def test_even_validation(self):
"""Test 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.bloch_messiah(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_decomposition_active(self, hbar, tol):
"""Test that an active symplectic is correctly decomposed into
two interferometers and squeezing"""
n = 3
S = random_symplectic(n, passive=False)
O1, Sq, O2 = dec.bloch_messiah(S)
X1 = O1[:n, :n]
P1 = O1[n:, :n]
X2 = O2[:n, :n]
P2 = O2[n:, :n]
U1 = X1 + 1j * P1
U2 = X2 + 1j * P2
prog = sf.Program(n, hbar=hbar)
with eng:
G = ops.GaussianTransform(S)
cmds = G.decompose(q)
assert np.all(U1 == G.U1)
assert np.all(U2 == G.U2)
assert np.all(np.diag(Sq)[:n] == G.Sq)
S = np.identity(2 * n)
# command queue should have 2 interferometers, 3 squeezers
assert len(cmds) == 5
# calculating the resulting decomposed symplectic
for cmd in cmds:
# all operations should be BSgates, Rgates, or Sgates
assert isinstance(cmd.op, (ops.Interferometer, ops.Sgate))
# build up the symplectic transform
modes = [i.ind for i in cmd.reg]
if isinstance(cmd.op, ops.Sgate):
S = _squeezing(cmd.op.p[0].x, cmd.op.p[1].x, modes, n) @ S
if isinstance(cmd.op, ops.Interferometer):
U1 = cmd.op.p[0].x
S_U = np.vstack([
np.hstack([U1.real, -U1.imag]),
np.hstack([U1.imag, U1.real])
])
S = S_U @ S
# the resulting covariance state
cov = S @ S.T
assert np.allclose(cov, S @ S.T * hbar / 2, atol=tol, rtol=0)
def test_active_on_vacuum(self, hbar, tol):
"""Test that an active symplectic applied to a vacuum is
correctly decomposed into just squeezing and one interferometer"""
n = 3
S = random_symplectic(n, passive=False)
O1, Sq, O2 = dec.bloch_messiah(S)
X1 = O1[:n, :n]
P1 = O1[n:, :n]
X2 = O2[:n, :n]
P2 = O2[n:, :n]
U1 = X1 + 1j * P1
U2 = X2 + 1j * P2
prog = sf.Program(n)
G = ops.GaussianTransform(S, vacuum=True)
cmds = G.decompose(prog.register)
S = np.identity(2 * n)
# command queue should have 3 Sgates, 1 interferometer
assert len(cmds) == 4
# calculating the resulting decomposed symplectic
for cmd in cmds:
# all operations should be Interferometers or Sgates
assert isinstance(cmd.op, (ops.Interferometer, ops.Sgate))
# build up the symplectic transform
modes = [i.ind for i in cmd.reg]
if isinstance(cmd.op, ops.Sgate):
S = _squeezing(cmd.op.p[0].x, cmd.op.p[1].x, modes, n) @ S
if isinstance(cmd.op, ops.Interferometer):
U1 = cmd.op.p[0].x
S_U = np.vstack([
np.hstack([U1.real, -U1.imag]),
np.hstack([U1.imag, U1.real])
])
S = S_U @ S
# the resulting covariance state
cov = S @ S.T
assert np.allclose(cov, S @ S.T, atol=tol, rtol=0)
def test_identity(self, tol):
"""Test identity"""
n = 2
S_in = np.identity(2 * n)
O1, S, O2 = dec.bloch_messiah(S_in)
assert np.allclose(O1 @ O2, np.identity(2 * n), atol=tol, rtol=0)
assert np.allclose(S, np.identity(2 * n), atol=tol, rtol=0)
# test orthogonality
assert np.allclose(O1.T, O1, atol=tol, rtol=0)
assert np.allclose(O2.T, O2, atol=tol, rtol=0)
# test symplectic
O = omega(n)
assert np.allclose(O1 @ O @ O1.T, O, atol=tol, rtol=0)
assert np.allclose(O2 @ O @ O2.T, O, atol=tol, rtol=0)
def test_active_transform(self, create_transform, tol):
"""Test passive transform with squeezing"""
n = 3
S_in = create_transform(3, passive=False)
O1, S, O2 = dec.bloch_messiah(S_in)
# test decomposition
assert np.allclose(O1 @ S @ O2, S_in, atol=tol, rtol=0)
# test orthogonality
assert np.allclose(O1.T @ O1, np.identity(2 * n), atol=tol, rtol=0)
assert np.allclose(O2.T @ O2, np.identity(2 * n), atol=tol, rtol=0)
# test symplectic
O = omega(n)
assert np.allclose(O1.T @ O @ O1, O, atol=tol, rtol=0)
assert np.allclose(O2.T @ O @ O2, O, atol=tol, rtol=0)
assert np.allclose(S @ O @ S.T, O, atol=tol, rtol=0)
def test_BM_random_degen_symplectic(self):
self.logTestName()
for k in range(nsamples):
n = 20
S = random_degen_symplectic(n)
O, s, Oo = dec.bloch_messiah(S)
omega = dec.sympmat(n)
self.assertAlmostEqual(np.linalg.norm(S @ omega @ S.T - omega), 0)
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_passive_transform(self, create_transform, tol):
"""Test passive transform has no squeezing.
Note: this test also tests the case with degenerate symplectic values"""
n = 3
S_in = create_transform(3, passive=True)
O1, S, O2 = dec.bloch_messiah(S_in)
# test decomposition
assert np.allclose(O1 @ S @ O2, S_in, atol=tol, rtol=0)
# test no squeezing
assert np.allclose(O1 @ O2, S_in, atol=tol, rtol=0)
assert np.allclose(S, np.identity(2 * n), atol=tol, rtol=0)
# test orthogonality
assert np.allclose(O1.T @ O1, np.identity(2 * n), atol=tol, rtol=0)
assert np.allclose(O2.T @ O2, np.identity(2 * n), atol=tol, rtol=0)
# test symplectic
O = omega(n)
# TODO: BUG:
# assert np.allclose(O1.T @ O @ O1, O, atol=tol, rtol=0)
# assert np.allclose(O2.T @ O @ O2, O, atol=tol, rtol=0)
assert np.allclose(S @ O @ S.T, O, atol=tol, rtol=0)
def test_symmplectic(self):
"""Test raises exception if not symmetric"""
A = np.random.random([6, 6]) + 1j * np.random.random([6, 6])
A += A.T
with pytest.raises(ValueError, match="matrix is not symplectic"):
dec.bloch_messiah(A)
def test_square_validation(self):
"""Test raises exception if not square"""
A = np.random.random([4, 5]) + 1j * np.random.random([4, 5])
with pytest.raises(ValueError, match="matrix is not square"):
dec.bloch_messiah(A)
