def xlogy(x, y):
"""
x*log(y)
If x is 0 and y is not nan, 0 is returned.
*See also:* `mpsci.fun.xlog1py`
"""
if mp.isnan(x) or mp.isnan(y):
return mp.nan
if x == 0:
return mp.zero
else:
return x * mp.log(y)
def xlog1py(x, y):
"""
x*log(1+y)
If x is 0 and y is not nan, 0 is returned.
This function is mathematically equivalent to `mpsci.fun.xlogy(1 + y)`.
It avoids the loss of precision that can result if y is very small.
*See also:* `mpsci.fun.xlogy`
"""
if mp.isnan(x) or mp.isnan(y):
return mp.nan
if x == 0:
return mp.zero
else:
return x * mp.log1p(y)
def _coset_probabilities(self, prob_dist, perm_mat, sample_pauli):
r"""
Return the (approximate) probability and sample Pauli for the left coset :math:`fG` of the stabilizer group
:math:`G` of the planar code with respect to the given sample Pauli :math:`f`,as well as for the cosets
:math:`f\bar{X}G`,:math:`f\bar{Y}G` and :math:`f\bar{Z}G`.
:param prob_dist: Tuple of probability distribution in the format (P(I),P(X),P(Y),P(Z)).
:type prob_dist: 4-tuple of float
:param sample_pauli: Sample planar Pauli.
:type sample_pauli: PlanarPauli
:return: Coset probabilities,Sample Paulis (both in order I,X,Y,Z)
E.g. (0.20,0.10,0.05,0.10),(PlanarPauli(...),PlanarPauli(...),PlanarPauli(...),PlanarPauli(...))
:rtype: 4-tuple of mp.mpf,4-tuple of PlanarPauli
"""
# NOTE: all list/tuples in this method are ordered (i,x,y,z)
# empty log warnings
log_warnings = []
# sample paulis
sample_paulis = (sample_pauli, sample_pauli.copy().logical_x(),
sample_pauli.copy().logical_x().logical_z(),
sample_pauli.copy().logical_z())
# tensor networks: tns are common to both contraction by column and by row (after transposition)
tns = [
self._tnc.create_tn(prob_dist, sp, perm_mat)
for sp in sample_paulis
]
# probabilities
coset_ps = (0.0, 0.0, 0.0, 0.0) # default coset probabilities
coset_ps_col = coset_ps_row = None # undefined coset probabilities by column and row
# N.B. After multiplication by mult,coset_ps will be of type mp.mpf so don't process with numpy!
if self._mode in ('c', 'a'):
# evaluate coset probabilities by column
coset_ps_col = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
for i in range(len(tns)):
try:
coset_ps_col[i] = tt.mps2d.contract(tns[i],
chi=self._chi,
tol=self._tol)
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY COL FOR {} COSET FAILED: {!r}'.format(
'IXYZ'[i], ex))
# treat nan as inf so it doesn't get lost
coset_ps_col = [
mp.inf if mp.isnan(coset_p) else coset_p
for coset_p in coset_ps_col
]
if self._mode in ('r', 'a'):
# evaluate coset probabilities by row
coset_ps_row = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
# transpose tensor networks
tns = [tt.mps2d.transpose(tn) for tn in tns]
for i in range(len(tns)):
try:
coset_ps_row[i] = tt.mps2d.contract(tns[i],
chi=self._chi,
tol=self._tol)
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY ROW FOR {} COSET FAILED: {!r}'.format(
'IXYZ'[i], ex))
# treat nan as inf so it doesn't get lost
coset_ps_row = [
mp.inf if mp.isnan(coset_p) else coset_p
for coset_p in coset_ps_row
]
if self._mode == 'c':
coset_ps = coset_ps_col
elif self._mode == 'r':
coset_ps = coset_ps_row
elif self._mode == 'a':
# average coset probabilities
coset_ps = [
sum(coset_p) / len(coset_p)
for coset_p in zip(coset_ps_col, coset_ps_row)
]
# renormalize probabilities
C = coset_ps[0] + coset_ps[1] + coset_ps[2] + coset_ps[3]
coset_ps[0] = coset_ps[0] / C
coset_ps[1] = coset_ps[1] / C
coset_ps[2] = coset_ps[2] / C
coset_ps[3] = coset_ps[3] / C
# logging
if log_warnings:
log_data = {
# instance
'decoder':
repr(self),
# method parameters
'prob_dist':
prob_dist,
'sample_pauli':
pt.pack(sample_pauli.to_bsf()),
# variables (convert to string because mp.mpf)
'coset_ps_col':
[repr(p) for p in coset_ps_col] if coset_ps_col else None,
'coset_ps_row':
[repr(p) for p in coset_ps_row] if coset_ps_row else None,
'coset_ps': [repr(p) for p in coset_ps],
}
logger.warning('{}: {}'.format(
' | '.join(log_warnings), json.dumps(log_data,
sort_keys=True)))
# results
return tuple(coset_ps), sample_paulis
def _coset_probabilities(self, prob_dist, hadamard_vec,hadamard_mat, sample_pauli):
r"""
Return the (approximate) probability and sample Pauli for the left coset :math:`fG` of the stabilizer group
:math:`G` of the planar code with respect to the given sample Pauli :math:`f`, as well as for the cosets
:math:`f\bar{X}G`, :math:`f\bar{Y}G` and :math:`f\bar{Z}G`.
