def _compute_taylor_order_terms(self, order, max_polynomial_vars, gpindices_array): # separated for profiling
terms = []
if len(self.factorops) > 0:
for p in _lt.partition_into(order, len(self.factorops)):
factor_lists = [self.factorops[i].taylor_order_terms(pi, max_polynomial_vars) for i, pi in enumerate(p)]
for factors in _itertools.product(*factor_lists):
terms.append(_term.compose_terms(factors))
elif order == 0: # special case: ComposedOp with no factors == identity
identityTerm = _term.RankOnePolynomialOpTerm.create_from(_Polynomial({(): 1.0}, max_polynomial_vars),
None, None, self._evotype, self.state_space)
terms.append(identityTerm)
self.terms[order] = terms
#def _decompose_indices(x):
# return tuple(_modelmember._decompose_gpindices(
# self.gpindices, _np.array(x, _np.int64)))
mapvec = _np.ascontiguousarray(_np.zeros(max_polynomial_vars, _np.int64))
for ii, i in enumerate(gpindices_array):
mapvec[i] = ii
#poly_coeffs = [t.coeff.map_indices(_decompose_indices) for t in terms] # with *local* indices
poly_coeffs = [t.coeff.mapvec_indices(mapvec) for t in terms] # with *local* indices
tapes = [poly.compact(complex_coeff_tape=True) for poly in poly_coeffs]
if len(tapes) > 0:
vtape = _np.concatenate([t[0] for t in tapes])
ctape = _np.concatenate([t[1] for t in tapes])
else:
vtape = _np.empty(0, _np.int64)
ctape = _np.empty(0, complex)
coeffs_as_compact_polys = (vtape, ctape)
self.local_term_poly_coeffs[order] = coeffs_as_compact_polys
def _compute_taylor_order_terms(
self, order, max_polynomial_vars): # separated for profiling
mapvec = _np.ascontiguousarray(
_np.zeros(max_polynomial_vars, _np.int64))
for ii, i in enumerate(self.gpindices_as_array()):
mapvec[ii] = i
def _compose_poly_indices(terms):
for term in terms:
#term.map_indices_inplace(lambda x: tuple(_modelmember._compose_gpindices(
# self.gpindices, _np.array(x, _np.int64))))
term.mapvec_indices_inplace(mapvec)
return terms
assert (self.gpindices
is not None), "LindbladOp must be added to a Model before use!"
mpv = max_polynomial_vars
#Note: for now, *all* of an error generator's terms are considered 0-th order,
# so the below call to taylor_order_terms just gets all of them. In the FUTURE
# we might want to allow a distinction among the error generator terms, in which
# case this term-exponentiation step will need to become more complicated...
postTerm = _term.RankOnePolynomialOpTerm.create_from(
_Polynomial({(): 1.0}, mpv), None, None, self._evotype,
self.state_space) # identity
loc_terms = _term.exponentiate_terms(
self.errorgen.taylor_order_terms(0, max_polynomial_vars), order,
postTerm, self.exp_terms_cache)
#OLD: loc_terms = [ t.collapse() for t in loc_terms ] # collapse terms for speed
poly_coeffs = [t.coeff for t in loc_terms]
tapes = [poly.compact(complex_coeff_tape=True) for poly in poly_coeffs]
if len(tapes) > 0:
vtape = _np.concatenate([t[0] for t in tapes])
ctape = _np.concatenate([t[1] for t in tapes])
else:
vtape = _np.empty(0, _np.int64)
ctape = _np.empty(0, complex)
coeffs_as_compact_polys = (vtape, ctape)
self.local_term_poly_coeffs[order] = coeffs_as_compact_polys
# only cache terms with *global* indices to avoid confusion...
self.terms[order] = _compose_poly_indices(loc_terms)
def taylor_order_terms(self, order, max_polynomial_vars=100, return_coeff_polys=False):
"""
Get the `order`-th order Taylor-expansion terms of this state vector.
This function either constructs or returns a cached list of the terms at
the given order. Each term is "rank-1", meaning that it is a state
preparation followed by or POVM effect preceded by actions on a
density matrix `rho` of the form:
`rho -> A rho B`
The coefficients of these terms are typically polynomials of the
State's parameters, where the polynomial's variable indices index the
*global* parameters of the State's parent (usually a :class:`Model`)
, not the State's local parameter array (i.e. that returned from
`to_vector`).
Parameters
----------
order : int
The order of terms to get.
max_polynomial_vars : int, optional
maximum number of variables the created polynomials can have.
return_coeff_polys : bool
Whether a parallel list of locally-indexed (using variable indices
corresponding to *this* object's parameters rather than its parent's)
polynomial coefficients should be returned as well.
Returns
-------
terms : list
A list of :class:`RankOneTerm` objects.
coefficients : list
Only present when `return_coeff_polys == True`.
A list of *compact* polynomial objects, meaning that each element
is a `(vtape,ctape)` 2-tuple formed by concatenating together the
output of :method:`Polynomial.compact`.
