def test_kron_factor_special_unitaries(f1, f2):
p = cirq.kron(f1, f2)
g, g1, g2 = cirq.kron_factor_4x4_to_2x2s(p)
assert np.allclose(cirq.kron(g1, g2), p)
assert abs(g - 1) < 0.000001
assert cirq.is_special_unitary(g1)
assert cirq.is_special_unitary(g2)
def test_kak_canonicalize_vector(x, y, z):
i = np.eye(2)
m = cirq.unitary(
cirq.KakDecomposition(
global_phase=1,
single_qubit_operations_after=(i, i),
interaction_coefficients=(x, y, z),
single_qubit_operations_before=(i, i),
))
kak = cirq.kak_canonicalize_vector(x, y, z, atol=1e-10)
a1, a0 = kak.single_qubit_operations_after
x2, y2, z2 = kak.interaction_coefficients
b1, b0 = kak.single_qubit_operations_before
m2 = cirq.unitary(kak)
assert 0.0 <= x2 <= np.pi / 4
assert 0.0 <= y2 <= np.pi / 4
assert -np.pi / 4 < z2 <= np.pi / 4
assert abs(x2) >= abs(y2) >= abs(z2)
assert x2 < np.pi / 4 - 1e-10 or z2 >= 0
assert cirq.is_special_unitary(a1)
assert cirq.is_special_unitary(a0)
assert cirq.is_special_unitary(b1)
assert cirq.is_special_unitary(b0)
assert np.allclose(m, m2)
def test_kron_factor_special_unitaries(f1, f2):
p = cirq.kron(f1, f2)
g, g1, g2 = cirq.kron_factor_4x4_to_2x2s(p)
assert np.allclose(cirq.kron(g1, g2), p)
assert abs(g - 1) < 0.000001
assert cirq.is_special_unitary(g1)
assert cirq.is_special_unitary(g2)
assert_kronecker_factorization_within_tolerance(p, g, g1, g2)
def recompose_so4(a: np.ndarray, b: np.ndarray) -> np.ndarray:
assert a.shape == (2, 2)
assert b.shape == (2, 2)
assert cirq.is_special_unitary(a)
assert cirq.is_special_unitary(b)
magic = np.array([[1, 0, 0, 1j], [0, 1j, 1, 0], [0, 1j, -1, 0], [1, 0, 0, -1j]]) * np.sqrt(0.5)
result = np.real(cirq.dot(np.conj(magic.T), cirq.kron(a, b), magic))
assert cirq.is_orthogonal(result)
return result
def recompose_so4(a: np.ndarray, b: np.ndarray) -> np.ndarray:
assert a.shape == (2, 2)
assert b.shape == (2, 2)
assert cirq.is_special_unitary(a)
assert cirq.is_special_unitary(b)
magic = np.array([[1, 0, 0, 1j],
[0, 1j, 1, 0],
[0, 1j, -1, 0],
[1, 0, 0, -1j]]) * np.sqrt(0.5)
result = np.real(cirq.dot(np.conj(magic.T),
cirq.kron(a, b),
magic))
assert cirq.is_orthogonal(result)
return result
def su_to_gates(m):
"""Decomposes two level special unitaries to Ry and Rz gates
Args:
m: Matrix to be converted into gates
Returns:
result: Returns list of gates to be applied
Raises:
AssertionError:
Matrix m is not a special unitary matrix
"""
assert cirq.is_special_unitary(m)
u00 = m[0, 0]
u01 = m[0, 1]
theta = np.arccos(np.abs(u00))
lmbda = np.angle(u00)
mu = np.angle(u01)
result = []
if np.abs(lmbda - mu) > 1e-9:
result.append(('Rz', lmbda - mu))
if np.abs(theta) > 1e-9:
result.append(('Ry', 2 * theta))
if np.abs(lmbda + mu) > 1e-9:
result.append(('Rz', lmbda + mu))
return result
def test_kak_canonicalize_vector(x, y, z):
i = np.eye(2)
m = recompose_kak(1, (i, i), (x, y, z), (i, i))
g, (a1, a0), (x2, y2, z2), (b1, b0) = cirq.kak_canonicalize_vector(
x, y, z)
m2 = recompose_kak(g, (a1, a0), (x2, y2, z2), (b1, b0))
assert 0.0 <= x2 <= np.pi / 4
assert 0.0 <= y2 <= np.pi / 4
assert -np.pi / 4 <= z2 <= np.pi / 4
assert abs(x2) >= abs(y2) >= abs(z2)
assert cirq.is_special_unitary(a1)
assert cirq.is_special_unitary(a0)
assert cirq.is_special_unitary(b1)
assert cirq.is_special_unitary(b0)
assert np.allclose(m, m2)
def test_is_special_unitary_tolerance():