:param prob_dist: Tuple of probability distribution in the format (P(I), P(X), P(Y), P(Z)).
:type prob_dist: 4-tuple of float
:param sample_pauli: Sample planar Pauli.
:type sample_pauli: PlanarPauli
:return: Coset probabilities, Sample Paulis (both in order I, X, Y, Z)
E.g. (0.20, 0.10, 0.05, 0.10), (PlanarPauli(...), PlanarPauli(...), PlanarPauli(...), PlanarPauli(...))
:rtype: 4-tuple of mp.mpf, 4-tuple of PlanarPauli
"""
# NOTE: all list/tuples in this method are ordered (i, x, y, z)
# empty log warnings
log_warnings = []
# sample paulis
sample_paulis = (
sample_pauli,
sample_pauli.copy().logical_x(),
sample_pauli.copy().logical_x().logical_z(),
sample_pauli.copy().logical_z()
)
# tensor networks: tns are common to both contraction by column and by row (after transposition)
tns = [self._tnc.create_tn(prob_dist, sp) for sp in sample_paulis]
tns= [self._tnc.modify_tn(tn, had_prob_dist, hadamard_mat,sample_pauli)
# probabilities
coset_ps = (0.0, 0.0, 0.0, 0.0) # default coset probabilities
coset_ps_col = coset_ps_row = None # undefined coset probabilities by column and row
# N.B. After multiplication by mult, coset_ps will be of type mp.mpf so don't process with numpy!
if self._mode in ('c', 'a'):
# evaluate coset probabilities by column
coset_ps_col = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
for i in range(len(tns)):
try:
coset_ps_col[i] = tt.mps2d.contract(tns[i], chi=self._chi, tol=self._tol)
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append('CONTRACTION BY COL FOR {} COSET FAILED: {!r}'.format('IXYZ'[i], ex))
# treat nan as inf so it doesn't get lost
coset_ps_col = [mp.inf if mp.isnan(coset_p) else coset_p for coset_p in coset_ps_col]
if self._mode in ('r', 'a'):
# evaluate coset probabilities by row
coset_ps_row = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
# transpose tensor networks
tns = [tt.mps2d.transpose(tn) for tn in tns]
for i in range(len(tns)):
try:
coset_ps_row[i] = tt.mps2d.contract(tns[i], chi=self._chi, tol=self._tol)
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append('CONTRACTION BY ROW FOR {} COSET FAILED: {!r}'.format('IXYZ'[i], ex))
# treat nan as inf so it doesn't get lost
coset_ps_row = [mp.inf if mp.isnan(coset_p) else coset_p for coset_p in coset_ps_row]
if self._mode == 'c':
coset_ps = coset_ps_col
elif self._mode == 'r':
coset_ps = coset_ps_row
elif self._mode == 'a':
# average coset probabilities
coset_ps = [sum(coset_p) / len(coset_p) for coset_p in zip(coset_ps_col, coset_ps_row)]
# logging
if log_warnings:
log_data = {
# instance
'decoder': repr(self),
# method parameters
'prob_dist': prob_dist,
'sample_pauli': pt.pack(sample_pauli.to_bsf()),
# variables (convert to string because mp.mpf)
'coset_ps_col': [repr(p) for p in coset_ps_col] if coset_ps_col else None,
'coset_ps_row': [repr(p) for p in coset_ps_row] if coset_ps_row else None,
'coset_ps': [repr(p) for p in coset_ps],
}
logger.warning('{}: {}'.format(' | '.join(log_warnings), json.dumps(log_data, sort_keys=True)))
# results
return tuple(coset_ps), sample_paulis
def decode(self, code, hadamard_vec,hadamard_mat, syndrome,
error_model=DepolarizingErrorModel(), # noqa: B008
error_probability=0.1, **kwargs):
"""
See :meth:`qecsim.model.Decoder.decode`
Note: The optional keyword parameters ``error_model`` and ``error_probability`` are used to determine the prior
probability distribution for use in the decoding algorithm. Any provided error model must implement
:meth:`~qecsim.model.ErrorModel.probability_distribution`.
:param code: Rotated planar code.
:type code: RotatedPlanarCode
:param syndrome: Syndrome as binary vector.
:type syndrome: numpy.array (1d)
:param error_model: Error model. (default=DepolarizingErrorModel())
:type error_model: ErrorModel
:param error_probability: Overall probability of an error on a single qubit. (default=0.1)
:type error_probability: float
:return: Recovery operation as binary symplectic vector.
