def test_reflection_matrix_sign_preference_under_perturbation():
x = np.array([[0, 1], [1, 0]])
sqrt_x = np.array([[1, -1j], [-1j, 1]]) * (1 + 1j) / 2
np.testing.assert_allclose(cirq.reflection_matrix_pow(x, 0.5), sqrt_x, atol=1e-8)
# Sqrt should behave well when phased by less than 90 degrees.
# (When rotating by more it's ambiguous. For example, 181 = 91*2 = -89*2.)
for perturbation in [0, 0.1, -0.1, 0.3, -0.3, 0.49, -0.49]:
px = x * complex(-1) ** perturbation
expected_sqrt_px = sqrt_x * complex(-1) ** (perturbation / 2)
sqrt_px = cirq.reflection_matrix_pow(px, 0.5)
np.testing.assert_allclose(np.dot(sqrt_px, sqrt_px), px, atol=1e-10)
np.testing.assert_allclose(sqrt_px, expected_sqrt_px, atol=1e-10)
def test_reflection_matrix_sign_preference_under_perturbation():
x = np.array([[0, 1], [1, 0]])
sqrt_x = np.array([[1, -1j], [-1j, 1]]) * (1 + 1j) / 2
np.testing.assert_allclose(cirq.reflection_matrix_pow(x, 0.5),
sqrt_x,
atol=1e-8)
# Sqrt should behave well when phased by less than 90 degrees.
# (When rotating by more it's ambiguous. For example, 181 = 91*2 = -89*2.)
for perturbation in [0, 0.1, -0.1, 0.3, -0.3, 0.49, -0.49]:
px = x * complex(-1)**perturbation
expected_sqrt_px = sqrt_x * complex(-1)**(perturbation / 2)
sqrt_px = cirq.reflection_matrix_pow(px, 0.5)
np.testing.assert_allclose(np.dot(sqrt_px, sqrt_px), px, atol=1e-10)
np.testing.assert_allclose(sqrt_px, expected_sqrt_px, atol=1e-10)
def test_reflection_matrix_pow_consistent_results():
x = np.array([[0, 1], [1, 0]])
sqrt_x = cirq.reflection_matrix_pow(x, 0.5)
np.testing.assert_allclose(np.dot(sqrt_x, sqrt_x), x, atol=1e-10)
ix = x * np.sqrt(1j)
sqrt_ix = cirq.reflection_matrix_pow(ix, 0.5)
np.testing.assert_allclose(np.dot(sqrt_ix, sqrt_ix), ix, atol=1e-10)
h = np.array([[1, 1], [1, -1]]) * np.sqrt(0.5)
cube_root_h = cirq.reflection_matrix_pow(h, 1 / 3)
np.testing.assert_allclose(np.dot(np.dot(cube_root_h, cube_root_h), cube_root_h), h, atol=1e-8)
y = np.array([[0, -1j], [1j, 0]])
h = np.array([[1, 1], [1, -1]]) * np.sqrt(0.5j)
yh = np.kron(y, h)
sqrt_yh = cirq.reflection_matrix_pow(yh, 0.5)
np.testing.assert_allclose(np.dot(sqrt_yh, sqrt_yh), yh, atol=1e-10)
def test_reflection_matrix_pow_consistent_results():
x = np.array([[0, 1], [1, 0]])
sqrt_x = cirq.reflection_matrix_pow(x, 0.5)
np.testing.assert_allclose(np.dot(sqrt_x, sqrt_x), x, atol=1e-10)
ix = x * np.sqrt(1j)
sqrt_ix = cirq.reflection_matrix_pow(ix, 0.5)
np.testing.assert_allclose(np.dot(sqrt_ix, sqrt_ix), ix, atol=1e-10)
h = np.array([[1, 1], [1, -1]]) * np.sqrt(0.5)
cube_root_h = cirq.reflection_matrix_pow(h, 1/3)
np.testing.assert_allclose(
np.dot(np.dot(cube_root_h, cube_root_h), cube_root_h),
h,
atol=1e-8)
y = np.array([[0, -1j], [1j, 0]])
h = np.array([[1, 1], [1, -1]]) * np.sqrt(0.5j)
yh = np.kron(y, h)
sqrt_yh = cirq.reflection_matrix_pow(yh, 0.5)
np.testing.assert_allclose(np.dot(sqrt_yh, sqrt_yh), yh, atol=1e-10)
