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germselection.py
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germselection.py
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"""
Functions for selecting a complete set of germs for a GST analysis.
"""
#***************************************************************************************************
# 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 warnings as _warnings
import numpy as _np
import numpy.linalg as _nla
import random as _random
import scipy.linalg as _sla
import itertools
from math import floor
from pygsti.algorithms import grasp as _grasp
from pygsti.algorithms import scoring as _scoring
from pygsti import circuits as _circuits
from pygsti import baseobjs as _baseobjs
from pygsti.tools import mpitools as _mpit
from pygsti.baseobjs.statespace import ExplicitStateSpace as _ExplicitStateSpace
from pygsti.baseobjs.statespace import QuditSpace as _QuditSpace
FLOATSIZE = 8 # in bytes: TODO: a better way
def find_germs(target_model, randomize=True, randomization_strength=1e-2,
num_gs_copies=5, seed=None, candidate_germ_counts=None,
candidate_seed=None, force="singletons", algorithm='greedy',
algorithm_kwargs=None, mem_limit=None, comm=None,
profiler=None, verbosity=1, num_nongauge_params=None,
assume_real=False, float_type=_np.cdouble,
mode="all-Jac", toss_random_frac=None,
force_rank_increase=False, save_cevd_cache_filename= None,
load_cevd_cache_filename=None, file_compression=False):
"""
Generate a germ set for doing GST with a given target model.
This function provides a streamlined interface to a variety of germ
selection algorithms. It's goal is to provide a method that typical users
can run by simply providing a target model and leaving all other settings
at their default values, while providing flexibility for users desiring
more control to fine tune some of the general and algorithm-specific
details.
Currently, to break troublesome degeneracies and provide some confidence
that the chosen germ set is amplificationally complete (AC) for all
models in a neighborhood of the target model (rather than only the
target model), an ensemble of models with random unitary perturbations
to their gates must be provided or generated.
Parameters
----------
target_model : Model or list of Model
The model you are aiming to implement, or a list of models that are
copies of the model you are trying to implement (either with or
without random unitary perturbations applied to the models).
randomize : bool, optional
Whether or not to add random unitary perturbations to the model(s)
provided.
randomization_strength : float, optional
The size of the random unitary perturbations applied to gates in the
model. See :meth:`~pygsti.objects.Model.randomize_with_unitary`
for more details.
num_gs_copies : int, optional
The number of copies of the original model that should be used.
seed : int, optional
Seed for generating random unitary perturbations to models. Also
passed along to stochastic germ-selection algorithms and to the
rng for dropping random fraction of germs.
candidate_germ_counts : dict, optional
A dictionary of *germ_length* : *count* key-value pairs, specifying
the germ "candidate list" - a list of potential germs to draw from.
*count* is either an integer specifying the number of random germs
considered at the given *germ_length* or the special values `"all upto"`
that considers all of the of all non-equivalent germs of length up to
the corresponding *germ_length*. If None, all germs of up to length
6 are used, the equivalent of `{6: 'all upto'}`.
candidate_seed : int, optional
A seed value used when randomly selecting candidate germs. For each
germ length being randomly selected, the germ length is added to
the value of `candidate_seed` to get the actual seed used.
force : str or list, optional
A list of Circuits which *must* be included in the final germ set.
If set to the special string "singletons" then all length-1 strings will
be included. Seting to None is the same as an empty list.
algorithm : {'greedy', 'grasp', 'slack'}, optional
Specifies the algorithm to use to generate the germ set. Current
options are:
'greedy'
Add germs one-at-a-time until the set is AC, picking the germ that
improves the germ-set score by the largest amount at each step. See
:func:`find_germs_breadthfirst` for more details.
'grasp'
Use GRASP to generate random greedy germ sets and then locally
optimize them. See :func:`find_germs_grasp` for more
details.
'slack'
From a initial set of germs, add or remove a germ at each step in
an attempt to improve the germ-set score. Will allow moves that
degrade the score in an attempt to escape local optima as long as
the degredation is within some specified amount of "slack". See
:func:`find_germs_integer_slack` for more details.
algorithm_kwargs : dict
Dictionary of ``{'keyword': keyword_arg}`` pairs providing keyword
arguments for the specified `algorithm` function. See the documentation
for functions referred to in the `algorithm` keyword documentation for
what options are available for each algorithm.
mem_limit : int, optional
A rough memory limit in bytes which restricts the amount of intermediate
values that are computed and stored.
comm : mpi4py.MPI.Comm, optional
When not None, an MPI communicator for distributing the computation
across multiple processors.
