def test_controlled_addition(self, tol):
"""Test the CX symplectic transform."""
s = 0.543
S = controlled_addition(s)
# test that S = B(theta+pi/2, 0) [S(z) x S(-z)] B(theta, 0)
r = np.arcsinh(-s / 2)
theta = 0.5 * np.arctan2(-1 / np.cosh(r), -np.tanh(r))
Sz = block_diag(squeezing(r, 0),
squeezing(-r, 0))[:, [0, 2, 1, 3]][[0, 2, 1, 3]]
expected = beamsplitter(theta + np.pi / 2, 0) @ Sz @ beamsplitter(
theta, 0)
assert S == pytest.approx(expected, abs=tol)
# test that S[x1, x2, p1, p2] -> [x1, x2+sx1, p1-sp2, p2]
x1 = 0.5432
x2 = -0.453
p1 = 0.154
p2 = -0.123
out = S @ np.array([x1, x2, p1, p2]) * np.sqrt(2 * hbar)
expected = np.array([x1, x2 + s * x1, p1 - s * p2, p2]) * np.sqrt(
2 * hbar)
assert out == pytest.approx(expected, abs=tol)
def test_controlled_phase(self, tol):
"""Test the CZ symplectic transform."""
s = 0.543
S = controlled_phase(s)
# test that S = R_2(pi/2) CX(s) R_2(pi/2)^\dagger
R2 = block_diag(np.identity(2),
rotation(np.pi / 2))[:, [0, 2, 1, 3]][[0, 2, 1, 3]]
expected = R2 @ controlled_addition(s) @ R2.conj().T
assert S == pytest.approx(expected, abs=tol)
# test that S[x1, x2, p1, p2] -> [x1, x2, p1+sx2, p2+sx1]
x1 = 0.5432
x2 = -0.453
p1 = 0.154
p2 = -0.123
out = S @ np.array([x1, x2, p1, p2]) * np.sqrt(2 * hbar)
expected = np.array([x1, x2, p1 + s * x2, p2 + s * x1]) * np.sqrt(
2 * hbar)
assert out == pytest.approx(expected, abs=tol)