def test_planar_mps_decoder_cosets_probability_pair_optimisation(mode):
code = PlanarCode(5, 5)
decoder = PlanarMPSDecoder(mode=mode)
# probabilities
prob_dist = BiasedDepolarizingErrorModel(bias=10).probability_distribution(
probability=0.1)
# coset probabilities for null Pauli
coset_i_ps, _ = decoder._coset_probabilities(prob_dist, code.new_pauli())
coset_x_ps, _ = decoder._coset_probabilities(prob_dist,
code.new_pauli().logical_x())
# expect Pr(iIG) ~= Pr(xXG)
assert _is_close(
coset_i_ps[0], coset_x_ps[1], rtol=0,
atol=0), ('Coset probabilites do not satisfy Pr(iIG) ~= Pr(xXG)')
# expect Pr(iXG) ~= Pr(xIG)
assert _is_close(
coset_i_ps[1], coset_x_ps[0], rtol=0,
atol=0), ('Coset probabilites do not satisfy Pr(iXG) ~= Pr(xIG)')
# expect Pr(iZG) ~= Pr(xYG)
assert _is_close(
coset_i_ps[3], coset_x_ps[2], rtol=0,
atol=0), ('Coset probabilites do not satisfy Pr(iZG) ~= Pr(xYG)')
# expect Pr(iYG) ~= Pr(xZG)
assert _is_close(
coset_i_ps[2], coset_x_ps[3], rtol=0,
atol=0), ('Coset probabilites do not satisfy Pr(iYG) ~= Pr(xZG)')
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_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_codes_exact_approx():
code = PlanarCode(4, 4)
exact_decoder = PlanarMPSDecoder()
approx_decoder = PlanarMPSDecoder(chi=8)
identity = code.new_pauli()
# probabilities
prob_dist = BiasedDepolarizingErrorModel(bias=10).probability_distribution(
probability=0.1)
# coset probabilities
exact_coset_ps, _ = exact_decoder._coset_probabilities(prob_dist, identity)
approx_coset_ps, _ = approx_decoder._coset_probabilities(
prob_dist, identity)
print('#exact Pr(G)=', exact_coset_ps)
print('#approx Pr(G)=', approx_coset_ps)
assert all(_is_close(
exact_coset_ps, approx_coset_ps, rtol=1e-11, atol=0)), (
'Coset probabilites do not satisfy exact Pr(G) ~= approx Pr(G)')
def test_planar_mps_decoder_cosets_probability_equivalence(
sample_pauli_f, sample_pauli_g):
decoder = PlanarMPSDecoder(chi=8)
# probabilities
prob_dist = BiasedDepolarizingErrorModel(bias=10).probability_distribution(
probability=0.1)
# coset probabilities
coset_f_ps, _ = decoder._coset_probabilities(prob_dist, sample_pauli_f)
coset_g_ps, _ = decoder._coset_probabilities(prob_dist, sample_pauli_g)
print('#Pr(fG)=', coset_f_ps)
print('#Pr(gG)=', coset_g_ps)
assert all(_is_close(
coset_f_ps, coset_g_ps, rtol=1e-12,
atol=0)), ('Coset probabilites do not satisfy Pr(fG) ~= Pr(gG)')
def test_planar_mps_decoder_cosets_probability_inequality_bsv(mode, rtol):
code = PlanarCode(25, 25)
decoder = PlanarMPSDecoder(chi=5, mode=mode)
# probabilities
prob_dist = DepolarizingErrorModel().probability_distribution(0.1)
# coset probabilities for null Pauli
coset_ps, _ = decoder._coset_probabilities(prob_dist, code.new_pauli())
coset_i_p, coset_x_p, coset_y_p, coset_z_p = coset_ps
# expect Pr(IG) > Pr(XG) ~= Pr(ZG) > Pr(YG)
print('{} > {} ~= {} > {}. rtol={}'.format(
coset_i_p, coset_x_p, coset_z_p, coset_y_p,
abs(coset_x_p - coset_z_p) / abs(coset_z_p)))
print('types: Pr(IG):{}, Pr(XG):{}, Pr(ZG):{}, Pr(YG):{}'.format(
type(coset_i_p), type(coset_x_p), type(coset_z_p), type(coset_y_p)))
assert coset_i_p > coset_x_p, 'Coset probabilites do not satisfy Pr(IG) > Pr(XG)'
assert coset_i_p > coset_z_p, 'Coset probabilites do not satisfy Pr(IG) > Pr(ZG)'
assert _is_close(
coset_x_p, coset_z_p, rtol=rtol,
atol=0), 'Coset probabilites do not satisfy Pr(XG) ~= Pr(ZG)'
assert coset_x_p > coset_y_p, 'Coset probabilites do not satisfy Pr(XG) > Pr(YG)'
assert coset_z_p > coset_y_p, 'Coset probabilites do not satisfy Pr(ZG) > Pr(YG)'
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)