profiler : Profiler, optional
A profiler object used for to track timing and memory usage.
verbosity : int, optional
The verbosity level of the :class:`~pygsti.objects.VerbosityPrinter`
used to print log messages.
num_nongauge_params : int, optional
Force the number of nongauge parameters rather than rely on automated gauge optimization.
float_type : numpy dtype object, optional
Numpy data type to use for floating point arrays.
toss_random_frac : float, optional
If specified this is a number between 0 and 1 that indicates the random fraction of candidate
germs to drop randomly following the deduping procedure.
mode : {'allJac', 'singleJac', 'compactEVD'}, optional (default 'allJac')
A flag to indicate the caching scheme used for storing the Jacobians for the candidate
germs. Default value of 'allJac' caches all of the Jacobians and requires the most memory.
'singleJac' doesn't cache anything and instead generates these Jacobians on the fly. The
final option, 'compactEVD', is currently only configured to work with the greedy search
algorithm. When selected the compact eigenvalue decomposition/compact SVD of each of
the Jacobians is constructed and is cached. This uses an intermediate amount of memory
between singleJac and allJac. When compactEVD mode is selected perform the greedy
search iterations using an alternative method based on low-rank updates to the
psuedoinverse. This alternative approach means that this mode also only works with the
score function option set to 'all'.
force_rank_increase : bool, optional (default False)
Optional flag that can be used in conjunction with the greedy search algorithm
in compactEVD mode. When set we require that each subsequant addition to the germ
set must increase the rank of the experiment design's composite Jacobian. Can potentially
speed up the search when set to True.
save_cevd_cache_filename : str, optional (default None)
When set and using the greedy search algorithm in 'compactEVD' mode this writes
the compact EVD cache to disk using the specified filename.
load_cevd_cache_filename : str, optional (default None)
A filename/path to load an existing compact EVD cache from. Useful for warmstarting
a germ set search with various cost function parameters, or for restarting a search
that failed/crashed/ran out of memory. Note that there are no safety checks to confirm
that the compact EVD cache indeed corresponds to that for of currently specified
candidate circuit list, so care must be take to confirm that the candidate
germ lists are consistent across runs.
file_compression : bool, optional (default False)
When True and a filename is given for the save_cevd_cache_filename the corresponding
numpy arrays are stored in a compressed format using numpy's savez_compressed.
Can significantly decrease the storage requirements on disk at the expense of
some additional computational cost writing and loading the files.
Returns
-------
list of Circuit
A list containing the germs making up the germ set.
"""
printer = _baseobjs.VerbosityPrinter.create_printer(verbosity, comm)
modelList = _setup_model_list(target_model, randomize,
randomization_strength, num_gs_copies, seed)
gates = list(target_model.operations.keys())
availableGermsList = []
if candidate_germ_counts is None: candidate_germ_counts = {6: 'all upto'}
for germLength, count in candidate_germ_counts.items():
if count == "all upto":
availableGermsList.extend(_circuits.list_all_circuits_without_powers_and_cycles(
gates, max_length=germLength))
else:
if (candidate_seed is None) and (seed is not None):
candidate_seed=seed
availableGermsList.extend(_circuits.list_random_circuits_onelen(
gates, germLength, count, seed=candidate_seed))
printer.log('Initial Length Available Germ List: '+ str(len(availableGermsList)), 1)
#Let's try deduping the available germ list too:
#build a ckt cache
ckt_cache= create_circuit_cache(target_model, availableGermsList)
#Then dedupe this cache:
#The second value returned is an updated ckt cache which we don't need right now
availableGermsList, _ = clean_germ_list(target_model, ckt_cache, eq_thresh= 1e-6)
printer.log('Length Available Germ List After Deduping: '+ str(len(availableGermsList)), 1)
#If specified, drop a random fraction of the remaining candidate germs.
if toss_random_frac is not None:
availableGermsList = drop_random_germs(availableGermsList, toss_random_frac, target_model, keep_bare=True, seed=seed)
printer.log('Length Available Germ List After Dropping Random Fraction: '+ str(len(availableGermsList)), 1)
#If we have specified a user specified germs to force inclusion of then there is a chance
#they got removed by the deduping and removal of random circuits above. The right way to fix this
#would be to add some logic to those subroutines that prevent this, but for now I am going to just
#manually add them back in (this will result almost suredly in a couple duplicate circuits, but oh well).
if force is not None:
#iterate through the list of forced germs to check for inclusion and
#if missing append to the list of available germs.