"""
if order == 0: # only 0-th order term exists (assumes static pure_state_vec)
coeff = _Polynomial({(): 1.0}, max_polynomial_vars)
#if self._prep_or_effect == "prep":
terms = [_term.RankOnePolynomialPrepTerm.create_from(coeff, self, self,
self._evotype, self.state_space)]
#else:
# terms = [_term.RankOnePolynomialEffectTerm.create_from(coeff, purevec, purevec,
# self._evotype, self.state_space)]
if return_coeff_polys:
coeffs_as_compact_polys = coeff.compact(complex_coeff_tape=True)
return terms, coeffs_as_compact_polys
else:
return terms
else:
if return_coeff_polys:
vtape = _np.empty(0, _np.int64)
ctape = _np.empty(0, complex)
return [], (vtape, ctape)
else:
return []
def taylor_order_terms(self,
order,
max_polynomial_vars=100,
return_coeff_polys=False):
"""
Get the `order`-th order Taylor-expansion terms of this operation.
This function either constructs or returns a cached list of the terms at
the given order. Each term is "rank-1", meaning that its action on a
density matrix `rho` can be written:
`rho -> A rho B`
The coefficients of these terms are typically polynomials of the operation's
parameters, where the polynomial's variable indices index the *global*
parameters of the operation's parent (usually a :class:`Model`), not the
operation's local parameter array (i.e. that returned from `to_vector`).
Parameters
----------
order : int
Which order terms (in a Taylor expansion of this :class:`LindbladOp`)
to retrieve.
max_polynomial_vars : int, optional
maximum number of variables the created polynomials can have.
return_coeff_polys : bool
Whether a parallel list of locally-indexed (using variable indices
corresponding to *this* object's parameters rather than its parent's)
polynomial coefficients should be returned as well.
Returns
-------
terms : list
A list of :class:`RankOneTerm` objects.
coefficients : list
Only present when `return_coeff_polys == True`.
A list of *compact* polynomial objects, meaning that each element
is a `(vtape,ctape)` 2-tuple formed by concatenating together the
output of :method:`Polynomial.compact`.
"""
#Same as unitary op -- assume this op acts as a single unitary term -- consolidate in FUTURE?
if order == 0: # only 0-th order term exists
coeff = _Polynomial({(): 1.0}, max_polynomial_vars)
terms = [
_term.RankOnePolynomialOpTerm.create_from(
coeff, self, self, self._evotype, self.state_space)
]
if return_coeff_polys:
coeffs_as_compact_polys = coeff.compact(
complex_coeff_tape=True)
return terms, coeffs_as_compact_polys
else:
return terms
else:
if return_coeff_polys:
vtape = _np.empty(0, _np.int64)
ctape = _np.empty(0, complex)
return [], (vtape, ctape)
else:
return []
def taylor_order_terms_above_mag(self, order, max_polynomial_vars,
min_term_mag):
"""
Get the `order`-th order Taylor-expansion terms of this operation that have magnitude above `min_term_mag`.
This function constructs the terms at the given order which have a magnitude (given by
the absolute value of their coefficient) that is greater than or equal to `min_term_mag`.
It calls :method:`taylor_order_terms` internally, so that all the terms at order `order`
are typically cached for future calls.
The coefficients of these terms are typically polynomials of the operation's
parameters, where the polynomial's variable indices index the *global*
parameters of the operation's parent (usually a :class:`Model`), not the
operation's local parameter array (i.e. that returned from `to_vector`).
Parameters
----------
order : int
The order of terms to get (and filter).
max_polynomial_vars : int, optional
maximum number of variables the created polynomials can have.
min_term_mag : float
the minimum term magnitude.
Returns
-------
list
A list of :class:`Rank1Term` objects.
"""
mapvec = _np.ascontiguousarray(
_np.zeros(max_polynomial_vars, _np.int64))
for ii, i in enumerate(self.gpindices_as_array()):
mapvec[ii] = i
assert (self.gpindices
is not None), "LindbladOp must be added to a Model before use!"
mpv = max_polynomial_vars
postTerm = _term.RankOnePolynomialOpTerm.create_from(
_Polynomial({(): 1.0}, mpv), None, None, self._evotype,
self.state_space) # identity term
postTerm = postTerm.copy_with_magnitude(1.0)
