def test_rand_super_bcsz_cptp():
"""
Random Qobjs: Tests that BCSZ-random superoperators are CPTP.
"""
random_qobj = rand_super_bcsz(5)
assert random_qobj.issuper
assert random_qobj.iscptp
def entropy_stationary(steps, d):
for _ in range(steps):
phi = q.rand_super_bcsz(int(np.sqrt(d)))
vals, vecs = np.linalg.eig(phi.data.todense())
idx = np.where(np.isclose(vals, 1.))[0]
rho = unres(vecs[:, idx])
rho = q.Qobj(rho/np.trace(rho))
q.entropy_vn(rho)
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 entropy_stationary(steps, d):
for _ in range(steps):
phi = q.rand_super_bcsz(int(np.sqrt(d)))
vals, vecs = np.linalg.eig(phi.data.todense())
idx = np.where(np.isclose(vals, 1.))[0]
rho = unres(vecs[:, idx])
rho = q.Qobj(rho / np.trace(rho))
q.entropy_vn(rho)
def _sample(self):
# Since the dense representation of S is a matrix and not an array,
# flattening in FORTRAN order gives MATLAB-like behavior (implicitly
# two-index). Thus, we need to index away the first axis.
return np.real(
conjugate(
self._basis,
qt.rand_super_bcsz(self._dims,
enforce_tp=self._enforce_tp,
rank=self._rank).data.todense().view(
np.ndarray)))[1:, :].flatten(order='F')
def _sample(self):
# Since the dense representation of S is a matrix and not an array,
# flattening in FORTRAN order gives MATLAB-like behavior (implicitly
# two-index). Thus, we need to index away the first axis.
return np.real(
conjugate(self._basis,
qt.rand_super_bcsz(
self._dims, enforce_tp=self._enforce_tp, rank=self._rank
).data.todense().view(np.ndarray)
)
)[1:, :].flatten(order='F')
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
def test_bounded(self, n_qubits):
tol = 1e-7
operator = rand_super_bcsz(2**n_qubits)
assert -tol <= unitarity(operator) <= 1 + tol
def test_bounded(self, dimension):
tol = 1e-7
channel = rand_super_bcsz(dimension)
assert -tol <= average_gate_fidelity(channel) <= 1 + tol
def random_channel(steps, d):
for _ in range(steps):
q.rand_super_bcsz(int(np.sqrt(d)))
def _sample_dm(self):
return qt.to_choi(
qt.rand_super_bcsz(self._hdim, self._enforce_tp, self._rank)
).unit()
def random_channel(steps, d):
for _ in range(steps):
q.rand_super_bcsz(int(np.sqrt(d)))