if isinstance(force, list):
for forced_germ in force:
if not forced_germ in availableGermsList:
availableGermsList.append(forced_germ)
printer.log('Length Available Germ List After Adding Back In Forced Germs: '+ str(len(availableGermsList)), 1)
#Add some checks related to the new option to switch up data types:
if not assume_real:
if not (float_type is _np.cdouble or float_type is _np.csingle):
printer.log('Selected numpy type: '+ str(float_type.dtype), 1)
raise ValueError('Unless working with (known) real-valued quantities only, please select an appropriate complex numpy dtype (either cdouble or csingle).')
else:
if not (float_type is _np.double or float_type is _np.single):
printer.log('Selected numpy type: '+ str(float_type.dtype), 1)
raise ValueError('When assuming real-valued quantities, please select a real-values numpy dtype (either double or single).')
#How many bytes per float?
FLOATSIZE= float_type(0).itemsize
dim = target_model.dim
#Np = model_list[0].num_params #wrong:? includes spam...
Np = target_model.num_params
if randomize==False:
num_gs_copies=1
memEstimatealljac = FLOATSIZE * num_gs_copies * len(availableGermsList) * Np**2
# for _compute_bulk_twirled_ddd
memEstimatealljac += FLOATSIZE * num_gs_copies * len(availableGermsList) * dim**2 * Np
# for _bulk_twirled_deriv sub-call
printer.log("Memory estimate of %.1f GB for all-Jac mode." %
(memEstimatealljac / 1024.0**3), 1)
memEstimatesinglejac = FLOATSIZE * 3 * len(modelList) * Np**2 + \
FLOATSIZE * 3 * len(modelList) * dim**2 * Np
#Factor of 3 accounts for currentDDDs, testDDDs, and bestDDDs
printer.log("Memory estimate of %.1f GB for single-Jac mode." %
(memEstimatesinglejac / 1024.0**3), 1)
if mem_limit is not None:
if memEstimatealljac > mem_limit:
printer.log("Not enough memory for all-Jac mode, mem_limit is %.1f GB." %
(mem_limit / 1024.0**3), 1)
if memEstimatesinglejac > mem_limit:
raise MemoryError("Too little memory, even for single-Jac mode!")
if algorithm_kwargs is None:
# Avoid danger of using empty dict for default value.
algorithm_kwargs = {}
if algorithm == 'greedy':
printer.log('Using greedy algorithm.', 1)
# Define defaults for parameters that currently have no default or
# whose default we want to change.
default_kwargs = {
'germs_list': availableGermsList,
'randomize': False,
'seed': seed,
'verbosity': max(0, verbosity - 1),
'force': force,
'op_penalty': 0.0,
'score_func': 'all',
'comm': comm,
'mem_limit': mem_limit,
'profiler': profiler,
'num_nongauge_params': num_nongauge_params,
'float_type': float_type,
'mode' : mode,
'force_rank_increase': force_rank_increase,
'save_cevd_cache_filename': save_cevd_cache_filename,
'load_cevd_cache_filename': load_cevd_cache_filename,
'file_compression': file_compression,
'evd_tol': 1e-10,
'initial_germ_set_test': True
}
for key in default_kwargs:
if key not in algorithm_kwargs:
algorithm_kwargs[key] = default_kwargs[key]
germList = find_germs_breadthfirst_greedy(model_list=modelList,
**algorithm_kwargs)
if germList is not None:
#TODO: We should already know the value of this from
#the final output of our optimization loop, so we ought
#to be able to avoid this function call and related overhead.
germsetScore = compute_germ_set_score(
germList, neighborhood=modelList,
score_func=algorithm_kwargs['score_func'],
op_penalty=algorithm_kwargs['op_penalty'],
num_nongauge_params=num_nongauge_params,
float_type=float_type)
printer.log('Constructed germ set:', 1)
printer.log(str([germ.str for germ in germList]), 1)
printer.log(germsetScore, 1)
elif algorithm == 'grasp':
printer.log('Using GRASP algorithm.', 1)
# Define defaults for parameters that currently have no default or
# whose default we want to change.
default_kwargs = {
'alpha': 0.1, # No real reason for setting this value of alpha.
