def test_force_solve(self, dimension, generator):
"""
Metrics: checks that special cases for dnorm agree with SDP solutions.
"""
A, B = generator(dimension), generator(dimension)
assert (dnorm(A, B, force_solve=False) == pytest.approx(dnorm(
A, B, force_solve=True),
abs=1e-5))
def test_sparse_against_dense_random(self, dimension):
"""
Test sparse versus dense dnorm calculation for random superoperators.
"""
A = rand_super_bcsz(dimension)
dense_run_result = dnorm(A, force_solve=True, sparse=False)
sparse_run_result = dnorm(A, force_solve=True, sparse=True)
assert dense_run_result == pytest.approx(sparse_run_result, abs=1e-7)
def test_sparse_against_dense_adc(self, variable):
"""
Test sparse versus dense dnorm calculation for a sample of
amplitude-damping channels.
"""
# Choi matrix for identity channel on 1 qubit
A = kraus_to_choi([qeye(2)])
B = adc_choi(variable)
dense = dnorm(A, B, force_solve=True, sparse=False)
sparse = dnorm(A, B, force_solve=True, sparse=True)
assert dense == pytest.approx(sparse, abs=1e-7)
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 test_cptp(self, dimension, sparse):
"""Check that the diamond norm is one for CPTP maps."""
A = rand_super_bcsz(dimension)
assert A.iscptp
assert dnorm(A, sparse=sparse) == pytest.approx(1, abs=1e-7)
def test_qubit_triangle(self, dimension):
"""Check that dnorm(A + B) <= dnorm(A) + dnorm(B)."""
A = rand_super_bcsz(dimension)
B = rand_super_bcsz(dimension)
assert dnorm(A + B) <= dnorm(A) + dnorm(B) + 1e-7
def test_qubit_scalar(self, dimension):
"""dnorm(a * A) == a * dnorm(A) for scalar a, qobj A."""
a = np.random.random()
A = rand_super_bcsz(dimension)
B = rand_super_bcsz(dimension)
assert dnorm(a * A, a * B) == pytest.approx(a * dnorm(A, B), abs=1e-7)
def test_bounded(self, dimension, sparse):
"""dnorm(A - B) in [0, 2] for random superops A, B."""
tol = 1e-7
A, B = rand_super_bcsz(dimension), rand_super_bcsz(dimension)
assert -tol <= dnorm(A, B, sparse=sparse) <= 2 + tol