#Note: for now, *all* of an error generator's terms are considered 0-th order,
# so the below call to taylor_order_terms just gets all of them. In the FUTURE
# we might want to allow a distinction among the error generator terms, in which
# case this term-exponentiation step will need to become more complicated...
errgen_terms = self.errorgen.taylor_order_terms(0, max_polynomial_vars)
#DEBUG CHECK MAGS OF ERRGEN COEFFS
#poly_coeffs = [t.coeff for t in errgen_terms]
#tapes = [poly.compact(complex_coeff_tape=True) for poly in poly_coeffs]
#if len(tapes) > 0:
# vtape = _np.concatenate([t[0] for t in tapes])
# ctape = _np.concatenate([t[1] for t in tapes])
#else:
# vtape = _np.empty(0, _np.int64)
# ctape = _np.empty(0, complex)
#v = self.to_vector()
#errgen_coeffs = _bulk_eval_compact_polynomials_complex(
# vtape, ctape, v, (len(errgen_terms),)) # an array of coeffs
#for coeff, t in zip(errgen_coeffs, errgen_terms):
# coeff2 = t.coeff.evaluate(v)
# if not _np.isclose(coeff,coeff2):
# assert(False), "STOP"
# t.set_magnitude(abs(coeff))
#evaluate errgen_terms' coefficients using their local vector of parameters
# (which happends to be the same as our paramvec in this case)
egvec = self.errorgen.to_vector(
) # we need errorgen's vector (usually not in rep) to perform evaluation
errgen_terms = [
egt.copy_with_magnitude(abs(egt.coeff.evaluate(egvec)))
for egt in errgen_terms
]
terms = []
for term in _term.exponentiate_terms_above_mag(
errgen_terms, order, postTerm, min_term_mag=min_term_mag):
#poly_coeff = term.coeff
#compact_poly_coeff = poly_coeff.compact(complex_coeff_tape=True)
term.mapvec_indices_inplace(mapvec) # local -> global indices
# DEBUG CHECK - to ensure term magnitudes are being set correctly (i.e. are in sync with evaluated coeffs)
# t = term
# vt, ct = t._rep.coeff.compact_complex()
# coeff_array = _bulk_eval_compact_polynomials_complex(vt, ct, self.parent.to_vector(), (1,))
# if not _np.isclose(abs(coeff_array[0]), t._rep.magnitude): # DEBUG!!!
# print(coeff_array[0], "vs.", t._rep.magnitude)
# import bpdb; bpdb.set_trace()
# c1 = _Polynomial.from_rep(t._rep.coeff)
terms.append(term)
return terms
def taylor_order_terms(self,
order,
max_polynomial_vars=100,
return_coeff_polys=False):
"""
Get the `order`-th order Taylor-expansion terms of this operation.
This function either constructs or returns a cached list of the terms at
the given order. Each term is "rank-1", meaning that its action on a
density matrix `rho` can be written:
`rho -> A rho B`
The coefficients of these terms are typically polynomials of the operation's
parameters, where the polynomial's variable indices index the *global*
parameters of the operation's parent (usually a :class:`Model`), not the
operation's local parameter array (i.e. that returned from `to_vector`).
Parameters
----------
order : int
Which order terms (in a Taylor expansion of this :class:`LindbladOp`)
to retrieve.
max_polynomial_vars : int, optional
maximum number of variables the created polynomials can have.
return_coeff_polys : bool
Whether a parallel list of locally-indexed (using variable indices
corresponding to *this* object's parameters rather than its parent's)
polynomial coefficients should be returned as well.
Returns
-------
terms : list
A list of :class:`RankOneTerm` objects.
coefficients : list
Only present when `return_coeff_polys == True`.
A list of *compact* polynomial objects, meaning that each element
is a `(vtape,ctape)` 2-tuple formed by concatenating together the
output of :method:`Polynomial.compact`.
"""
def _compose_poly_indices(terms):
for term in terms:
term.map_indices_inplace(lambda x: tuple(
_modelmember._compose_gpindices(self.gpindices,
_np.array(x, _np.int64))))
return terms
IDENT = None # sentinel for the do-nothing identity op
mpv = max_polynomial_vars
if order == 0:
polydict = {(): 1.0}
for pd in self._get_rate_poly_dicts():
polydict.update({
k: -v
for k, v in pd.items()
}) # subtracts the "rate" `pd` from `polydict`
loc_terms = [
_term.RankOnePolynomialOpTerm.create_from(
_Polynomial(polydict, mpv), IDENT, IDENT, self._evotype,
self.state_space)
]
elif order == 1:
loc_terms = [
_term.RankOnePolynomialOpTerm.create_from(
_Polynomial(pd, mpv), bel, bel, self._evotype,
self.state_space) for i, (pd, bel) in enumerate(
zip(self.rate_poly_dicts, self.basis.elements[1:]))
]
else:
loc_terms = [] # only first order "taylor terms"
poly_coeffs = [t.coeff for t in loc_terms]
tapes = [poly.compact(complex_coeff_tape=True) for poly in poly_coeffs]
if len(tapes) > 0:
vtape = _np.concatenate([t[0] for t in tapes])
ctape = _np.concatenate([t[1] for t in tapes])
else:
vtape = _np.empty(0, _np.int64)
ctape = _np.empty(0, complex)
coeffs_as_compact_polys = (vtape, ctape)
local_term_poly_coeffs = coeffs_as_compact_polys
global_param_terms = _compose_poly_indices(loc_terms)
if return_coeff_polys:
return global_param_terms, local_term_poly_coeffs
else:
return global_param_terms
