def test_coherent_squeezed():
"""Test density matrix for a squeezed displaced state"""
r = 0.43
mu = np.array([0.24, -0.2])
V = np.diag(np.array(np.exp([-2 * r, 2 * r])))
res = density_matrix(mu, V)
# fmt: off
expected = np.array(
[[
0.89054874, 0.15018085 + 0.05295904j, -0.23955467 + 0.01263025j,
-0.0734589 - 0.02452154j, 0.07862323 - 0.00868528j
],
[
0.15018085 - 0.05295904j, 0.02847564, -0.03964706 + 0.01637575j,
-0.01384625 + 0.00023317j, 0.01274241 - 0.00614023j
],
[
-0.23955467 - 0.01263025j, -0.03964706 - 0.01637575j, 0.06461854,
0.01941242 + 0.00763805j, -0.02127257 + 0.00122123j
],
[
-0.0734589 + 0.02452154j, -0.01384625 - 0.00023317j,
0.01941242 - 0.00763805j, 0.00673463, -0.00624626 + 0.00288134j
],
[
0.07862323 + 0.00868528j, 0.01274241 + 0.00614023j,
-0.02127257 - 0.00122123j, -0.00624626 - 0.00288134j, 0.00702606
]])
# fmt:on
assert np.allclose(res, expected)
def test_density_matrix_displaced_squeezed_postselect():
"""Test density matrix for a squeezed state with postselection"""
r = 0.43
mu = np.array([0, 0.24, 0, -0.2])
V = np.diag(np.array(np.exp([1, -2 * r, 1, 2 * r])))
res = density_matrix(mu, V, post_select={0: 0}, cutoff=20,
normalize=True)[:5, :5]
# fmt:off
expected = np.array(
[[
0.89054874, 0.15018085 + 0.05295904j, -0.23955467 + 0.01263025j,
-0.0734589 - 0.02452154j, 0.07862323 - 0.00868528j
],
[
0.15018085 - 0.05295904j, 0.02847564, -0.03964706 + 0.01637575j,
-0.01384625 + 0.00023317j, 0.01274241 - 0.00614023j
],
[
-0.23955467 - 0.01263025j, -0.03964706 - 0.01637575j, 0.06461854,
0.01941242 + 0.00763805j, -0.02127257 + 0.00122123j
],
[
-0.0734589 + 0.02452154j, -0.01384625 - 0.00023317j,
0.01941242 - 0.00763805j, 0.00673463, -0.00624626 + 0.00288134j
],
[
0.07862323 + 0.00868528j, 0.01274241 + 0.00614023j,
-0.02127257 - 0.00122123j, -0.00624626 - 0.00288134j, 0.00702606
]])
# fmt:on
assert np.allclose(res, expected)
def fock_amplitudes_one_mode(alpha, cov, cutoff):
""" Returns the Fock space density matrix of gaussian state characterized
by a complex displacement alpha and a (symmetric) covariance matrix
The Fock ladder ladder goes from 0 to cutoff-1"""
r = 2 * np.array([alpha.real, alpha.imag])
if is_pure_cov(cov):
psi = state_vector(r, cov, normalize=True, cutoff=cutoff)
rho = np.outer(psi, psi.conj())
return rho
return density_matrix(r, cov, normalize=True, cutoff=cutoff)
def test_density_matrix_vacuum():
"""Test density matrix for a vacuum state"""
mu = np.zeros([2])
V = np.identity(2)
res = density_matrix(mu, V)
expected = np.zeros([5, 5])
expected[0, 0] = 1
assert np.allclose(res, expected)
def test_density_matrix_squeezed_postselect():
"""Test density matrix for a squeezed state with postselection"""
r = 0.43
mu = np.zeros([4])
V = np.diag(np.array(np.exp([1, -2 * r, 1, 2 * r])))
res = density_matrix(mu, V, post_select={0: 0}, cutoff=15, normalize=True)[:5, :5]
expected = np.array([[0.91417429, 0, -0.26200733, 0, 0.09196943], [0, 0, 0, 0, 0], [-0.26200733, 0, 0.07509273, 0, -0.02635894], [0, 0, 0, 0, 0], [0.09196943, 0, -0.02635894, 0, 0.00925248],])
assert np.allclose(res, expected)
def test_density_matrix_squeezed():
"""Test density matrix for a squeezed state"""
r = 0.43
mu = np.zeros([2])
V = np.diag(np.array(np.exp([-2 * r, 2 * r])))
res = density_matrix(mu, V)
expected = np.array([[0.91417429, 0, -0.26200733, 0, 0.09196943], [0, 0, 0, 0, 0], [-0.26200733, 0, 0.07509273, 0, -0.02635894], [0, 0, 0, 0, 0], [0.09196943, 0, -0.02635894, 0, 0.00925248],])