'germs_list': availableGermsList,
'randomize': False,
'seed': seed,
'l1_penalty': 0.0,
'op_penalty': 0.0,
'verbosity': max(0, verbosity - 1),
'force': force,
'return_all': False,
'score_func': 'all',
'num_nongauge_params': num_nongauge_params,
'float_type': float_type
}
for key in default_kwargs:
if key not in algorithm_kwargs:
algorithm_kwargs[key] = default_kwargs[key]
germList = find_germs_grasp(model_list=modelList,
**algorithm_kwargs)
printer.log('Constructed germ set:', 1)
if algorithm_kwargs['return_all'] and germList[0] is not None:
germsetScore = compute_germ_set_score(
germList[0], neighborhood=modelList,
score_func=algorithm_kwargs['score_func'],
op_penalty=algorithm_kwargs['op_penalty'],
l1_penalty=algorithm_kwargs['l1_penalty'],
num_nongauge_params=num_nongauge_params,
float_type=float_type)
printer.log(str([germ.str for germ in germList[0]]), 1)
printer.log(germsetScore)
elif not algorithm_kwargs['return_all'] and germList is not None:
germsetScore = compute_germ_set_score(
germList, neighborhood=modelList,
score_func=algorithm_kwargs['score_func'],
op_penalty=algorithm_kwargs['op_penalty'],
l1_penalty=algorithm_kwargs['l1_penalty'],
num_nongauge_params=num_nongauge_params,
float_type=float_type)
printer.log(str([germ.str for germ in germList]), 1)
printer.log(germsetScore, 1)
elif algorithm == 'slack':
printer.log('Using slack algorithm.', 1)
# Define defaults for parameters that currently have no default or
# whose default we want to change.
default_kwargs = {
'germs_list': availableGermsList,
'randomize': False,
'seed': seed,
'verbosity': max(0, verbosity - 1),
'l1_penalty': 0.0,
'op_penalty': 0.0,
'force': force,
'score_func': 'all',
'float_type': float_type
}
if ('slack_frac' not in algorithm_kwargs
and 'fixed_slack' not in algorithm_kwargs):
algorithm_kwargs['slack_frac'] = 0.1
for key in default_kwargs:
if key not in algorithm_kwargs:
algorithm_kwargs[key] = default_kwargs[key]
germList = find_germs_integer_slack(modelList,
**algorithm_kwargs)
if germList is not None:
germsetScore = compute_germ_set_score(
germList, neighborhood=modelList,
score_func=algorithm_kwargs['score_func'],
op_penalty=algorithm_kwargs['op_penalty'],
l1_penalty=algorithm_kwargs['l1_penalty'],
num_nongauge_params=num_nongauge_params,
float_type=float_type)
printer.log('Constructed germ set:', 1)
printer.log(str([germ.str for germ in germList]), 1)
printer.log(germsetScore, 1)
else:
raise ValueError("'{}' is not a valid algorithm "
"identifier.".format(algorithm))
return germList
def compute_germ_set_score(germs, target_model=None, neighborhood=None,
neighborhood_size=5,
randomization_strength=1e-2, score_func='all',
op_penalty=0.0, l1_penalty=0.0, num_nongauge_params=None,
float_type=_np.cdouble):
"""
Calculate the score of a germ set with respect to a model.
More precisely, this function computes the maximum score (roughly equal
to the number of amplified parameters) for a cloud of models.
If `target_model` is given, it serves as the center of the cloud,
otherwise the cloud must be supplied directly via `neighborhood`.
Parameters
----------
germs : list
The germ set
target_model : Model, optional
The target model, used to generate a neighborhood of randomized models.
neighborhood : list of Models, optional
The "cloud" of models for which scores are computed. If not None, this
overrides `target_model`, `neighborhood_size`, and `randomization_strength`.
neighborhood_size : int, optional
Number of randomized models to construct around `target_model`.
randomization_strength : float, optional
Strength of unitary randomizations, as passed to :method:`target_model.randomize_with_unitary`.
score_func : {'all', 'worst'}
Sets the objective function for scoring the eigenvalues. If 'all',
score is ``sum(1/input_array)``. If 'worst', score is ``1/min(input_array)``.
op_penalty : float, optional
Coefficient for a penalty linear in the sum of the germ lengths.
l1_penalty : float, optional
Coefficient for a penalty linear in the number of germs.
num_nongauge_params : int, optional
Force the number of nongauge parameters rather than rely on automated gauge optimization.
float_type : numpy dtype object, optional
Numpy data type to use for floating point arrays.
Returns
-------
CompositeScore
The maximum score for `germs`, indicating how many parameters it amplifies.
