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fogistore.py
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fogistore.py
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"""
Defines the FirstOrderGaugeInvariantStore class and supporting functionality.
"""
#***************************************************************************************************
# 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
import scipy.sparse as _sps
import copy as _copy
import warnings as _warnings
import itertools as _itertools
import collections as _collections
from pygsti.baseobjs import Basis as _Basis
from pygsti.tools import matrixtools as _mt
from pygsti.tools import optools as _ot
from pygsti.tools import slicetools as _slct
from pygsti.tools import fogitools as _fogit
class FirstOrderGaugeInvariantStore(object):
"""
An object that computes and stores the first-order-gauge-invariant quantities of a model.
Currently, it is only compatible with :class:`ExplicitOpModel` objects.
"""
def __init__(self, gauge_action_matrices_by_op, gauge_action_gauge_spaces_by_op, errorgen_coefficient_labels_by_op,
op_label_abbrevs=None, reduce_to_model_space=True,
dependent_fogi_action='drop', norm_order=None):
"""
TODO: docstring
"""
self.primitive_op_labels = tuple(gauge_action_matrices_by_op.keys())
# Construct common gauge space by special way of intersecting the gauge spaces for all the ops
# Note: the gauge_space of each op is constructed (see `setup_fogi`) so that the gauge action is
# zero on any elementary error generator not in the elementary-errorgen basis associated with
# gauge_space (gauge_space is the span of linear combos of a elemgen basis that was chosen to
# include all possible non-trivial (non-zero) gauge actions by the operator (gauge action is the
# *difference* K - UKU^dag in the Lindblad mapping under gauge transform exp(K), L -> L + K - UKU^dag)
common_gauge_space = None
for op_label, gauge_space in gauge_action_gauge_spaces_by_op.items():
#FOGI DEBUG print("DEBUG gauge space of ", op_label, "has dim", gauge_space.vectors.shape[1])
if common_gauge_space is None:
common_gauge_space = gauge_space
else:
common_gauge_space = common_gauge_space.intersection(gauge_space,
free_on_unspecified_space=True,
use_nice_nullspace=True)
# column space of self.fogi_directions
#FOGI DEBUG print("DEBUG common gauge space of has dim", common_gauge_space.vectors.shape[1])
common_gauge_space.normalize()
self.gauge_space = common_gauge_space
# row space of self.fogi_directions - "errgen-set space" lookups
# -- maybe make this into an "ErrgenSetSpace" object in FUTURE?
self.elem_errorgen_labels_by_op = errorgen_coefficient_labels_by_op
self.op_errorgen_indices = _fogit._create_op_errgen_indices_dict(self.primitive_op_labels,
self.elem_errorgen_labels_by_op)
self.errorgen_space_op_elem_labels = tuple([(op_label, elem_lbl) for op_label in self.primitive_op_labels
for elem_lbl in self.elem_errorgen_labels_by_op[op_label]])
# above is same as flattened self.elem_errorgen_labels_by_op - labels final "row basis" of fogi dirs
num_elem_errgens = sum([len(labels) for labels in self.elem_errorgen_labels_by_op.values()])
allop_gauge_action = _sps.lil_matrix((num_elem_errgens, self.gauge_space.vectors.shape[1]), dtype=complex)
# Now update (restrict) each op's gauge_action to use common gauge space
# - need to write the vectors of the common (final) gauge space, w_i, as linear combos of
# the op's original gauge space vectors, v_i.
# - ignore elemgens that are not in the op's orig_gauge_space's elemgen basis
# W = V * alpha, and we want to find alpha. W and V are the vectors in the op's elemgen basis
# (these could be seen as staring in the union of the common gauge's and op's elemgen
# bases - which would just be the common gauge's elemgen basis since it's strictly larger -
# restricted to the op's elemben basis)
for op_label, orig_gauge_space in gauge_action_gauge_spaces_by_op.items():
#FOGI DEBUG print("DEBUG: ", op_label, orig_gauge_space.vectors.shape, len(orig_gauge_space.elemgen_basis))
gauge_action = gauge_action_matrices_by_op[op_label] # a sparse matrix
op_elemgen_lbls = orig_gauge_space.elemgen_basis.labels
W = common_gauge_space.vectors[common_gauge_space.elemgen_basis.label_indices(op_elemgen_lbls), :]
V = orig_gauge_space.vectors
alpha = _np.dot(_np.linalg.pinv(V), W) # make SPARSE compatible in future if space vectors are sparse
alpha = _sps.csr_matrix(alpha) # convert to dense -> CSR for now, as if we did sparse math above
# update gauge action to use common gauge space
sparse_gauge_action = gauge_action.dot(alpha)
allop_gauge_action[self.op_errorgen_indices[op_label], :] = sparse_gauge_action[:, :]
gauge_action_matrices_by_op[op_label] = sparse_gauge_action.toarray() # make **DENSE** here
