def decode(
self,
code,
perm_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, perm_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(), coset_ps, max_coset_p
def test_planar_mps_decoder_positive_max_coset_probability(mode):
# parameters
code = PlanarCode(9, 9)
decoder = PlanarMPSDecoder(chi=48, mode=mode)
error_model = BiasedDepolarizingErrorModel(bias=100)
error_probability = 0.41
# logged run values
error = pt.unpack([
"c96aa012210dc2254031f15d9ce80c871fb864b510c91086e112a018f8aece7406638fdc00",
290
])
syndrome = pt.unpack(["8f59cd273bd1c027b3b925085af85f2aaf22", 144])
assert np.array_equal(syndrome, pt.bsp(error, code.stabilizers.T))
# debug
# print(code.ascii_art(syndrome, code.new_pauli(error)))
# decode
prob_dist = error_model.probability_distribution(error_probability)
any_recovery = decoder.sample_recovery(code, syndrome)
# coset probabilities
coset_ps, recoveries = decoder._coset_probabilities(
prob_dist, any_recovery)
print('mode={}, coset_ps={}'.format(mode, coset_ps))
max_coset_p, max_recovery = max(
zip(coset_ps, recoveries),
key=lambda coset_p_recovery: coset_p_recovery[0])
success = np.all(
pt.bsp(max_recovery.to_bsf() ^ error, code.logicals.T) == 0)
print('### success=', success)
assert mp.isfinite(
max_coset_p
) and max_coset_p > 0, 'Max coset probability not as expected'
def test_planar_mps_decoder_small_code_negative_coset_probability(chi, mode):
# parameters
code = PlanarCode(3, 3)
decoder = PlanarMPSDecoder(chi=chi, mode=mode)
error_model = DepolarizingErrorModel()
error_probability = 0.1
# logged run values
error = pt.unpack(["e0048000", 26])
syndrome = pt.bsp(error, code.stabilizers.T)
# debug
print()
print(code.ascii_art(syndrome, code.new_pauli(error)))
# decode
prob_dist = error_model.probability_distribution(error_probability)
any_recovery = decoder.sample_recovery(code, syndrome)
# coset probabilities
coset_ps, recoveries = decoder._coset_probabilities(
prob_dist, any_recovery)
print('chi={}, mode={}, coset_ps={}'.format(chi, mode, coset_ps))
max_coset_p, max_recovery = max(
zip(coset_ps, recoveries),
key=lambda coset_p_recovery: coset_p_recovery[0])
success = np.all(
pt.bsp(max_recovery.to_bsf() ^ error, code.logicals.T) == 0)
print('### success=', success)
assert mp.isfinite(
max_coset_p
) and max_coset_p > 0, 'Max coset probability not as expected'
assert np.all(
np.array(coset_ps) >= 0), 'At least one coset probability is negative'
def test_planar_mps_decoder_zero_max_coset_probability(code, chi):
decoder = PlanarMPSDecoder(chi=chi, mode='c')
error_model = BiasedDepolarizingErrorModel(bias=1000)
random_seed = 69
# probabilities
probability = 0.4
prob_dist = error_model.probability_distribution(probability)
# error
error = error_model.generate(code, probability,
np.random.default_rng(random_seed))
# syndrome
syndrome = pt.bsp(error, code.stabilizers.T)
# any_recovery
any_recovery = decoder.sample_recovery(code, syndrome)
# coset probabilities
coset_ps, _ = decoder._coset_probabilities(prob_dist, any_recovery)
print(coset_ps)
max_coset_p = max(coset_ps)
assert mp.isfinite(
max_coset_p
) and max_coset_p > 0, 'Max coset probability out of bounds {}'.format(
coset_ps)
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