"""
def score_fn(x): return _scoring.list_score(x, score_func=score_func)
if neighborhood is None:
neighborhood = [target_model.randomize_with_unitary(randomization_strength)
for n in range(neighborhood_size)]
scores = [compute_composite_germ_set_score(score_fn, model=model,
partial_germs_list=germs,
op_penalty=op_penalty,
l1_penalty=l1_penalty,
num_nongauge_params=num_nongauge_params,
float_type=float_type)
for model in neighborhood]
return max(scores)
def _get_model_params(model_list, printer=None):
"""
Get the number of gates and gauge parameters of the models in a list.
Also verifies all models have the same number of gates and gauge parameters.
Parameters
----------
model_list : list of Model
A list of models for which you want an AC germ set.
Returns
-------
reducedModelList : list of Model
The original list of models with SPAM removed
numGaugeParams : int
The number of non-SPAM gauge parameters for all models.
numNonGaugeParams : int
The number of non-SPAM non-gauge parameters for all models.
numOps : int
The number of gates for all models.
Raises
------
ValueError
If the number of gauge parameters or gates varies among the models.
"""
if printer is not None:
printer.log('Calculating number of gauge and non-gauge parameters', 1)
# We don't care about SPAM, since it can't be amplified.
reducedModelList = [_remove_spam_vectors(model)
for model in model_list]
# All the models should have the same number of parameters and gates, but
# let's be paranoid here for the time being and make sure.
numGaugeParamsList = [reducedModel.num_gauge_params
for reducedModel in reducedModelList]
numGaugeParams = numGaugeParamsList[0]
if not all([numGaugeParams == otherNumGaugeParams
for otherNumGaugeParams in numGaugeParamsList[1:]]):
raise ValueError("All models must have the same number of gauge "
"parameters!")
numNonGaugeParamsList = [reducedModel.num_nongauge_params
for reducedModel in reducedModelList]
numNonGaugeParams = numNonGaugeParamsList[0]
if not all([numNonGaugeParams == otherNumNonGaugeParams
for otherNumNonGaugeParams in numNonGaugeParamsList[1:]]):
raise ValueError("All models must have the same number of non-gauge "
"parameters!")
numOpsList = [len(reducedModel.operations)
for reducedModel in reducedModelList]
numOps = numOpsList[0]
if not all([numOps == otherNumOps
for otherNumOps in numOpsList[1:]]):
raise ValueError("All models must have the same number of gates!")
return reducedModelList, numGaugeParams, numNonGaugeParams, numOps
def _setup_model_list(model_list, randomize, randomization_strength,
num_copies, seed):
"""
Sets up a list of randomize models (helper function).
"""
if not isinstance(model_list, (list, tuple)):
model_list = [model_list]
if len(model_list) > 1 and num_copies is not None:
_warnings.warn("Ignoring num_copies={} since multiple models were "
"supplied.".format(num_copies))
if randomize:
model_list = randomize_model_list(model_list, randomization_strength,
num_copies, seed)
return model_list
def compute_composite_germ_set_score(score_fn, threshold_ac=1e6, init_n=1,
partial_deriv_dagger_deriv=None, model=None,
partial_germs_list=None, eps=None, germ_lengths=None,
op_penalty=0.0, l1_penalty=0.0, num_nongauge_params=None,
float_type=_np.cdouble):
"""
Compute the score for a germ set when it is not AC against a model.
Normally scores computed for germ sets against models for which they are
not AC will simply be astronomically large. This is fine if AC is all you
care about, but not so useful if you want to compare partial germ sets
against one another to see which is closer to being AC. This function
will see if the germ set is AC for the parameters corresponding to the
largest `N` eigenvalues for increasing `N` until it finds a value of `N`
for which the germ set is not AC or all the non gauge parameters are
accounted for and report the value of `N` as well as the score.
This allows partial germ set scores to be compared against one-another
sensibly, where a larger value of `N` always beats a smaller value of `N`,
and ties in the value of `N` are broken by the score for that value of `N`.
Parameters
----------
score_fn : callable
A function that takes as input a list of sorted eigenvalues and returns
a score for the partial germ set based on those eigenvalues, with lower
scores indicating better germ sets. Usually some flavor of
:func:`~pygsti.algorithms.scoring.list_score`.
threshold_ac : float, optional
Value which the score (before penalties are applied) must be lower than
for the germ set to be considered AC.
init_n : int
The number of largest eigenvalues to begin with checking.
partial_deriv_dagger_deriv : numpy.array, optional
Array with three axes, where the first axis indexes individual germs
within the partial germ set and the remaining axes index entries in the
positive square of the Jacobian of each individual germ's parameters
with respect to the model parameters.