# Hopefully matrices aren't too large after this reduction and dense matrices are ok,
# otherwise we need to change downstream nullspace and pseduoinverse operations to be sparse compatible.
#FUTURE: if update above creates zero-rows in gauge action matrix, maybe remove
# these rows from the row basis, i.e. self.elem_errorgen_labels_by_op[op_label]
self.gauge_action_for_op = gauge_action_matrices_by_op
(indep_fogi_directions, indep_fogi_metadata, dep_fogi_directions, dep_fogi_metadata) = \
_fogit.construct_fogi_quantities(self.primitive_op_labels, self.gauge_action_for_op,
self.elem_errorgen_labels_by_op, self.op_errorgen_indices,
self.gauge_space, op_label_abbrevs, dependent_fogi_action, norm_order)
self.fogi_directions = _sps.hstack((indep_fogi_directions, dep_fogi_directions))
self.fogi_metadata = indep_fogi_metadata + dep_fogi_metadata # list concatenation
self.dependent_dir_indices = _np.arange(len(indep_fogi_metadata), len(self.fogi_metadata))
for j, meta in enumerate(self.fogi_metadata):
meta['raw'] = _fogit.op_elem_vec_name(self.fogi_directions[:, j], self.errorgen_space_op_elem_labels,
op_label_abbrevs if (op_label_abbrevs is not None) else {})
assert(len(self.errorgen_space_op_elem_labels) == self.fogi_directions.shape[0])
# Note: currently PUNT on doing below with sparse math, as a sparse nullspace routine is unavailable
#First order gauge *variant* directions (the complement of FOGI directions in errgen set space)
# (directions in errorgen space that correspond to gauge transformations -- to first order)
#fogv_directions = _mt.nice_nullspace(self.fogi_directions.T) # can be dependent!
self.fogv_directions = _mt.nullspace(self.fogi_directions.toarray().T) # complement of fogi directions
self.fogv_directions = _sps.csc_matrix(self.fogv_directions) # as though we used sparse math above
self.fogv_labels = ["%d gauge action" % i for i in range(self.fogv_directions.shape[1])]
#self.fogv_labels = ["%s gauge action" % nm
# for nm in _fogit.elem_vec_names(gauge_space_directions, gauge_elemgen_labels)]
#Get gauge-space directions corresponding to the fogv directions
# (pinv_allop_gauge_action takes errorgen-set -> gauge-gen space)
self.allop_gauge_action = allop_gauge_action
pinv_allop_gauge_action = _np.linalg.pinv(self.allop_gauge_action.toarray(), rcond=1e-7)
gauge_space_directions = _np.dot(pinv_allop_gauge_action,
self.fogv_directions.toarray()) # in gauge-generator space
self.gauge_space_directions = gauge_space_directions
#Notes on error-gen vs gauge-gen space:
