def test_grad_two_mode_squeezing():
"""Tests the value of the analytic gradient for the S2gate against finite differences"""
cutoff = 4
r = 1.0
theta = np.pi / 8
T = two_mode_squeezing(r, theta, cutoff)
Dr, Dtheta = grad_two_mode_squeezing(T, r, theta)
dr = 0.001
dtheta = 0.001
Drp = two_mode_squeezing(r + dr, theta, cutoff)
Drm = two_mode_squeezing(r - dr, theta, cutoff)
Dthetap = two_mode_squeezing(r, theta + dtheta, cutoff)
Dthetam = two_mode_squeezing(r, theta - dtheta, cutoff)
Drapprox = (Drp - Drm) / (2 * dr)
Dthetaapprox = (Dthetap - Dthetam) / (2 * dtheta)
assert np.allclose(Dr, Drapprox, atol=1e-5, rtol=0)
assert np.allclose(Dtheta, Dthetaapprox, atol=1e-5, rtol=0)
def test_two_mode_squeezing_values(tol):
"""Tests the correct construction of the single mode squeezing operation"""
r = 0.5
theta = 0.7
cutoff = 5
T = two_mode_squeezing(r, theta, cutoff)
expected = ((np.tanh(r) * np.exp(1j * theta)) ** np.arange(cutoff)) / np.cosh(r)
assert np.allclose(np.diag(T[:, :, 0, 0]), expected, atol=tol, rtol=0)
def test_S2_selection_rules(tol):
r"""Tests the selection rules of a two mode squeezing operation.
If one writes the squeezing gate as :math:`S_2` and its matrix elements as
:math:`\langle p_0 p_1|S_2|q_0 q_1 \rangle` then these elements are nonzero
if and only if :math:`p_0 - q_0 = p_1 - q_1`. This test checks that this
selection rule holds.
"""
cutoff = 5
s = np.arcsinh(1.0)
phi = np.pi / 6
T = two_mode_squeezing(s, phi, cutoff)
m = np.arange(cutoff).reshape(-1, 1, 1, 1)
n = np.arange(cutoff).reshape(1, -1, 1, 1)
k = np.arange(cutoff).reshape(1, 1, -1, 1)
l = np.arange(cutoff).reshape(1, 1, 1, -1)
# create a copy of T, but replace all elements where
# m+n != k+l with 0.
S = np.where(m - n != k - l, 0, T)
# check that S and T remain equal
assert np.allclose(S, T, atol=tol, rtol=0)