If this array is not supplied it will need to be computed from
`germs_list` and `model`, which will take longer, so it is recommended
to precompute this array if this routine will be called multiple times.
model : Model, optional
The model against which the germ set is to be scored. Not needed if
`partial_deriv_dagger_deriv` is provided.
partial_germs_list : list of Circuit, optional
The list of germs in the partial germ set to be evaluated. Not needed
if `partial_deriv_dagger_deriv` (and `germ_lengths` when
``op_penalty > 0``) are provided.
eps : float, optional
Used when calculating `partial_deriv_dagger_deriv` to determine if two
eigenvalues are equal (see :func:`_bulk_twirled_deriv` for details). Not
used if `partial_deriv_dagger_deriv` is provided.
op_penalty : float, optional
Coefficient for a penalty linear in the sum of the germ lengths.
germ_lengths : numpy.array, optional
The length of each germ. Not needed if `op_penalty` is ``0.0`` or
`partial_germs_list` is provided.
l1_penalty : float, optional
Coefficient for a penalty linear in the number of germs.
num_nongauge_params : int, optional
Force the number of nongauge parameters rather than rely on automated gauge optimization.
Returns
-------
CompositeScore
The score for the germ set indicating how many parameters it amplifies
and its numerical score restricted to those parameters.
"""
if partial_deriv_dagger_deriv is None:
if model is None or partial_germs_list is None:
raise ValueError("Must provide either partial_deriv_dagger_deriv or "
"(model, partial_germs_list)!")
else:
Np= model.num_params
combinedDDD=_np.zeros((Np, Np), dtype=float_type)
pDDD_kwargs = {'float_type':float_type}
if eps is not None:
pDDD_kwargs['eps'] = eps
#use a more memory efficient calculation when generating
#twirled ddd from scratch again.
for germ in partial_germs_list:
combinedDDD += _compute_twirled_ddd(model, germ, **pDDD_kwargs)
if num_nongauge_params is None:
if model is None:
raise ValueError("Must provide either num_nongauge_params or model!")
else:
reduced_model = _remove_spam_vectors(model)
num_nongauge_params = reduced_model.num_params - reduced_model.num_gauge_params
# Calculate penalty scores
if partial_deriv_dagger_deriv is None:
numGerms= len(partial_germs_list)
else:
numGerms = partial_deriv_dagger_deriv.shape[0]
l1Score = l1_penalty * numGerms
opScore = 0.0
if op_penalty != 0.0:
if germ_lengths is None:
if partial_germs_list is None:
raise ValueError("Must provide either germ_lengths or "
"partial_germs_list when op_penalty != 0.0!")
else:
germ_lengths = _np.array([len(germ)
for germ in partial_germs_list])
opScore = op_penalty * _np.sum(germ_lengths)
if partial_deriv_dagger_deriv is not None:
combinedDDD = _np.sum(partial_deriv_dagger_deriv, axis=0)
sortedEigenvals = _np.sort(_np.real(_nla.eigvalsh(combinedDDD)))
observableEigenvals = sortedEigenvals[-num_nongauge_params:]
N_AC = 0
AC_score = _np.inf
for N in range(init_n, len(observableEigenvals) + 1):
scoredEigenvals = observableEigenvals[-N:]
candidate_AC_score = score_fn(scoredEigenvals)
if candidate_AC_score > threshold_ac:
break # We've found a set of parameters for which the germ set
# is not AC.
else:
AC_score = candidate_AC_score
N_AC = N
# OLD Apply penalties to the minor score; major part is just #amplified
#major_score = N_AC
#minor_score = AC_score + l1Score + opScore
# Apply penalties to the major score
major_score = -N_AC + opScore + l1Score
minor_score = AC_score
ret = _scoring.CompositeScore(major_score, minor_score, N_AC)
#DEBUG: ret.extra = {'opScore': opScore,
# 'sum(germ_lengths)': _np.sum(germ_lengths), 'l1': l1Score}
return ret
def _compute_bulk_twirled_ddd(model, germs_list, eps=1e-6, check=False,
germ_lengths=None, comm=None, float_type=_np.cdouble):
"""
Calculate the positive squares of the germ Jacobians.
twirledDerivDaggerDeriv == array J.H*J contributions from each germ
(J=Jacobian) indexed by (iGerm, iModelParam1, iModelParam2)
size (nGerms, vec_model_dim, vec_model_dim)
Parameters
----------
model : Model
The model defining the parameters to differentiate with respect to.
germs_list : list
The germ set
eps : float, optional
Tolerance used for testing whether two eigenvectors are degenerate
(i.e. abs(eval1 - eval2) < eps ? )
check : bool, optional
Whether to perform internal consistency checks, at the expense of
making the function slower.
germ_lengths : numpy.ndarray, optional
A pre-computed array of the length (depth) of each germ.
comm : mpi4py.MPI.Comm, optional
When not ``None``, an MPI communicator for distributing the computation
across multiple processors.
float_type : numpy dtype object, optional
Numpy data type to use in floating point arrays.
