def test_all(self, hbar, tol):
"""Test requesting all wires returns the full state"""
mu, cov = symplectic.vacuum_state(4, hbar=hbar)
res = symplectic.reduced_state(mu, cov, [0, 1, 2, 3])
expected = np.zeros([8]), np.identity(8) * hbar / 2
assert np.allclose(res[0], expected[0], atol=tol, rtol=0)
assert np.allclose(res[1], expected[1], atol=tol, rtol=0)
def test_integer(self, hbar, tol):
"""Test requesting via an integer"""
mu, cov = symplectic.vacuum_state(4, hbar=hbar)
res = symplectic.reduced_state(mu, cov, 0)
expected = np.zeros([2]), np.identity(2) * hbar / 2
assert np.allclose(res[0], expected[0], atol=tol, rtol=0)
assert np.allclose(res[1], expected[1], atol=tol, rtol=0)
def test_vacuum_state(self, hbar, tol):
"""Test the vacuum state is correct."""
modes = 3
means, cov = symplectic.vacuum_state(modes, hbar=hbar)
assert np.allclose(means, np.zeros([2 * modes]), atol=tol, rtol=0)
assert np.allclose(cov,
np.identity(2 * modes) * hbar / 2,
atol=tol,
rtol=0)
def test_inverse_ops_cancel(self, hbar, tol):
"""Test that applying squeezing and interferometers to a four mode circuit,
followed by applying the inverse operations, return the state to the vacuum"""
# the symplectic matrix
O = np.block([[np.zeros([4, 4]), np.identity(4)],
[-np.identity(4), np.zeros([4, 4])]])
# begin in the vacuum state
mu_init, cov_init = symplectic.vacuum_state(4, hbar=hbar)
# add displacement
alpha = np.random.random(size=[4]) + np.random.random(size=[4]) * 1j
D = np.concatenate([alpha.real, alpha.imag])
mu = mu_init + D
cov = cov_init.copy()
# random squeezing
r = np.random.random()
phi = np.random.random()
S = symplectic.expand(symplectic.two_mode_squeezing(r, phi),
modes=[0, 1],
N=4)
# check symplectic
assert np.allclose(S @ O @ S.T, O, atol=tol, rtol=0)
# random interferometer
# fmt:off
u = np.array([[
-0.06658906 - 0.36413058j, 0.07229868 + 0.65935896j,
0.59094625 - 0.17369183j, -0.18254686 - 0.10140904j
],
[
0.53854866 + 0.36529723j, 0.61152793 + 0.15022026j,
0.05073631 + 0.32624882j, -0.17482023 - 0.20103772j
],
[
0.34818923 + 0.51864844j, -0.24334624 + 0.0233729j,
0.3625974 - 0.4034224j, 0.10989667 + 0.49366039j
],
[
0.16548085 + 0.14792642j, -0.3012549 - 0.11387682j,
-0.12731847 - 0.44851389j, -0.55816075 - 0.5639976j
]])
# fmt on
U = symplectic.interferometer(u)
# check unitary
assert np.allclose(u @ u.conj().T, np.identity(4), atol=tol, rtol=0)
# check symplectic
assert np.allclose(U @ O @ U.T, O, atol=tol, rtol=0)
# apply squeezing and interferometer
cov = U @ S @ cov @ S.T @ U.T
mu = U @ S @ mu
# check we are no longer in the vacuum state
assert not np.allclose(mu, mu_init, atol=tol, rtol=0)
assert not np.allclose(cov, cov_init, atol=tol, rtol=0)
# return the inverse operations
Sinv = symplectic.expand(symplectic.two_mode_squeezing(-r, phi),
modes=[0, 1],
N=4)
Uinv = symplectic.interferometer(u.conj().T)
# check inverses
assert np.allclose(Uinv, np.linalg.inv(U), atol=tol, rtol=0)
assert np.allclose(Sinv, np.linalg.inv(S), atol=tol, rtol=0)
# apply the inverse operations
cov = Sinv @ Uinv @ cov @ Uinv.T @ Sinv.T
mu = Sinv @ Uinv @ mu
# inverse displacement
mu -= D
# check that we return to the vacuum state
assert np.allclose(mu, mu_init, atol=tol, rtol=0)
assert np.allclose(cov, cov_init, atol=tol, rtol=0)