# self.fogi_directions and self.fogv_directions are dual vectors in error-generator space,
# i.e. with elements corresponding to the elementary error generators given by
# self.errorgen_space_op_elem_labels.
# self.fogi_gaugespace_directions contains, when applicable, a gauge-space direction that
# correspondings to the FOGI quantity in self.fogi_directions. Such a gauge-space direction
# exists for relational FOGI quantities, where the FOGI quantity is constructed by taking the
# *difference* of a gauge-space action (given by the gauge-space direction) on two operations
# (or sets of operations).
#Store auxiliary info for later use
self.norm_order = norm_order
self._dependent_fogi_action = dependent_fogi_action
#Assertions to check that everything looks good
if True:
fogi_dirs = self.fogi_directions.toarray() # don't bother with sparse math yet
fogv_dirs = self.fogv_directions.toarray()
# We must reduce X_gauge_action to the "in-model gauge space" before testing if the computed vecs are FOGI:
assert(_np.linalg.norm(_np.dot(self.allop_gauge_action.toarray().T, fogi_dirs)) < 1e-8)
#Check that pseudo-inverse was computed correctly (~ matrices are full rank)
# fogi_coeffs = dot(fogi_directions.T, elem_errorgen_vec), where elem_errorgen_vec is filled from model
# params, since fogi_directions columns are *dual* vectors in error-gen space. Thus,
# to go in reverse:
# elem_errogen_vec = dot(pinv_fogi_dirs_T, fogi_coeffs), where dot(fogi_directions.T, pinv_fogi_dirs_T) == I
# (This will only be the case when fogi_vecs are linearly independent, so when dependent_indices == 'drop')
if dependent_fogi_action == 'drop':
#assert(_mt.columns_are_orthogonal(self.fogi_directions)) # not true unless we construct them so...
assert(_np.linalg.norm(_np.dot(fogi_dirs.T, _np.linalg.pinv(fogi_dirs.T))
- _np.identity(fogi_dirs.shape[1], 'd')) < 1e-6)
# A similar relationship should always hold for the gauge directions, except for these we never
# keep linear dependencies
assert(_mt.columns_are_orthogonal(fogv_dirs))
assert(_np.linalg.norm(_np.dot(fogv_dirs.T, _np.linalg.pinv(fogv_dirs.T))
- _np.identity(fogv_dirs.shape[1], 'd')) < 1e-6)
def find_nice_fogiv_directions(self):
# BELOW: an attempt to find nice FOGV directions - but we'd like all the vecs to be
# orthogonal and this seems to interfere with that, so we'll just leave the fogv dirs messy for now.
#
# # like to find LCs mix s.t. dot(gauge_space_directions, mix) ~= identity, so use pinv
# # then propagate this mixing to fogv_directions = dot(allop_gauge_action, mixed_gauge_space_directions)
# mix = _np.linalg.pinv(gauge_space_directions)[:, 0:fogv_directions.shape[1]] # use "full-rank" part of pinv
# mixed_gauge_space_dirs = _np.dot(gauge_space_directions, mix)
#
# #TODO - better mix matrix?
# #print("gauge_space_directions shape = ",gauge_space_directions.shape)
# #print("mixed_gauge_space_dirs = "); _mt.print_mx(gauge_space_directions, width=6, prec=2)
# #U, s, Vh = _np.linalg.svd(gauge_space_directions, full_matrices=True)
# #inv_s = _np.array([1/x if abs(x) > 1e-4 else 0 for x in s])
# #print("shapes = ",U.shape, s.shape, Vh.shape)
# #print("s = ",s)
# #print(_np.linalg.norm(_np.dot(U,_np.conjugate(U.T)) - _np.identity(U.shape[0])))
# #_mt.print_mx(U, width=6, prec=2)
# #print("U * Udag = ")
# #_mt.print_mx(_np.dot(U,_np.conjugate(U.T)), width=6, prec=2)
# #print(_np.linalg.norm(_np.dot(Vh,Vh.T) - _np.identity(Vh.shape[0])))
# #full_mix = _np.dot(Vh.T, _np.dot(_np.diag(inv_s), U.T)) # _np.linalg.pinv(gauge_space_directions)
# #full_mixed_gauge_space_dirs = _np.dot(gauge_space_directions, full_mix)
# #print("full_mixed_gauge_space_dirs = "); _mt.print_mx(full_mixed_gauge_space_dirs, width=6, prec=2)
#
# self.fogv_labels = ["%s gauge action" % nm
# for nm in _fogit.elem_vec_names(mixed_gauge_space_dirs, gauge_elemgen_labels)]
# self.fogv_directions = _np.dot(self.allop_gauge_action, mixed_gauge_space_dirs)
# # - directions in errorgen space that correspond to gauge transformations (to first order)
#UNUSED - maybe useful just as a check? otherwise REMOVE