Returns
-------
twirledDerivDaggerDeriv : numpy.ndarray
A complex array of shape `(len(germs), model.num_params, model.num_params)`.
"""
if germ_lengths is None:
germ_lengths = _np.array([len(germ) for germ in germs_list])
twirledDeriv = _bulk_twirled_deriv(model, germs_list, eps, check, comm, float_type=float_type) / germ_lengths[:, None, None]
#OLD: slow, I think because conjugate *copies* a large tensor, causing a memory bottleneck
#twirledDerivDaggerDeriv = _np.einsum('ijk,ijl->ikl',
# _np.conjugate(twirledDeriv),
# twirledDeriv)
#NEW: faster, one-germ-at-a-time computation requires less memory.
nGerms, _, vec_model_dim = twirledDeriv.shape
twirledDerivDaggerDeriv = _np.empty((nGerms, vec_model_dim, vec_model_dim),
dtype=float_type)
for i in range(nGerms):
twirledDerivDaggerDeriv[i, :, :] = _np.dot(
twirledDeriv[i, :, :].conjugate().T, twirledDeriv[i, :, :])
return twirledDerivDaggerDeriv
def _compute_twirled_ddd(model, germ, eps=1e-6, float_type=_np.cdouble):
"""
Calculate the positive squares of the germ Jacobian.
twirledDerivDaggerDeriv == array J.H*J contributions from `germ`
(J=Jacobian) indexed by (iModelParam1, iModelParam2)
size (vec_model_dim, vec_model_dim)
Parameters
----------
model : Model
The model defining the parameters to differentiate with respect to.
germ : Circuit
The (single) germ circuit to consider. `J` above is the twirled
derivative of this circuit's action (process matrix).
eps : float, optional
Tolerance used for testing whether two eigenvectors are degenerate
(i.e. abs(eval1 - eval2) < eps ? )
Returns
-------
numpy.ndarray
"""
twirledDeriv = _twirled_deriv(model, germ, eps, float_type) / len(germ)
#twirledDerivDaggerDeriv = _np.einsum('jk,jl->kl',
# _np.conjugate(twirledDeriv),
# twirledDeriv)
twirledDerivDaggerDeriv = _np.tensordot(_np.conjugate(twirledDeriv),
twirledDeriv, (0, 0))
return twirledDerivDaggerDeriv
def _germ_set_score_slack(weights, model_num, score_func, deriv_dagger_deriv_list,
force_indices, force_score,
n_gauge_params, op_penalty, germ_lengths, l1_penalty=1e-2,
score_dict=None):
"""
Returns a germ set "score" in which smaller is better.
Also returns intentionally bad score (`force_score`) if `weights` is zero on any of
the "forced" germs (i.e. at any index in `forcedIndices`).
This function is included for use by :func:`find_germs_integer_slack`,
but is not convenient for just computing the score of a germ set. For that,
use :func:`compute_germ_set_score`.
Parameters
----------
weights : list
The per-germ "selection weight", indicating whether the germ
is present in the selected germ set or not.
model_num : int
index into `deriv_dagger_deriv_list` indicating which model (typically in
a neighborhood) we're computing scores for.
score_func : {'all', 'worst'}
Sets the objective function for scoring the eigenvalues. If 'all',
score is ``sum(1/input_array)``. If 'worst', score is ``1/min(input_array)``.
deriv_dagger_deriv_list : numpy.ndarray
Array of J.T * J contributions for each model.
force_indices : list of ints
Indices marking the germs that *must* be in the final set (or else `force_score`
will be returned).
force_score : float
The score that is returned when any of the germs indexed by `force_indices` are
not present (i.e. their weights are <= 0).
n_gauge_params : int
The number of gauge (not amplifiable) parameters in the model.
op_penalty : float
Coefficient for a penalty linear in the sum of the germ lengths.
germ_lengths : numpy.ndarray
A pre-computed array of the length (depth) of each germ.
l1_penalty : float
Coefficient for a penalty linear in the number of germs.
score_dict : dict, optional
A dictionary to cache the score valies for the given `model_num` and
`weights`, i.e. `score_dict[model_num, tuple(weights)]` is set to the
returned value.