assert np.allclose(res, expected)
def test_cubic_phase():
"""Test that all the possible ways of obtaining a cubic phase state using the different methods agree"""
mu = np.array([
-0.50047867, 0.37373598, 0.01421683, 0.26999427, 0.04450994, 0.01903583
])
cov = np.array([
[
1.57884241, 0.81035494, 1.03468307, 1.14908791, 0.09179507,
-0.11893174
],
[
0.81035494, 1.06942863, 0.89359234, 0.20145142, 0.16202296,
0.4578259
],
[
1.03468307, 0.89359234, 1.87560498, 0.16915661, 1.0836528,
-0.09405278
],
[
1.14908791, 0.20145142, 0.16915661, 2.37765137, -0.93543385,
-0.6544286
],
[
0.09179507, 0.16202296, 1.0836528, -0.93543385, 2.78903152,
-0.76519088
],
[
-0.11893174, 0.4578259, -0.09405278, -0.6544286, -0.76519088,
1.51724222
],
])
cutoff = 7
# the Fock state measurement of mode 0 to be post-selected
m1 = 1
# the Fock state measurement of mode 1 to be post-selected
m2 = 2
psi = state_vector(mu,
cov,
post_select={
0: m1,
1: m2
},
cutoff=cutoff,
hbar=2)
psi_c = state_vector(mu, cov, cutoff=cutoff, hbar=2)[m1, m2, :]
rho = density_matrix(mu,
cov,
post_select={
0: m1,
1: m2
},
cutoff=cutoff,
hbar=2)
rho_c = density_matrix(mu, cov, cutoff=cutoff, hbar=2)[m1, m2, :, m1,
m2, :]
assert np.allclose(np.outer(psi, psi.conj()), rho)
assert np.allclose(np.outer(psi_c, psi_c.conj()), rho)
assert np.allclose(rho_c, rho)
def circuit(cutoff, l1=0.85, l2=1):
"""Runs the heralded circuit with specified parameters,
returning the output fidelity to the requested weak cubic phase state,
the post-selection probability, and the Wigner log negativity.
Args:
cutoff (int): the Fock basis truncation
l1 (float): squeeze cavity loss
l2 (float): PNR loss
Returns:
tuple: a tuple containing the output fidelity to the target ON state,
the probability of post-selection, the state norm before entering the beamsplitter,
the state norm after exiting the beamsplitter, and the density matrix of the output state.
"""
# weak cubic phase state parameter
a = 0.53
# the Fock state measurement of mode 0 to be post-selected
m1 = 1
# the Fock state measurement of mode 1 to be post-selected
m2 = 2
# define target state
target_state = cubic_phase_state(a, cutoff)
# gate parameters for the heralded quantum circuit.
# squeezing magnitudes
sq_r = [0.71, 0.67, -0.42]
# squeezing phase
sq_phi = [-2.07, 0.06, -3.79]
# displacement magnitudes
d_r = [-0.02, 0.34, 0.02]
# beamsplitter theta
bs_theta1, bs_theta2, bs_theta3 = [-1.57, 0.68, 2.5]
# beamsplitter phi
bs_phi1, bs_phi2, bs_phi3 = [0.53, -4.51, 0.72]
# quantum circuit prior to entering the beamsplitter
prog = sf.Program(3)
with prog.context as q:
for k in range(3):
ops.Sgate(sq_r[k], sq_phi[k]) | q[k]
ops.Dgate(d_r[k]) | q[k]
ops.LossChannel(l1) | q[k]
ops.BSgate(bs_theta1, bs_phi1) | (q[0], q[1])
ops.BSgate(bs_theta2, bs_phi2) | (q[1], q[2])
ops.BSgate(bs_theta3, bs_phi3) | (q[0], q[1])
ops.LossChannel(l2) | q[0]
ops.LossChannel(l2) | q[1]
eng = sf.Engine("gaussian")
state = eng.run(prog).state
mu = state.means()
cov = state.cov()
rho = density_matrix(mu,
cov,
post_select={
0: m1,
1: m2
},
cutoff=cutoff,
hbar=2)
# probability of measuring m1 and m2
prob = np.abs(np.trace(rho))
# output state
if prob != 0:
rho = rho / prob
# fidelity with the target state
fidelity = np.abs(np.trace(np.einsum("ij,jk->ik", rho, target_state)))
return fidelity, prob, rho
def get_density_matrix(self, cutoff = 5):
return quantum.density_matrix(self.mu, self.cov, cutoff=cutoff)