def test_even_validation(self):
"""Test that the graph_embed decomposition raises exception if not even number of rows"""
A = np.random.random([5, 5]) + 1j * np.random.random([5, 5])
A += A.T
with pytest.raises(ValueError,
match="must have an even number of rows/columns"):
dec.williamson(A)
def test_williamson_BM_random_circuit_pure(self):
self.logTestName()
for k in range(nsamples):
n = 3
U2 = haar_measure(n)
state = gaussiancircuit.GaussianModes(n, hbar=2)
for i in range(n):
state.squeeze(np.log(0.2 * i + 2), 0, i)
state.apply_u(U2)
V = state.scovmatxp()
D, S = dec.williamson(V)
omega = dec.sympmat(n)
self.assertAlmostEqual(np.linalg.norm(S @ omega @ S.T - omega), 0)
self.assertAlmostEqual(np.linalg.norm(S @ D @ S.T - V), 0)
O, s, Oo = dec.bloch_messiah(S)
self.assertAlmostEqual(
np.linalg.norm(np.transpose(O) @ omega @ O - omega), 0)
self.assertAlmostEqual(
np.linalg.norm(np.transpose(O) @ O - np.identity(2 * n)), 0)
self.assertAlmostEqual(
np.linalg.norm(np.transpose(Oo) @ omega @ Oo - omega), 0)
self.assertAlmostEqual(
np.linalg.norm(np.transpose(Oo) @ Oo - np.identity(2 * n)), 0)
self.assertAlmostEqual(
np.linalg.norm(np.transpose(s) @ omega @ s - omega), 0)
self.assertAlmostEqual(np.linalg.norm(O @ s @ Oo - S), 0)
def test_pure_state(self, create_cov, hbar, tol):
"""Test pure state"""
n = 3
O = omega(n)
cov, _ = create_cov(np.zeros([n]))
Db, S = dec.williamson(cov)
nbar = np.diag(Db) / hbar - 0.5
# check decomposition is correct
assert np.allclose(S @ Db @ S.T, cov, atol=tol, rtol=0)
# check nbar = 0
assert np.allclose(nbar, 0, atol=tol, rtol=0)
# check S is symplectic
assert np.allclose(S @ O @ S.T, O, atol=tol, rtol=0)
def test_mixed_state(self, create_cov, hbar, tol):
"""Test mixed state"""
n = 3
O = omega(n)
nbar_in = np.abs(np.random.random(n))
cov, _ = create_cov(nbar_in)
Db, S = dec.williamson(cov)
nbar = np.diag(Db) / hbar - 0.5
# check decomposition is correct
assert np.allclose(S @ Db @ S.T, cov, atol=tol, rtol=0)
# check nbar
assert np.allclose(sorted(nbar[:n]), sorted(nbar_in), atol=tol, rtol=0)
# check S is symplectic
assert np.allclose(S @ O @ S.T, O, atol=tol, rtol=0)
def test_vacuum_state(self, tol, hbar):
"""Test vacuum state"""
V = np.identity(4)
Db, S = dec.williamson(V)
assert np.allclose(Db, np.identity(4), atol=tol, rtol=0)
assert np.allclose(S, np.identity(4), atol=tol, rtol=0)
def test_positive_definite_validation(self):
"""Test that the graph_embed decomposition raises exception if not positive definite"""
A = np.diag([-2, 0.1, 2, 3])
with pytest.raises(ValueError,
match="matrix is not positive definite"):
dec.williamson(A)
def test_symmetric_validation(self):
"""Test that the graph_embed decomposition raises exception if not symmetric"""
A = np.random.random([5, 5]) + 1j * np.random.random([5, 5])
with pytest.raises(ValueError, match="matrix is not symmetric"):
dec.williamson(A)