Returns
-------
float
"""
if force_indices is not None and _np.any(weights[force_indices] <= 0):
score = force_score
else:
#combinedDDD = _np.einsum('i,ijk', weights,
# deriv_dagger_deriv_list[model_num])
combinedDDD = _np.squeeze(
_np.tensordot(_np.expand_dims(weights, 1),
deriv_dagger_deriv_list[model_num], (0, 0)))
assert len(combinedDDD.shape) == 2
sortedEigenvals = _np.sort(_np.real(_nla.eigvalsh(combinedDDD)))
observableEigenvals = sortedEigenvals[n_gauge_params:]
score = (_scoring.list_score(observableEigenvals, score_func)
+ l1_penalty * _np.sum(weights)
+ op_penalty * _np.dot(germ_lengths, weights))
if score_dict is not None:
# Side effect: calling _germ_set_score_slack caches result in score_dict
score_dict[model_num, tuple(weights)] = score
return score
def randomize_model_list(model_list, randomization_strength, num_copies,
seed=None):
"""
Applies random unitary perturbations to a model or list of models.
If `model_list` is a length-1 list, then `num_copies` determines how
many randomizations to create. If `model_list` containes multiple
models, then `num_copies` must be `None` and each model is
randomized once to create the corresponding returned model.
Parameters
----------
model_list : Model or list
A list of Model objects.
randomization_strength : float, optional
Strength of unitary randomizations, as passed to :method:`Model.randomize_with_unitary`.
num_copies : int
The number of random perturbations of `model_list[0]` to generate when
`len(model_list) == 1`. A value of `None` will result in 1 copy. If
`len(model_list) > 1` then `num_copies` must be set to None.
seed : int, optional
Starting seed for randomization. Successive randomizations receive
successive seeds. `None` results in random seeds.
Returns
-------
list
A list of the randomized Models.
"""
if len(model_list) > 1 and num_copies is not None:
raise ValueError("Input multiple models XOR request multiple "
"copies only!")
newmodelList = []
if len(model_list) > 1:
for modelnum, model in enumerate(model_list):
newmodelList.append(model.randomize_with_unitary(
randomization_strength,
seed=None if seed is None else seed + modelnum))
else:
for modelnum in range(num_copies if num_copies is not None else 1):
newmodelList.append(model_list[0].randomize_with_unitary(
randomization_strength,
seed=None if seed is None else seed + modelnum))
return newmodelList
def test_germs_list_completeness(model_list, germs_list, score_func, threshold, float_type=_np.cdouble):
"""
Check to see if the germs_list is amplificationally complete (AC).
Checks for AC with respect to all the Models in `model_list`, returning
the index of the first Model for which it is not AC or `-1` if it is AC
for all Models.
Parameters
----------
model_list : list
A list of models to test. Often this list is a neighborhood ("cloud") of
models around a model of interest.
germs_list : list
A list of the germ :class:`Circuit`s (the "germ set") to test for completeness.
score_func : {'all', 'worst'}
Sets the objective function for scoring the eigenvalues. If 'all',
score is ``sum(1/eigval_array)``. If 'worst', score is ``1/min(eigval_array)``.
threshold : float, optional
An eigenvalue of jacobian^T*jacobian is considered zero and thus a
parameter un-amplified when its reciprocal is greater than threshold.
Also used for eigenvector degeneracy testing in twirling operation.
float_type : numpy dtype object, optional
Numpy data type to use for floating point arrays.
Returns
-------
int
The index of the first model in `model_list` to fail the amplficational
completeness test.
"""
for modelNum, model in enumerate(model_list):
initial_test = test_germ_set_infl(model, germs_list,
score_func=score_func,
threshold=threshold, float_type=float_type)
if not initial_test:
return modelNum
# If the germs_list is complete for all models, return -1
return -1
def _remove_spam_vectors(model):
"""
Returns a copy of `model` with state preparations and effects removed.
Parameters
----------
model : Model
The model to act on.
Returns
-------
Model
"""
reducedModel = model.copy()
for prepLabel in list(reducedModel.preps.keys()):
del reducedModel.preps[prepLabel]
for povmLabel in list(reducedModel.povms.keys()):
del reducedModel.povms[povmLabel]
reducedModel._mark_for_rebuild()
return reducedModel
def _num_non_spam_gauge_params(model):
"""
Return the number of non-gauge, non-SPAM parameters in `model`.