#pinv_allop_gauge_action = _np.linalg.pinv(self.allop_gauge_action, rcond=1e-7) # maps error -> gauge-gen space
#gauge_space_directions = _np.dot(pinv_allop_gauge_action, self.fogv_directions) # in gauge-generator space
#assert(_np.linalg.matrix_rank(gauge_space_directions) <= self._gauge_space_dim) # should be nearly full rank
pass
@property
def errorgen_space_dim(self):
return self.fogi_directions.shape[0]
@property
def gauge_space_dim(self):
return self.gauge_space.vectors.shape[1]
@property
def num_fogi_directions(self):
return self.fogi_directions.shape[1]
@property
def num_fogv_directions(self):
return self.fogv_directions.shape[1]
def fogi_errorgen_direction_labels(self, typ='normal'):
""" typ can be 'raw' or 'abbrev' too """
if typ == 'normal': return tuple([meta['name'] for meta in self.fogi_metadata])
elif typ == 'raw': return tuple([meta['raw'] for meta in self.fogi_metadata])
elif typ == 'abrev': return tuple([meta['abbrev'] for meta in self.fogi_metadata])
else: raise ValueError("Invalid `typ` argument: %s" % str(typ))
def fogv_errorgen_direction_labels(self, typ='normal'):
if typ == 'normal': labels = self.fogv_labels
else: labels = [''] * len(self.fogv_labels)
return tuple(labels)
def errorgen_vec_to_fogi_components_array(self, errorgen_vec):
fogi_coeffs = self.fogi_directions.transpose().dot(errorgen_vec)
assert(_np.linalg.norm(fogi_coeffs.imag) < 1e-8)
return fogi_coeffs.real
def errorgen_vec_to_fogv_components_array(self, errorgen_vec):
fogv_coeffs = self.fogv_directions.transpose().dot(errorgen_vec)
assert(_np.linalg.norm(fogv_coeffs.imag) < 1e-8)
return fogv_coeffs.real
def opcoeffs_to_fogi_components_array(self, op_coeffs):
errorgen_vec = _np.zeros(self.errorgen_space_dim, 'd')
for i, (op_label, elem_lbl) in enumerate(self.errorgen_space_op_elem_labels):
errorgen_vec[i] += op_coeffs[op_label].get(elem_lbl, 0.0)
return self.errorgen_vec_to_fogi_components_array(errorgen_vec)
def opcoeffs_to_fogv_components_array(self, op_coeffs):
errorgen_vec = _np.zeros(self.errorgen_space_dim, 'd')
for i, (op_label, elem_lbl) in enumerate(self.errorgen_space_op_elem_labels):
errorgen_vec[i] += op_coeffs[op_label].get(elem_lbl, 0.0)
return self.errorgen_vec_to_fogv_components_array(errorgen_vec)
def opcoeffs_to_fogiv_components_array(self, op_coeffs):
errorgen_vec = _np.zeros(self.errorgen_space_dim, 'd')
for i, (op_label, elem_lbl) in enumerate(self.errorgen_space_op_elem_labels):
errorgen_vec[i] += op_coeffs[op_label].get(elem_lbl, 0.0)
return self.errorgen_vec_to_fogi_components_array(errorgen_vec), \
self.errorgen_vec_to_fogv_components_array(errorgen_vec)
def fogi_components_array_to_errorgen_vec(self, fogi_components):
assert(self._dependent_fogi_action == 'drop'), \
("Cannot convert *from* fogi components to an errorgen-set vec when fogi directions are linearly-dependent!"
" (Set `dependent_fogi_action='drop'` to ensure directions are independent.)")
# DENSE - need to use sparse solve to enact sparse pinv on vector TODO
return _np.dot(_np.linalg.pinv(self.fogi_directions.toarray().T, rcond=1e-7), fogi_components)
def fogv_components_array_to_errorgen_vec(self, fogv_components):
assert(self._dependent_fogi_action == 'drop'), \
("Cannot convert *from* fogv components to an errorgen-set vec when fogi directions are linearly-dependent!"
" (Set `dependent_fogi_action='drop'` to ensure directions are independent.)")
# DENSE - need to use sparse solve to enact sparse pinv on vector TODO
return _np.dot(_np.linalg.pinv(self.fogv_directions.toarray().T, rcond=1e-7), fogv_components)
def fogiv_components_array_to_errorgen_vec(self, fogi_components, fogv_components):
assert(self._dependent_fogi_action == 'drop'), \
("Cannot convert *from* fogiv components to an errorgen-set vec when fogi directions are "
"linearly-dependent! (Set `dependent_fogi_action='drop'` to ensure directions are independent.)")
