def test_pnd_thermal(tol, n, N, hbar):
"""Test the photon number distribution for thermal states"""
cov = np.eye(2 * N) * hbar / 2 * (2 * n + 1)
mu = np.zeros(2 * N)
pnd_cov = photon_number_covmat(mu, cov, hbar=hbar)
assert np.allclose(pnd_cov, np.diag([n ** 2 + n] * N), atol=tol, rtol=0)
def test_pnd_coherent_state(tol, list_func, N, hbar):
r"""Test the covariance matrix :math:`\frac{\hbar}{2} \mathbb{I}`."""
cov = np.eye(2 * N) * hbar / 2
mu = list_func(2 * N)
pnd_cov = photon_number_covmat(mu, cov, hbar=hbar)
alpha = (mu[:N] ** 2 + mu[N:] ** 2) / (2 * hbar)
assert np.allclose(pnd_cov, np.diag(alpha), atol=tol, rtol=0)
def test_pnd_two_mode_squeeze_vacuum(tol, r, phi, hbar):
"""Test the photon number distribution for the two-mode squeezed vacuum"""
S = two_mode_squeezing(r, phi)
mu = np.zeros(4)
cov = hbar / 2 * (S @ S.T)
pnd_cov = photon_number_covmat(mu, cov, hbar=hbar)
n = np.sinh(r) ** 2
assert np.allclose(pnd_cov, np.full((2, 2), n ** 2 + n), atol=tol, rtol=0)
def get_photon_number_moments(gate_args,
device,
phi_loop=None,
delays=[1, 6, 36]):
"""Computes first and second moment of the photon number distribution
obtained from a single
Args:
gate_args (_type_): dictionary with the collected arguments for
squeezing gate, phase gates and beamsplitter gates
device (sf.Device): the Borealis device
phi_loop (list, optional): list containing the three loop offsets.
Defaults to None.
delays (list, optional): the delay applied by each loop in time bins.
Returns:
tuple: two np.ndarrays with the mean photon numbers and photon-number
covariance matrix, respectively
"""
args_list = to_args_list(gate_args, device)
n, N = get_mode_indices(delays)
prog = sf.TDMProgram(N)
with prog.context(*args_list) as (p, q):
ops.Sgate(p[0]) | q[n[0]]
for i in range(len(delays)):
ops.Rgate(p[2 * i + 1]) | q[n[i]]
ops.BSgate(p[2 * i + 2], np.pi / 2) | (q[n[i]], q[n[i + 1]])
if phi_loop is not None:
ops.Rgate(phi_loop[i]) | q[n[i]]
prog.space_unroll()
eng = sf.Engine("gaussian")
results = eng.run(prog)
assert isinstance(results.state, BaseGaussianState)
# quadrature mean vector and covariance matrix
mu = results.state.means()
cov_q = results.state.cov()
# photon-number mean vector and covariance matrix
mean_n = photon_number_mean_vector(mu, cov_q)
cov_n = photon_number_covmat(mu, cov_q)
return mean_n, cov_n
def test_pnd_squeeze_displace(tol, r, phi, alpha, hbar):
"""Test the photon number distribution for the squeezed displaced state
Eq. (17) in 'Benchmarking of Gaussian boson sampling using two-point correlators',
Phillips et al. (https://ris.utwente.nl/ws/files/122721825/PhysRevA.99.023836.pdf).
"""
S = squeezing(r, phi)
mu = [np.sqrt(2 * hbar) * np.real(alpha), np.sqrt(2 * hbar) * np.imag(alpha)]
cov = hbar / 2 * (S @ S.T)
pnd_cov = photon_number_covmat(mu, cov, hbar=hbar)
pnd_cov_analytic = np.sinh(r) ** 2 * np.cosh(r) ** 2 + np.sinh(r) ** 4 \
+ np.sinh(r) ** 2 + np.abs(alpha) ** 2 * (1 + 2 * np.sinh(r) ** 2) \
- 2 * np.real(alpha ** 2 * np.exp(-1j * phi) * np.sinh(r) * np.cosh(r))
assert np.isclose(float(pnd_cov), pnd_cov_analytic, atol=tol, rtol=0)
Sgate(p[0]) | q[n[0]]
LossChannel(eta_glob) | q[n[0]]
for i in range(len(delays)):
Rgate(p[2 * i + 1]) | q[n[i]]
BSgate(p[2 * i + 2], np.pi / 2) | (q[n[i + 1]], q[n[i]])
LossChannel(etas_loop[i]) | q[n[i]]
LossChannel(p[7]) | q[0]
MeasureFock() | q[0]
prog_sim.space_unroll()
# create Gaussian engine and submit program to it
eng_sim = sf.Engine(backend="gaussian")
results_sim = eng_sim.run(prog_sim, shots=None, crop=True)
# obtain quadrature covariance matrix
cov = results_sim.state.cov()
# obtain first and second moment
mu = np.zeros(len(cov))
mean_n_sim = photon_number_mean_vector(mu, cov)
cov_n_sim = photon_number_covmat(mu, cov)
# plot first and second moment of the simulated data
plot_photon_number_moments(mean_n_sim, cov_n_sim)
# plot statistical comparison between data and simulation
plot_photon_number_moment_comparison(mean_n, mean_n_sim, cov_n, cov_n_sim)
# show all plots
plt.show()