:rtype: numpy.array (1d)
"""
# any recovery
any_recovery = self.sample_recovery(code, syndrome)
# probability distribution
prob_dist = error_model.probability_distribution(error_probability)
# coset probabilities, recovery operations
coset_ps, recoveries = self._coset_probabilities(prob_dist, hadamard_vec,hadamard_mat, any_recovery)
# most likely recovery operation
max_coset_p, max_recovery = max(zip(coset_ps, recoveries), key=lambda coset_p_recovery: coset_p_recovery[0])
# logging
if not (mp.isfinite(max_coset_p) and max_coset_p > 0):
log_data = {
# instance
'decoder': repr(self),
# method parameters
'code': repr(code),
'syndrome': pt.pack(syndrome),
'error_model': repr(error_model),
'error_probability': error_probability,
# variables
'prob_dist': prob_dist,
'coset_ps': [repr(p) for p in coset_ps], # convert to string because mp.mpf
# context
'error': pt.pack(kwargs['error']) if 'error' in kwargs else None,
}
logger.warning('NON-POSITIVE-FINITE MAX COSET PROBABILITY: {}'.format(json.dumps(log_data, sort_keys=True)))
# return most likely recovery operation as bsf
return max_recovery.to_bsf()
@property
def label(self):
"""See :meth:`qecsim.model.Decoder.label`"""
params = [('chi', self._chi), ('mode', self._mode), ('tol', self._tol), ]
return 'Rotated planar MPS ({})'.format(', '.join('{}={}'.format(k, v) for k, v in params if v))
def __repr__(self):
return '{}({!r}, {!r}, {!r})'.format(type(self).__name__, self._chi, self._mode, self._tol)
class TNC:
"""Tensor network creator"""
@functools.lru_cache()
def h_node_value(self, prob_dist, f, n, e, s, w):
"""Return horizontal edge tensor element value."""
paulis = ('I', 'X', 'Y', 'Z')
op_to_pr = dict(zip(paulis, prob_dist))
f = pt.pauli_to_bsf(f)
I, X, Y, Z = pt.pauli_to_bsf(paulis)
# n, e, s, w are in {0, 1} so multiply op to turn on or off
op = (f + (n * Z) + (e * X) + (s * Z) + (w * X)) % 2
return op_to_pr[pt.bsf_to_pauli(op)]
@functools.lru_cache()
def v_node_value(self, prob_dist, f, n, e, s, w):
"""Return vertical edge tensor element value."""
# N.B. for v_node order of nesw is rotated relative to h_node
return self.h_node_value(prob_dist, f, e, s, w, n)
@functools.lru_cache()
def create_h_node(self, prob_dist, f, compass_direction=None):
"""Return horizontal qubit tensor, i.e. has X plaquettes to left/right and Z plaquettes above/below."""
def _shape(compass_direction=None):
"""Return shape of tensor including dummy indices."""
return { # (ne, se, sw, nw)
'n': (2, 2, 2, 1),
'ne': (1, 2, 2, 1),
'e': (1, 2, 2, 2),
'se': (1, 1, 2, 2),
's': (2, 1, 2, 2),
'sw': (2, 1, 1, 2),
'w': (2, 2, 1, 2),
'nw': (2, 2, 1, 1),
}.get(compass_direction, (2, 2, 2, 2))
# create bare h_node
node = np.empty(_shape(compass_direction), dtype=np.float64)
# fill values
for n, e, s, w in np.ndindex(node.shape):
node[(n, e, s, w)] = self.h_node_value(prob_dist, f, n, e, s, w)
return node
@functools.lru_cache()
def create_v_node(self, prob_dist, f, compass_direction=None):
"""Return vertical qubit tensor, i.e. has Z plaquettes to left/right and X plaquettes above/below."""
def _shape(compass_direction=None):
"""Return shape of tensor including dummy indices."""
return { # (ne, se, sw, nw)
'n': (1, 2, 2, 2),
'ne': (1, 1, 2, 2),
'e': (2, 1, 2, 2),
'se': (2, 1, 1, 2),
's': (2, 2, 1, 2),
# 'sw': (2, 2, 1, 1), # cannot happen
'w': (2, 2, 2, 1),
'nw': (1, 2, 2, 1),
}.get(compass_direction, (2, 2, 2, 2))
# create bare v_node
node = np.empty(_shape(compass_direction), dtype=np.float64)
# fill values
for n, e, s, w in np.ndindex(node.shape):
node[(n, e, s, w)] = self.v_node_value(prob_dist, f, n, e, s, w)
return node
@functools.lru_cache()
def create_s_node(self, compass_direction=None):
"""Return stabilizer tensor."""
def _shape(compass_direction=None):
"""Return shape of tensor including dummy indices."""
return { # (ne, se, sw, nw)
'n': (1, 2, 2, 1),
'e': (1, 1, 2, 2),
's': (2, 1, 1, 2),
'w': (2, 2, 1, 1),
}.get(compass_direction, (2, 2, 2, 2))
node = tt.tsr.delta(_shape(compass_direction))
return node
def create_tn(self, prob_dist, sample_pauli):
"""Return a network (numpy.array 2d) of tensors (numpy.array 4d).