# DENSE - need to use sparse solve to enact sparse pinv on vector TODO
return _np.dot(_np.linalg.pinv(
_np.concatenate((self.fogi_directions.toarray(), self.fogv_directions.toarray()), axis=1).T,
rcond=1e-7), _np.concatenate((fogi_components, fogv_components)))
def errorgen_vec_to_opcoeffs(self, errorgen_vec):
op_coeffs = {op_label: {} for op_label in self.primitive_op_labels}
for (op_label, elem_lbl), coeff_value in zip(self.errorgen_space_op_elem_labels, errorgen_vec):
op_coeffs[op_label][elem_lbl] = coeff_value
return op_coeffs
def fogi_components_array_to_opcoeffs(self, fogi_components):
return self.errorgen_vec_to_opcoeffs(self.fogi_components_array_to_errorgen_vec(fogi_components))
def fogv_components_array_to_opcoeffs(self, fogv_components):
return self.errorgen_vec_to_opcoeffs(self.fogv_components_array_to_errorgen_vec(fogv_components))
def fogiv_components_array_to_opcoeffs(self, fogi_components, fogv_components):
return self.errorgen_vec_to_opcoeffs(self.fogiv_components_array_to_errorgen_vec(
fogi_components, fogv_components))
def create_binned_fogi_infos(self, tol=1e-5):
"""
Creates an 'info' dictionary for each FOGI quantity and places it within a
nested dictionary structure by the operators involved, the types of error generators,
and the qubits acted upon (a.k.a. the "target" qubits).
TODO: docstring
Returns
-------
dict
"""
# Construct a dict of information for each elementary error-gen basis element (the basis for error-gen space)
elemgen_info = {}
for k, (op_label, eglabel) in enumerate(self.errorgen_space_op_elem_labels):
elemgen_info[k] = {
'type': eglabel.errorgen_type,
'qubits': eglabel.sslbls,
'op_label': op_label,
'elemgen_label': eglabel,
}
bins = {}
dependent_indices = set(self.dependent_dir_indices) # indices of one set of linearly dep. fogi dirs
for i, meta in enumerate(self.fogi_metadata):
fogi_dir = self.fogi_directions[:, i].toarray().ravel()
label = meta['name']
label_raw = meta['raw']
label_abbrev = meta['abbrev']
gauge_dir = meta['gaugespace_dir']
r_factor = meta['r']
present_elgen_indices = _np.where(_np.abs(fogi_dir) > tol)[0]
#Aggregate elemgen_info data for all elemgens that contribute to this FOGI qty (as determined by `tol`)
ops_involved = set(); qubits_acted_upon = set(); types = set() # basismx = None
for k in present_elgen_indices:
k_info = elemgen_info[k]
ops_involved.add(k_info['op_label'])
qubits_acted_upon.update(k_info['qubits'])
types.add(k_info['type'])
#Create the "info" dictionary for this FOGI quantity
info = {'op_set': ops_involved,
'types': types,
'qubits': qubits_acted_upon,
'fogi_index': i,
'label': label,
'label_raw': label_raw,
'label_abbrev': label_abbrev,
'dependent': bool(i in dependent_indices),
'gauge_dir': gauge_dir,
'fogi_dir': fogi_dir,
'r_factor': r_factor
}
ops_involved = tuple(sorted(ops_involved))
types = tuple(sorted(types))
qubits_acted_upon = tuple(sorted(qubits_acted_upon))
if ops_involved not in bins: bins[ops_involved] = {}
if types not in bins[ops_involved]: bins[ops_involved][types] = {}
if qubits_acted_upon not in bins[ops_involved][types]: bins[ops_involved][types][qubits_acted_upon] = []
bins[ops_involved][types][qubits_acted_upon].append(info)
return bins
def create_elementary_errorgen_space(self, op_elem_errgen_labels):
"""
Construct a matrix whose column space spans the given list of elementary error generators.
Parameters
----------
op_elem_errgen_labels : iterable
A list of `(operation_label, elementary_error_generator_label)` tuples, where
`operation_label` is one of the primitive operation labels in `self.primitive_op_labels`
and `elementary_error_generator_label` is a :class:`GlobalElementaryErrorgenLabel`
object.
