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_two_mode_squeezing(self, tol):
"""Test the two mode squeezing symplectic transform."""
r = 0.543
phi = 0.123
S = two_mode_squeezing(r, phi)
# test that S = B^\dagger(pi/4, 0) [S(z) x S(-z)] B(pi/4)
B = beamsplitter(np.pi / 4, 0)
Sz = block_diag(squeezing(r, phi),
squeezing(-r, phi))[:, [0, 2, 1, 3]][[0, 2, 1, 3]]
expected = B.conj().T @ Sz @ B
assert S == pytest.approx(expected, abs=tol)
# test that S |a1, a2> = |ta1+ra2, ta2+ra1>
a1 = 0.23 + 0.12j
a2 = 0.23 + 0.12j
out = S @ np.array([a1.real, a2.real, a1.imag, a2.imag]) * np.sqrt(
2 * hbar)
T = np.cosh(r)
R = np.exp(1j * phi) * np.sinh(r)
a1out = T * a1 + R * np.conj(a2)
a2out = T * a2 + R * np.conj(a1)
expected = np.array([a1out.real, a2out.real, a1out.imag, a2out.imag
]) * np.sqrt(2 * hbar)
assert out == pytest.approx(expected, abs=tol)
def test_controlled_addition(self):
"""Test the CX symplectic transform."""
self.logTestName()
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)
self.assertAllAlmostEqual(S, expected, delta=self.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)
self.assertAllAlmostEqual(out, expected, delta=self.tol)
def test_two_mode_squeezing(self):
"""Test the two mode squeezing symplectic transform."""
self.logTestName()
r = 0.543
phi = 0.123
S = two_mode_squeezing(r, phi)
# test that S = B^\dagger(pi/4, 0) [S(z) x S(-z)] B(pi/4)
B = beamsplitter(np.pi / 4, 0)
Sz = block_diag(squeezing(r, phi),
squeezing(-r, phi))[:, [0, 2, 1, 3]][[0, 2, 1, 3]]
expected = B.conj().T @ Sz @ B
self.assertAllAlmostEqual(S, expected, delta=self.tol)
# test that S |a1, a2> = |ta1+ra2, ta2+ra1>
a1 = 0.23 + 0.12j
a2 = 0.23 + 0.12j
out = S @ np.array([a1.real, a2.real, a1.imag, a2.imag]) * np.sqrt(
2 * hbar)
T = np.cosh(r)
R = np.exp(1j * phi) * np.sinh(r)
a1out = T * a1 + R * np.conj(a2)
a2out = T * a2 + R * np.conj(a1)
expected = np.array([a1out.real, a2out.real, a1out.imag, a2out.imag
]) * np.sqrt(2 * hbar)
self.assertAllAlmostEqual(out, expected, delta=self.tol)
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_squeezing(self):
"""Test the squeezing symplectic transform."""
self.logTestName()
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
self.assertAllAlmostEqual(out, expected, delta=self.tol)
