def __init__(self, fiducial_distribution, mean):
super(GADFLIDistribution, self).__init__(fiducial_distribution.basis)
self._fid = fiducial_distribution
mean = (
qt.to_choi(mean).unit()
if mean.type == 'super' and not mean.superrep == 'choi' else
mean
)
self._mean = mean
alpha = 1
lambda_min = min(mean.eigenenergies())
if lambda_min < 0:
raise ValueError("Negative eigenvalue {} in informative mean.".format(lambda_min))
d = self.dim
beta = (
1 / (d * lambda_min - 1) - 1
) if lambda_min > 0.5 else (
(d * lambda_min) / (1 - d * lambda_min)
)
if beta < 0:
raise ValueError("Beta < 0 for informative mean.")
self._alpha = alpha
self._beta = beta
eye = qt.qeye(self._dim).unit()
eye.dims = mean.dims
self._rho_star = (alpha + beta) / alpha * (
mean - (beta) / (alpha + beta) * eye.unit()
)
def verify_CPTP(U):
# args: U(Qobj): superoperator or unitary
# returns: trace dist of the partial trace that should be the identity, i.e. trace dist should be zero for TP maps
choi = qtp.to_choi(U)
candidate_identity = choi.ptrace([0, 1]) # 3 since we have a qutrit
ptrace = qtp.tracedist(candidate_identity,
qtp.tensor(qtp.qeye(3), qtp.qeye(3)))
return ptrace
def test_qubit_known_cases(self, variable, expected, generator, sparse):
"""
Test cases based on comparisons to pre-existing dnorm implementations.
In particular, the targets for the following test cases were generated
using QuantumUtils for MATLAB (https://goo.gl/oWXhO9).
"""
id_chan = to_choi(qeye(2))
channel = generator(variable)
assert (dnorm(channel, id_chan,
sparse=sparse) == pytest.approx(expected, abs=1e-7))
def test_qubit_simple_known_cases(self, sparse):
"""Check agreement for known qubit channels."""
id_chan = to_choi(qeye(2))
X_chan = to_choi(sigmax())
depol = to_choi(
Qobj(
qeye(4),
dims=[[[2], [2]], [[2], [2]]],
superrep='chi',
))
# We need to restrict the number of iterations for things on the
# boundary, such as perfectly distinguishable channels.
assert (dnorm(id_chan, X_chan,
sparse=sparse) == pytest.approx(2, abs=1e-7))
assert (dnorm(id_chan, depol,
sparse=sparse) == pytest.approx(1.5, abs=1e-7))
# Finally, we add a known case from Johnston's QETLAB documentation,
# || Phi - I ||_♢,
# where Phi(X) = UXU⁺ and U = [[1, 1], [-1, 1]] / sqrt(2).
U = np.sqrt(0.5) * Qobj([[1, 1], [-1, 1]])
assert (dnorm(U, qeye(2), sparse=sparse) == pytest.approx(np.sqrt(2),
abs=1e-7))
def had_mixture(x):
id_chan = to_choi(qeye(2))
S_eye = to_super(id_chan)
S_H = to_super(hadamard_transform())
return (1 - x) * S_eye + x * S_H
def _sample_dm(self):
return qt.to_choi(
qt.rand_super_bcsz(self._hdim, self._enforce_tp, self._rank)
).unit()