Returns
-------
numpy.ndarray
A two-dimensional array of shape `(self.errorgen_space_dim, len(op_elem_errgen_labels))`.
Columns correspond to elements of `op_elem_errgen_labels` and the rowspace is the
full elementary error generator space of this FOGI analysis.
"""
lbl_to_index = {}
for op_label in self.primitive_op_labels:
elem_errgen_lbls = self.elem_errorgen_labels_by_op[op_label]
elem_errgen_indices = _slct.indices(self.op_errorgen_indices[op_label])
assert(len(elem_errgen_indices) == len(elem_errgen_lbls))
lbl_to_index.update({(op_label, lbl): index for lbl, index in zip(elem_errgen_lbls, elem_errgen_indices)})
ret = _np.zeros((self.fogi_directions.shape[0], len(op_elem_errgen_labels)))
for i, lbl in enumerate(op_elem_errgen_labels):
ret[lbl_to_index[lbl], i] = 1.0
return ret
#UNUSED in our final analyses so far - deprecate in favor of create_fogi_aggregate_single_op_space?
#TODO: maybe can combine with function below, expanding it to take an op_set?
def create_fogi_aggregate_space(self, op_set='all', errorgen_types='all', target='all'):
"""
Construct a matrix with columns equal to the FOGI directions within the specified categories.
Projecting a model's error-generator vector onto such a space can be used
to obtain the contribution of a desired subset of the model's errors.
Parameters
----------
op_set : tuple or "all"
Restrict to (intrinsic) FOGI quantities of a single operation, given as a 1-tuple,
e.g. `(('Gxpi2',0),)` or relational error between multiple operations, e.g.,
`(('Gxpi2',0), ('Gypi2',0))`. The special `"all"` value includes quantities on
all operations (no restriction).
errorgen_types : tuple of {"H", "S"} or "all"
Restrict to FOGI quantities containing elementary error generators of the given
type(s). Note that a tuple with multiple types only selects FOGI quantities
containing *all* the give types (e.g., `('H','S')` will not match quantities
composed of solely Hamiltonian-type generators). The special `"all"` value includes
quantities of all types (no restriction).
target : tuple or "all"
A tuple of state space (qubit) labels to restrict to, e.g., `('Q0','Q1')`.
Note that includeing multiple labels selects only those quantities that
target *all* the labels. The special `"all"` value includes quantities
on all targets (no restriction).
Returns
-------
numpy.ndarray
A two-dimensional array with `self.errorgen_space_dim` rows and a number of
columns dependent on the number of FOGI quantities matching the argument
criteria.
"""
binned_infos = self.create_binned_fogi_infos()
selected_infos = []
for ops, infos_by_type in binned_infos.items():
if op_set == 'all' or ops == op_set:
for type_tup, infos_by_target in infos_by_type.items():
if errorgen_types == 'all' or type_tup == errorgen_types:
for tgt, info_lst in infos_by_target.items():
if target == 'all' or tgt == target:
selected_infos.extend(info_lst)
fogi_indices = [info['fogi_index'] for info in selected_infos]
space = _np.take(self.fogi_directions, fogi_indices, axis=1)
return space
def create_fogi_aggregate_single_op_space(self, op_label, errorgen_type='H',
intrinsic_or_relational='intrinsic', target='all'):
"""
Construct a matrix with columns spanning a particular FOGI subspace for a single operation.
This is a subspace of the full error-generator space of this FOGI analysis,
and projecting a model's error-generator vector onto this space can be used
to obtain the contribution of a desired subset of the `op_label`'s errors.
Parameters
----------
op_label : Label or str
The operation to construct a subspace for. This should be an element of
`self.primitive_op_labels`.
errorgen_type : {"H", "S", "all"}
Potentially restrict to the subspace containing just Hamiltonian (H) or Pauli
stochastic (S) errors. `"all"` imposes no restriction.
intrinsic_or_relational : {"intrinsic", "relational", "all"}
Restrict to intrinsic or relational errors (or not, using `"all"`).
target : tuple or "all"
A tuple of state space (qubit) labels to restrict to, e.g., `('Q0','Q1')`.
Note that including multiple labels selects only those quantities that
target *all* the labels. The special `"all"` value includes quantities
on all targets (no restriction).