Note: The network contracts to the coset probability of the given sample_pauli.
"""
def _rotate_q_index(index, code):
"""Convert code site index in format (x, y) to tensor network q-node index in format (r, c)"""
site_x, site_y = index # qubit index in (x, y)
site_r, site_c = code.site_bounds[1] - site_y, site_x # qubit index in (r, c)
return code.site_bounds[0] - site_c + site_r, site_r + site_c # q-node index in (r, c)
def _rotate_p_index(index, code):
"""Convert code plaquette index in format (x, y) to tensor network s-node index in format (r, c)"""
q_node_r, q_node_c = _rotate_q_index(index, code) # q-node index in (r, c)
return q_node_r - 1, q_node_c # s-node index in (r, c)
def _compass_q_direction(index, code):
"""if the code site index lies on border of lattice then give that direction, else empty string."""
direction = {code.site_bounds[1]: 'n', 0: 's'}.get(index[1], '')
direction += {0: 'w', code.site_bounds[0]: 'e'}.get(index[0], '')
return direction
def _compass_p_direction(index, code):
"""if the code plaquette index lies on border of lattice then give that direction, else empty string."""
direction = {code.site_bounds[1]: 'n', -1: 's'}.get(index[1], '')
direction += {-1: 'w', code.site_bounds[0]: 'e'}.get(index[0], '')
return direction
pi,px,py,pz=prob_dist
had_prob_dist= pi,pz,py,px
# extract code
code = sample_pauli.code
# initialise empty tn
tn_max_r, _ = _rotate_q_index((0, 0), code)
_, tn_max_c = _rotate_q_index((code.site_bounds[0], 0), code)
tn = np.empty((tn_max_r + 1, tn_max_c + 1), dtype=object)
# iterate over
max_site_x, max_site_y = code.site_bounds
for code_index in itertools.product(range(-1, max_site_x + 1), range(-1, max_site_y + 1)):
is_z_plaquette = code.is_z_plaquette(code_index)
if code.is_in_site_bounds(code_index):
q_node_index = _rotate_q_index(code_index, code)
q_pauli = sample_pauli.operator(code_index)
if is_z_plaquette:
#print(code_index)
q_node = self.create_h_node(prob_dist, q_pauli, _compass_q_direction(code_index, code))
else:
q_node = self.create_v_node(prob_dist, q_pauli, _compass_q_direction(code_index, code))
tn[q_node_index] = q_node
if code.is_in_plaquette_bounds(code_index):
s_node_index = _rotate_p_index(code_index, code)
s_node = self.create_s_node(_compass_p_direction(code_index, code))
tn[s_node_index] = s_node
return tn
def modify_tn(tn, had_prob_dist, hadamard_mat,sample_pauli):
"""Return a network (numpy.array 2d) of tensors (numpy.array 4d).
Note: The network contracts to the coset probability of the given sample_pauli.
"""
def _rotate_q_index(index, code):
"""Convert code site index in format (x, y) to tensor network q-node index in format (r, c)"""
site_x, site_y = index # qubit index in (x, y)
site_r, site_c = code.site_bounds[1] - site_y, site_x # qubit index in (r, c)
return code.site_bounds[0] - site_c + site_r, site_r + site_c # q-node index in (r, c)
def _compass_q_direction(index, code):
"""if the code site index lies on border of lattice then give that direction, else empty string."""
direction = {code.site_bounds[1]: 'n', 0: 's'}.get(index[1], '')
direction += {0: 'w', code.site_bounds[0]: 'e'}.get(index[0], '')
return direction
code = sample_pauli.code
max_site_x, max_site_y = code.site_bounds
for code_index in itertools.product(range(-1, max_site_x + 1), range(-1, max_site_y + 1)):
is_z_plaquette = code.is_z_plaquette(code_index)
if code.is_in_site_bounds(code_index):
q_node_index = _rotate_q_index(code_index, code)
q_pauli = sample_pauli.operator(code_index)
if is_z_plaquette:
#print(code_index)
if hadamard_mat[code_index]:
q_node = self.create_h_node(had_prob_dist, q_pauli, _compass_q_direction(code_index, code))
else:
if hadamard_mat[code_index]:
q_node = self.create_v_node(had_prob_dist, q_pauli, _compass_q_direction(code_index, code))
tn[q_node_index] = q_node
return tn
def _coset_probabilities(self, prob_dist, sample_pauli):
r"""
Return the (approximate) probability and sample Pauli for the left coset :math:`fG` of the stabilizer group
:math:`G` of the planar code with respect to the given sample Pauli :math:`f`, as well as for the cosets
:math:`f\bar{X}G`, :math:`f\bar{Y}G` and :math:`f\bar{Z}G`.