atol = 0.5
# Pays attention to specified tolerance.
assert cirq.is_special_unitary(np.array([[1, 0], [-0.5, 1]]), atol=atol)
assert not cirq.is_special_unitary(np.array([[1, 0], [-0.6, 1]]), atol=atol)
assert cirq.is_special_unitary(np.array([[1, 0], [0, 1]]) * cmath.exp(1j * 0.1), atol=atol)
assert not cirq.is_special_unitary(np.array([[1, 0], [0, 1]]) * cmath.exp(1j * 0.3), atol=atol)
# Error isn't accumulated across entries, except for determinant factors.
assert cirq.is_special_unitary(np.array([[1.2, 0, 0], [0, 1.2, 0], [0, 0, 1 / 1.2]]), atol=atol)
assert not cirq.is_special_unitary(np.array([[1.2, 0, 0], [0, 1.2, 0], [0, 0, 1.2]]), atol=atol)
assert not cirq.is_special_unitary(
np.array([[1.2, 0, 0], [0, 1.3, 0], [0, 0, 1 / 1.2]]), atol=atol
)
def test_to_special():
u = cirq.testing.random_unitary(4)
su = cirq.to_special(u)
assert not cirq.is_special_unitary(u)
assert cirq.is_special_unitary(su)
def test_is_special_unitary():
assert cirq.is_special_unitary(np.empty((0, 0)))
assert not cirq.is_special_unitary(np.empty((1, 0)))
assert not cirq.is_special_unitary(np.empty((0, 1)))
assert cirq.is_special_unitary(np.array([[1]]))
assert not cirq.is_special_unitary(np.array([[-1]]))
assert not cirq.is_special_unitary(np.array([[5]]))
assert not cirq.is_special_unitary(np.array([[3j]]))
assert not cirq.is_special_unitary(np.array([[1, 0], [0, -2]]))
assert not cirq.is_special_unitary(np.array([[1, 0], [0, -1]]))
assert cirq.is_special_unitary(np.array([[-1, 0], [0, -1]]))
assert not cirq.is_special_unitary(np.array([[1j, 0], [0, 1]]))
assert cirq.is_special_unitary(np.array([[1j, 0], [0, -1j]]))
assert not cirq.is_special_unitary(np.array([[1, 0], [1, 1]]))
assert not cirq.is_special_unitary(np.array([[1, 1], [0, 1]]))
assert not cirq.is_special_unitary(np.array([[1, 1], [1, 1]]))
assert not cirq.is_special_unitary(np.array([[1, -1], [1, 1]]))
assert cirq.is_special_unitary(np.array([[1, -1], [1, 1]]) * np.sqrt(0.5))
assert cirq.is_special_unitary(np.array([[1, 1j], [1j, 1]]) * np.sqrt(0.5))
assert not cirq.is_special_unitary(
np.array([[1, -1j], [1j, 1]]) * np.sqrt(0.5))
assert cirq.is_special_unitary(
np.array([[1, 1j + 1e-11], [1j, 1 + 1j * 1e-9]]) * np.sqrt(0.5))
