : {'IE','AGI'}
The type of RB error rate that the 'r' in these fit results corresponds to.
success : bool
Whether the fit was successful.
estimates : dict
A dictionary containing the estimates of all parameters
variable : dict
A dictionary that specifies which of the parameters in "estimates" where variables
to estimate (set to True for estimated parameters, False for fixed constants). This
is useful when fitting to A + B*p^m and fixing one or more of these parameters: because
then the "estimates" dict can still be queried for all three parameters.
stds : dict, optional
Estimated standard deviations for the parameters.
bootstraps : dict, optional
Bootstrapped values for the estimated parameters, from which the standard deviations
were calculated.
bootstraps_failrate : float, optional
The proporition of the estimates of the parameters from bootstrapped dataset failed.
"""
self.fittype = fittype
self.seed = seed
self.rtype = rtype
self.success = success
self.estimates = estimates
self.variable = variable
self.stds = stds
self.bootstraps = bootstraps
self.bootstraps_failrate = bootstraps_failrate
# Obsolute RB results class
# class SimpleRBResults(object):
# """
# An object to contain the results of an RB analysis.
# """
# def __init__(self, data, rtype, fits):
# """
# Initialize an RBResults object.
# Parameters
# ----------
# data : RBSummaryDataset
# The RB summary data that the analysis was performed for.
# rtype : {'IE','AGI'}
# The type of RB error rate, corresponding to different dimension-dependent
# re-scalings of (1-p), where p is the RB decay constant in A + B*p^m.
# fits : dict
# A dictionary containing FitResults objects, obtained from one or more
# fits of the data (e.g., a fit with all A, B and p as free parameters and
# a fit with A fixed to 1/2^n).
# """
# self.data = data
# self.rtype = rtype
# self.fits = fits
# def plot(self, fitkey=None, decay=True, success_probabilities=True, size=(8, 5), ylim=None, xlim=None,
# legend=True, title=None, figpath=None):
# """
# Plots RB data and, optionally, a fitted exponential decay.
# Parameters
# ----------
# fitkey : dict key, optional
# The key of the self.fits dictionary to plot the fit for. If None, will
# look for a 'full' key (the key for a full fit to A + Bp^m if the standard
# analysis functions are used) and plot this if possible. It otherwise checks
# that there is only one key in the dict and defaults to this. If there are
# multiple keys and none of them are 'full', `fitkey` must be specified when
# `decay` is True.
# decay : bool, optional
# Whether to plot a fit, or just the data.
# success_probabilities : bool, optional
# Whether to plot the success probabilities distribution, as a violin plot. (as well
# as the *average* success probabilities at each length).
# size : tuple, optional
# The figure size
# ylim, xlim : tuple, optional
# The x and y limits for the figure.
# legend : bool, optional
# Whether to show a legend.
# title : str, optional
# A title to put on the figure.
# figpath : str, optional
# If specified, the figure is saved with this filename.
# """
# # Future : change to a plotly plot.
# try: import matplotlib.pyplot as _plt
# except ImportError: raise ValueError("This function requires you to install matplotlib!")
# if decay and fitkey is None:
# allfitkeys = list(self.fits.keys())
# if 'full' in allfitkeys: fitkey = 'full'
# else:
# assert(len(allfitkeys) == 1), \
# "There are multiple fits and none have the key 'full'. Please specify the fit to plot!"
# fitkey = allfitkeys[0]
# _plt.figure(figsize=size)
# _plt.plot(self.data.lengths, self.data.ASPs, 'o', label='Average success probabilities')
# if decay:
# lengths = _np.linspace(0, max(self.data.lengths), 200)
# A = self.fits[fitkey].estimates['A']
# B = self.fits[fitkey].estimates['B']
# p = self.fits[fitkey].estimates['p']
# _plt.plot(lengths, A + B * p**lengths,
# label='Fit, r = {:.2} +/- {:.1}'.format(self.fits[fitkey].estimates['r'],
# self.fits[fitkey].stds['r']))
# if success_probabilities:
# _plt.violinplot(list(self.data.success_probabilities), self.data.lengths, points=10, widths=1.,
# showmeans=False, showextrema=False, showmedians=False) # , label='Success probabilities')
# if title is not None: _plt.title(title)
# _plt.ylabel("Success probability")
# _plt.xlabel("RB sequence length $(m)$")
# _plt.ylim(ylim)
# _plt.xlim(xlim)
# if legend: _plt.legend()
# if figpath is not None: _plt.savefig(figpath, dpi=1000)
# else: _plt.show()
# return