:param prob_dist: Tuple of probability distribution in the format (P(I), P(X), P(Y), P(Z)).
:type prob_dist: 4-tuple of float
:param sample_pauli: Sample color 666 Pauli.
:type sample_pauli: Color666Pauli
:return: Coset probabilities, Sample Paulis (both in order I, X, Y, Z)
E.g. (0.20, 0.10, 0.05, 0.10), (Color666Pauli(...), Color666Pauli(...), Color666Pauli(...), Color666Pauli(...))
:rtype: 4-tuple of mp.mpf, 4-tuple of Color666Pauli
"""
# NOTE: all list/tuples in this method are ordered (i, x, y, z)
# empty log warnings
log_warnings = []
# sample_paulis
sample_paulis = [
sample_pauli,
sample_pauli.copy().logical_x(),
sample_pauli.copy().logical_x().logical_z(),
sample_pauli.copy().logical_z()
]
# tensor networks
tns = [
self._tnc.create_tn(prob_dist, pauli) for pauli in sample_paulis
]
# probabilities
coset_ps = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
# N.B. After multiplication by mult, coset_ps will be of type mp.mpf so don't process with numpy!
try:
# note: cosets differ only in the first column
ket_i, mult = tt.mps2d.contract(tns[0],
chi=self._chi,
tol=self._tol,
start=-1,
stop=0,
step=-1) # tns.i
coset_ps[0] = tt.mps.inner_product(tns[0][:, 0],
ket_i) * mult # coset_ps.i
coset_ps[1] = tt.mps.inner_product(tns[1][:, 0],
ket_i) * mult # coset_ps.x
coset_ps[2] = tt.mps.inner_product(tns[2][:, 0],
ket_i) * mult # coset_ps.y
coset_ps[3] = tt.mps.inner_product(tns[3][:, 0],
ket_i) * mult # coset_ps.z
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION FOR I COSET FAILED: {!r}'.format(ex))
# treat nan as inf so it doesn't get lost
coset_ps = [
mp.inf if mp.isnan(coset_p) else coset_p for coset_p in coset_ps
]
# logging
if log_warnings:
log_data = {
# instance
'decoder': repr(self),
# method parameters
'prob_dist': prob_dist,
'sample_pauli': pt.pack(sample_pauli.to_bsf()),
# variables (convert to string because mp.mpf)
'coset_ps': [repr(p) for p in coset_ps],
}
logger.warning('{}: {}'.format(
' | '.join(log_warnings), json.dumps(log_data,
sort_keys=True)))
# results
return tuple(coset_ps), tuple(sample_paulis)
def _coset_probabilities(self, prob_dist, sample_pauli, perm_mat):
r"""
Return the (approximate) probability and sample Pauli for the left coset :math:`fG` of the stabilizer group
:math:`G` of the planar code with respect to the given sample Pauli :math:`f`, as well as for the cosets
:math:`f\bar{X}G`, :math:`f\bar{Y}G` and :math:`f\bar{Z}G`.
:param prob_dist: Tuple of probability distribution in the format (P(I), P(X), P(Y), P(Z)).
:type prob_dist: 4-tuple of float
:param sample_pauli: Sample planar Pauli.
:type sample_pauli: PlanarPauli
:return: Coset probabilities, Sample Paulis (both in order I, X, Y, Z)
E.g. (0.20, 0.10, 0.05, 0.10), (PlanarPauli(...), PlanarPauli(...), PlanarPauli(...), PlanarPauli(...))
:rtype: 4-tuple of mp.mpf, 4-tuple of PlanarPauli
"""
# NOTE: all list/tuples in this method are ordered (i, x, y, z)
# empty log warnings
log_warnings = []
# sample_paulis
sample_paulis = [
sample_pauli,
sample_pauli.copy().logical_x(),
sample_pauli.copy().logical_x().logical_z(),
sample_pauli.copy().logical_z()
]
# tensor networks
tns = [
self._tnc.create_tn(prob_dist, pauli, perm_mat)
for pauli in sample_paulis
]
mask = self._tnc.create_mask(self._stp,
tns[0].shape) # same mask for all tns
# probabilities
coset_ps = (0.0, 0.0, 0.0, 0.0) # default coset probabilities
coset_ps_col = coset_ps_row = None # undefined coset probabilities by column and row