Returns
-------
numpy.ndarray
A two-dimensional array with `self.errorgen_space_dim` rows and a number of
columns dependent on the dimension of the selected subspace.
"""
binned_infos = self.create_binned_fogi_infos()
elem_errgen_lbls = self.elem_errorgen_labels_by_op[op_label]
elem_errgen_indices = _slct.indices(self.op_errorgen_indices[op_label])
assert(len(elem_errgen_indices) == len(elem_errgen_lbls))
op_elem_space = _np.zeros((self.fogi_directions.shape[0], len(elem_errgen_indices)))
for i, index in enumerate(elem_errgen_indices):
op_elem_space[index, i] = 1.0
if target == 'all' and errorgen_type == 'all':
on_target_elem_errgen_indices = elem_errgen_indices
else:
on_target_elem_errgen_indices = []
for index, lbl in zip(elem_errgen_indices, elem_errgen_lbls):
if errorgen_type == 'all' or errorgen_type == lbl.errorgen_type:
support = lbl.support
if (target == 'all') or (target == support):
on_target_elem_errgen_indices.append(index)
support_elem_space = _np.zeros((self.fogi_directions.shape[0], len(on_target_elem_errgen_indices)))
for i, index in enumerate(on_target_elem_errgen_indices):
support_elem_space[index, i] = 1.0
#P_support_elem_space = support_elem_space @ np.linalg.pinv(support_elem_space)
if intrinsic_or_relational in ('intrinsic', 'relational'):
# easy case - can just use FOGIs to identify intrinsic errors
selected_infos = []
for ops, infos_by_type in binned_infos.items():
if ops == (op_label,):
for types, infos_by_target in infos_by_type.items(): # use all types
#if types == (egtype,):
for _, info_lst in infos_by_target.items(): # use all targets here
selected_infos.extend(info_lst)
fogi_indices = [info['fogi_index'] for info in selected_infos]
full_int_space = _np.take(self.fogi_directions.toarray(), fogi_indices, axis=1)
#space = P_op_elem_space @ full_int_space
if intrinsic_or_relational == 'intrinsic':
# full intrinsic space is a subspace of op_elem_space but perhaps not of support_elem_space
#target_int_space = P_op_elem_space @ full_int_space
support_int_space = _mt.intersection_space(support_elem_space, full_int_space, use_nice_nullspace=True)
space = support_int_space
elif intrinsic_or_relational == 'relational':
local_support_space = op_elem_space.T @ support_elem_space
local_int_space = op_elem_space.T @ full_int_space
local_rel_space = _mt.nice_nullspace(local_int_space.T)
support_rel_space = _mt.intersection_space(local_support_space, local_rel_space,
use_nice_nullspace=True)
space = op_elem_space @ support_rel_space
elif intrinsic_or_relational == 'all':
space = support_elem_space
else:
raise ValueError("Invalid intrinsic_or_relational value: `%s`" % str(intrinsic_or_relational))
space = _mt.remove_dependent_cols(space)
return space
@classmethod
def merge_binned_fogi_infos(cls, binned_fogi_infos, index_offsets):
"""
Merge together multiple FOGI-info dictionaries created by :method:`create_binned_fogi_infos`.
Parameters
----------
binned_fogi_infos : list
A list of FOGI-info dictionaries.
index_offsets : list
A list of length `len(binned_fogi_infos)` that gives the offset
into an assumed-to-exist corresponding vector of components for
all the FOGI infos.
Returns
-------
dict
The merged dictionary
"""
def _merge_into(dest, src, offset, nlevels_to_merge, store_index):
if nlevels_to_merge == 0: # special last-level case where src and dest are *lists*
for info in src:
new_info = _copy.deepcopy(info)
new_info['fogi_index'] += offset
new_info['store_index'] = store_index
dest.append(new_info)
else:
for k, d in src.items():
if k not in dest: dest[k] = {} if (nlevels_to_merge > 1) else [] # last level = list
_merge_into(dest[k], d, offset, nlevels_to_merge - 1, store_index)
bins = {}
nLevels = 3 # ops_involved, types, qubits_acted_upon
for i, (sub_bins, offset) in enumerate(zip(binned_fogi_infos, index_offsets)):
_merge_into(bins, sub_bins, offset, nLevels, i)
return bins