def test_axis_angle():
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.ry(1e-10))),
cirq.AxisAngleDecomposition(angle=0, axis=(1, 0, 0), global_phase=1),
atol=1e-8,
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.rx(np.pi))),
cirq.AxisAngleDecomposition(angle=np.pi, axis=(1, 0, 0), global_phase=1),
atol=1e-8,
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.X)),
cirq.AxisAngleDecomposition(angle=np.pi, axis=(1, 0, 0), global_phase=1j),
atol=1e-8,
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.X ** 0.5)),
cirq.AxisAngleDecomposition(
angle=np.pi / 2, axis=(1, 0, 0), global_phase=np.exp(1j * np.pi / 4)
),
atol=1e-8,
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.X ** -0.5)),
cirq.AxisAngleDecomposition(
angle=-np.pi / 2, axis=(1, 0, 0), global_phase=np.exp(-1j * np.pi / 4)
),
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.Y)),
cirq.AxisAngleDecomposition(angle=np.pi, axis=(0, 1, 0), global_phase=1j),
atol=1e-8,
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.Z)),
cirq.AxisAngleDecomposition(angle=np.pi, axis=(0, 0, 1), global_phase=1j),
atol=1e-8,
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.H)),
cirq.AxisAngleDecomposition(
angle=np.pi, axis=(np.sqrt(0.5), 0, np.sqrt(0.5)), global_phase=1j
),
atol=1e-8,
)
assert cirq.approx_eq(
cirq.axis_angle(cirq.unitary(cirq.H ** 0.5)),
cirq.AxisAngleDecomposition(
angle=np.pi / 2,
axis=(np.sqrt(0.5), 0, np.sqrt(0.5)),
global_phase=np.exp(1j * np.pi / 4),
),
atol=1e-8,
)
def test_axis_angle_decomposition_str():
assert str(cirq.axis_angle(cirq.unitary(cirq.X))) == '1*π around X'
assert str(cirq.axis_angle(cirq.unitary(cirq.Y))) == '1*π around Y'
assert str(cirq.axis_angle(cirq.unitary(cirq.Z))) == '1*π around Z'
assert str(cirq.axis_angle(cirq.unitary(
cirq.H))) == '1*π around 0.707*X+0.707*Z'
assert str(cirq.axis_angle(cirq.unitary(
cirq.H**0.5))) == '0.5*π around 0.707*X+0.707*Z'
assert str(
cirq.axis_angle(
cirq.unitary(cirq.X**0.25) @ cirq.unitary(cirq.Y**0.25)
@ cirq.unitary(cirq.Z**
0.25))) == '0.477*π around 0.679*X+0.281*Y+0.679*Z'
def test_axis_angle_decomposition_unitary():
u = cirq.testing.random_unitary(2)
u = cirq.unitary(cirq.T)
a = cirq.axis_angle(u)
np.testing.assert_allclose(u, cirq.unitary(a), atol=1e-8)