# N.B. After multiplication by mult, coset_ps will be of type mp.mpf so don't process with numpy!
if self._mode in ('c', 'a'):
# evaluate coset probabilities by column
coset_ps_col = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
# note: I,X and Z,Y cosets differ only in the last column (logical X)
try:
bra_i, mult = tt.mps2d.contract(tns[0],
chi=self._chi,
tol=self._tol,
stop=-1,
mask=mask) # tns.i
coset_ps_col[0] = tt.mps.inner_product(
bra_i, tns[0][:, -1]) * mult # coset_ps_col.i
coset_ps_col[1] = tt.mps.inner_product(
bra_i, tns[1][:, -1]) * mult # coset_ps_col.x
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY COL FOR I COSET FAILED: {!r}'.format(ex))
try:
bra_z, mult = tt.mps2d.contract(tns[3],
chi=self._chi,
tol=self._tol,
stop=-1,
mask=mask) # tns.z
coset_ps_col[2] = tt.mps.inner_product(
bra_z, tns[2][:, -1]) * mult # coset_ps_col.y
coset_ps_col[3] = tt.mps.inner_product(
bra_z, tns[3][:, -1]) * mult # coset_ps_col.z
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY COL FOR Z COSET FAILED: {!r}'.format(ex))
# treat nan as inf so it doesn't get lost
coset_ps_col = [
mp.inf if mp.isnan(coset_p) else coset_p
for coset_p in coset_ps_col
]
if self._mode in ('r', 'a'):
# evaluate coset probabilities by row
coset_ps_row = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
# transpose tensor networks
tns = [tt.mps2d.transpose(tn) for tn in tns]
mask = None if mask is None else mask.transpose()
# note: I,Z and X,Y cosets differ only in the last row (logical Z)
try:
bra_i, mult = tt.mps2d.contract(tns[0],
chi=self._chi,
tol=self._tol,
stop=-1,
mask=mask) # tns.i
coset_ps_row[0] = tt.mps.inner_product(
bra_i, tns[0][:, -1]) * mult # coset_ps_row.i
coset_ps_row[3] = tt.mps.inner_product(
bra_i, tns[3][:, -1]) * mult # coset_ps_row.z
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY ROW FOR I COSET FAILED: {!r}'.format(ex))
try:
bra_x, mult = tt.mps2d.contract(tns[1],
chi=self._chi,
tol=self._tol,
stop=-1,
mask=mask) # tns.x
coset_ps_row[1] = tt.mps.inner_product(
bra_x, tns[1][:, -1]) * mult # coset_ps_row.x
coset_ps_row[2] = tt.mps.inner_product(
bra_x, tns[2][:, -1]) * mult # coset_ps_row.y
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY ROW FOR X COSET FAILED: {!r}'.format(ex))
# treat nan as inf so it doesn't get lost
coset_ps_row = [
mp.inf if mp.isnan(coset_p) else coset_p
for coset_p in coset_ps_row
]
if self._mode == 'c':
coset_ps = coset_ps_col
elif self._mode == 'r':
coset_ps = coset_ps_row
elif self._mode == 'a':
# average coset probabilities
coset_ps = [
sum(coset_p) / len(coset_p)
for coset_p in zip(coset_ps_col, coset_ps_row)
]
# logging
if log_warnings:
log_data = {
# instance
'decoder':
repr(self),
# method parameters
'prob_dist':
prob_dist,
'sample_pauli':
pt.pack(sample_pauli.to_bsf()),
# variables (convert to string because mp.mpf)
'coset_ps_col':
[repr(p) for p in coset_ps_col] if coset_ps_col else None,
'coset_ps_row':
[repr(p) for p in coset_ps_row] if coset_ps_row else None,
'coset_ps': [repr(p) for p in coset_ps],
}
logger.warning('{}: {}'.format(
' | '.join(log_warnings), json.dumps(log_data,
sort_keys=True)))
# results
return tuple(coset_ps), tuple(sample_paulis)
def _coset_probabilities(self, prob_dist, sample_pauli):
r"""
Return the (approximate) probability and sample Pauli for the left coset :math:`fG` of the stabilizer group
:math:`G` of the planar code with respect to the given sample Pauli :math:`f`, as well as for the cosets
:math:`f\bar{X}G`, :math:`f\bar{Y}G` and :math:`f\bar{Z}G`.
:param prob_dist: Tuple of probability distribution in the format (P(I), P(X), P(Y), P(Z)).
:type prob_dist: 4-tuple of float
:param sample_pauli: Sample planar Pauli.
:type sample_pauli: PlanarPauli
:return: Coset probabilities, Sample Paulis (both in order I, X, Y, Z)
E.g. (0.20, 0.10, 0.05, 0.10), (PlanarPauli(...), PlanarPauli(...), PlanarPauli(...), PlanarPauli(...))
