def test_squeezing(self, tol):
"""Test the squeezing symplectic transform."""
r = 0.543
phi = 0.123
S = squeezing(r, phi)
# apply to an identity covariance matrix
out = S @ S.T
expected = rotation(phi / 2) @ np.diag(np.exp(
[-2 * r, 2 * r])) @ rotation(phi / 2).T
assert out == pytest.approx(expected, abs=tol)
def test_rotation(self, tol):
"""Test the Fourier transform of a displaced state."""
# pylint: disable=invalid-unary-operand-type
alpha = 0.23 + 0.12j
S = rotation(np.pi / 2)
# apply to a coherent state. F{x, p} -> {-p, x}
out = S @ np.array([alpha.real, alpha.imag]) * np.sqrt(2 * hbar)
expected = np.array([-alpha.imag, alpha.real]) * np.sqrt(2 * hbar)
assert out == pytest.approx(expected, abs=tol)
def test_squeezed_state(self, tol):
"""Test the squeezed state is correct."""
r = 0.432
phi = 0.123
means, cov = squeezed_state(r, phi, hbar=hbar)
# test vector of means is zero
assert means == pytest.approx(np.zeros([2]), abs=tol)
R = rotation(phi / 2)
expected = R @ np.array([[np.exp(-2 * r), 0], [0, np.exp(2 * r)]
]) * hbar / 2 @ R.T
# test covariance matrix is correct
assert cov == pytest.approx(expected, abs=tol)
def test_displaced_squeezed_state(self, tol):
"""Test the displaced squeezed state is correct."""
alpha = 0.541 + 0.109j
a = abs(alpha)
phi_a = np.angle(alpha)
r = 0.432
phi_r = 0.123
means, cov = displaced_squeezed_state(a, phi_a, r, phi_r, hbar=hbar)
# test vector of means is correct
assert means == pytest.approx(np.array([alpha.real, alpha.imag]) *
np.sqrt(2 * hbar),
abs=tol)
R = rotation(phi_r / 2)
expected = R @ np.array([[np.exp(-2 * r), 0], [0, np.exp(2 * r)]
]) * hbar / 2 @ R.T
# test covariance matrix is correct
assert cov == 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)