:rtype: 4-tuple of mp.mpf, 4-tuple of PlanarPauli
"""
# NOTE: OPTIMIZED CONTRACTION BY COLUMN
#
# * Partial contraction of coset-I tensor network by _column_
#
# pauli create contract contract
# rotated TN 0-1 as bra_i 5-4 as ket_i
# (left_stop=2) (right_stop=3)
#
# 0123456 012345 012345 012345
# 0. . . . 0 . 0 . 0 .
# 1 . . . 1 ... 1 *.. 1 *..
# 2. . . . --> 2..... --> 2 *... --> 2 *..*
# 3 . . . 3 ..... 3 *.... 3 *..*
# 4. . . . 4 ... 4 ... 4 ..*
# 5 . 5 . 5 .
#
# * Optimized contraction of coset-Z tensor network (for example) by _column_
# using partial contraction of coset-I tensor network
#
# pauli with create combine and contract
# logical rotated TN (bra_i + 2-3 + ket_i)
#
# 0123456 012345 012345
# 0z . . . 0 z 0 z
# 1 z . . 1 .z. 1 *z.
# 2. z . . --> 2..z.. --> 2 *z.* --> \pi
# 3 . z . 3 .z... 3 *z.*
# 4. . z z 4 z.. 4 z.*
# 5 z 5 z
#
# NOTE: OPTIMIZED CONTRACTION BY ROW
#
# * Partial contraction of coset-I tensor network by _row_
#
# pauli create transpose contract contract
# rotated TN 0-1 as bra_i 5-4 as ket_i
# (left_stop=2) (right_stop=3)
#
# 0123456 012345 012345 012345 012345
# 0. . . . 0 . 0 . 0 . 0 .
# 1 . . . 1 ... 1 ... 1 *.. 1 *..
# 2. . . . --> 2..... --> 2..... --> 2 *... --> 2 *..*
# 3 . . . 3 ..... 3 ..... 3 *.... 3 *..*
# 4. . . . 4 ... 4 ... 4 ... 4 ..*
# 5 . 5 . 5 . 5 .
#
# * Optimized contraction of coset-Z tensor network (for example) by _row_
# using partial contraction of coset-I tensor network
#
# pauli with create transpose combine and contract
# logical rotated TN (bra_i + 2-3 + ket_i)
#
# 0123456 012345 012345 012345
# 0. . z z 0 . 0 z 0 z
# 1 . z . 1 ... 1 .z. 1 *z.
# 2. z . . --> 2zzzzz --> 2..z.. --> 2 *z.* --> \pi
# 3 z . . 3 ....z 3 .z... 3 *z.*
# 4z . . . 4 ... 4 z.. 4 z.*
# 5 . 5 z 5 z
#
# NOTE: logicals along major diagonal for various shape codes
#
# logical I logical X logical Y logical Z
#
# 01234 01234 01234 01234
# 0. . . 0x . . 0y . . 0z . .
# 1 . . 1 x . 1 y . 1 z .
# 2. . . 2. x . 2. y . 2. z .
# 3 . . 3 . x 3 . y 3 . z
# 4. . . 4. . x 4. . y 4. . z
#
# 0123456 0123456 0123456 0123456
# 0. . . . 0x . . . 0y . . . 0z . . .
# 1 . . . 1 x . . 1 y . . 1 z . .
# 2. . . . 2. x . . 2. y . . 2. z . .
# 3 . . . 3 . x . 3 . y . 3 . z .
# 4. . . . 4. . x . 4. . y z 4. . z z
#
# 01234 01234 01234 01234
# 0. . . 0x . . 0y . . 0z . .
# 1 . . 1 x . 1 y . 1 z .
# 2. . . 2. x . 2. y . 2. z .
# 3 . . 3 . x 3 . y 3 . z
# 4. . . 4. . x 4. . y 4. . z
# 5 . . 5 . . 5 . . 5 . .
# 6. . . 6. . x 6. . x 4. . .
#
def _logical_x(pauli, major=True):
"""return pauli after applying X along the major/minor diagonal"""
max_row, max_col = pauli.code.bounds
# define site indices
site_indices = itertools.chain(
zip(range(max_row + 1),
range(max_col + 1)), # along major diagonal
((r, max_col) for r in range(max_col + 2, max_row +
1, 2)), # down rightmost column
)
# if not major, switch to minor diagonal
if not major:
site_indices = ((max_row - r, c) for r, c in site_indices)
# apply X on sites
return pauli.site('X', *site_indices)
def _logical_z(pauli, major=True):
"""return pauli after applying Z along the major/minor diagonal"""
max_row, max_col = pauli.code.bounds
# define site indices
site_indices = itertools.chain(
zip(range(max_row + 1),
range(max_col + 1)), # along major diagonal
((max_row, c) for c in range(max_row + 2, max_col +
1, 2)), # across bottom row
)
# if not major, switch to minor diagonal
if not major:
site_indices = ((max_row - r, c) for r, c in site_indices)
# apply X on sites
return pauli.site('Z', *site_indices)
def _tn_contract_optimized(code, coset_ps, tns, mask):
"""update coset_ps with optimized contraction of tns"""
# left_stop
left_stop = min(code.size) - 1
# note: for optimization we contract tn_i from left to left_stop as bra common to all cosets
bra_i, bra_i_mult = tt.mps2d.contract(tns[0],
chi=self._chi,
tol=self._tol,
mask=mask,
stop=left_stop)
# right_stop
right_stop = tns[0].shape[1] - min(code.size)
# note: for optimization we contract tn_i from right to right_stop as ket common to all cosets
ket_i, ket_i_mult = tt.mps2d.contract(tns[0],
chi=self._chi,
tol=self._tol,
mask=mask,
start=-1,
stop=right_stop,
step=-1)
# for each tn, combine and contract to coset probability
for j in range(len(tns)):
# combine bra_i, tn_j[:, left_stop:right_stop + 1], ket_i as partially contracted tn
partial_tn = np.column_stack(
(bra_i, tns[j][:, left_stop:right_stop + 1], ket_i))
# slice mask to match partially contracted tn
partial_mask = None if mask is None else mask[:, left_stop -
1:right_stop + 2]
# contract
result = tt.mps2d.contract(partial_tn,
chi=self._chi,
tol=self._tol,
mask=partial_mask,
step=-1)
# multiply by multipliers
coset_ps[j] = result * bra_i_mult * ket_i_mult
# NOTE: all list/tuples in this method are ordered (i, x, y, z)
# empty log warnings
log_warnings = []
# tensor networks: tn_i is common to both contraction by column and by row (after transposition)
tn_i = self._tnc.create_tn(prob_dist, sample_pauli)
mask = self._tnc.create_mask(self._stp,
tn_i.shape) # same mask for all tns
# probabilities
coset_ps = (0.0, 0.0, 0.0, 0.0) # default coset probabilities
coset_ps_col = coset_ps_row = None # undefined coset probabilities by column and row
# N.B. After multiplication by mult, coset_ps will be of type mp.mpf so don't process with numpy!
if self._mode in ('c', 'a'):
# note: for optimization we choose cosets to differ only on the major diagonal
sample_x = _logical_x(sample_pauli.copy())
tns = [
tn_i,
self._tnc.create_tn(prob_dist, sample_x),
self._tnc.create_tn(prob_dist, _logical_z(sample_x.copy())),
self._tnc.create_tn(prob_dist, _logical_z(sample_pauli.copy()))
]
# evaluate coset probabilities by column
coset_ps_col = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
try:
_tn_contract_optimized(sample_pauli.code, coset_ps_col, tns,
mask)
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY COL FAILED: {!r}'.format(ex))
# treat nan as inf so it doesn't get lost
coset_ps_col = [
mp.inf if mp.isnan(coset_p) else coset_p
for coset_p in coset_ps_col
]
if self._mode in ('r', 'a'):
# note: for optimization we choose cosets to differ only on the minor diagonal
sample_x = _logical_x(sample_pauli.copy(), major=False)
tns = [
tn_i,
self._tnc.create_tn(prob_dist, sample_x),
self._tnc.create_tn(prob_dist,
_logical_z(sample_x.copy(), major=False)),
self._tnc.create_tn(
prob_dist, _logical_z(sample_pauli.copy(), major=False))
]
# evaluate coset probabilities by row
coset_ps_row = [0.0, 0.0, 0.0, 0.0] # default coset probabilities
# transpose tensor networks
tns = [tt.mps2d.transpose(tn) for tn in tns]
mask = None if mask is None else mask.transpose()
try:
_tn_contract_optimized(sample_pauli.code, coset_ps_row, tns,
mask)
except (ValueError, np.linalg.LinAlgError) as ex:
log_warnings.append(
'CONTRACTION BY ROW FAILED: {!r}'.format(ex))
# treat nan as inf so it doesn't get lost
coset_ps_row = [
mp.inf if mp.isnan(coset_p) else coset_p
for coset_p in coset_ps_row
]
if self._mode == 'c':
coset_ps = coset_ps_col
elif self._mode == 'r':
coset_ps = coset_ps_row
elif self._mode == 'a':
# average coset probabilities
coset_ps = [
sum(coset_p) / len(coset_p)
for coset_p in zip(coset_ps_col, coset_ps_row)
]
# logging
if log_warnings:
log_data = {
# instance
'decoder':
repr(self),
# method parameters
'prob_dist':
prob_dist,
'sample_pauli':
pt.pack(sample_pauli.to_bsf()),
# variables (convert to string because mp.mpf)
'coset_ps_col':
[repr(p) for p in coset_ps_col] if coset_ps_col else None,
'coset_ps_row':
[repr(p) for p in coset_ps_row] if coset_ps_row else None,
'coset_ps': [repr(p) for p in coset_ps],
}
logger.warning('{}: {}'.format(
' | '.join(log_warnings), json.dumps(log_data,
sort_keys=True)))
# results
sample_paulis = (sample_pauli, sample_pauli.copy().logical_x(),
sample_pauli.copy().logical_x().logical_z(),
sample_pauli.copy().logical_z())
return tuple(coset_ps), sample_paulis
