def decompose_rotation(self) -> Sequence[Tuple[Pauli, int]]:
"""Decomposes this clifford into a series of pauli rotations.
Each rotation is given as a tuple of (axis, quarter_turns),
where axis is a Pauli giving the axis to rotate about. The
result will be a sequence of zero, one, or two rotations.
Note that the combined unitary effect of these rotations may
differ from cirq.unitary(self) by a global phase.
"""
x_rot = self.pauli_tuple(pauli_gates.X)
y_rot = self.pauli_tuple(pauli_gates.Y)
z_rot = self.pauli_tuple(pauli_gates.Z)
whole_arr = (
x_rot[0] == pauli_gates.X,
y_rot[0] == pauli_gates.Y,
z_rot[0] == pauli_gates.Z,
)
num_whole = sum(whole_arr)
flip_arr = (x_rot[1], y_rot[1], z_rot[1])
num_flip = sum(flip_arr)
if num_whole == 3:
if num_flip == 0:
# Gate is identity
return []
# 180 rotation about some axis
pauli = Pauli.by_index(flip_arr.index(False))
return [(pauli, 2)]
if num_whole == 1:
index = whole_arr.index(True)
pauli = Pauli.by_index(index)
next_pauli = Pauli.by_index(index + 1)
flip = flip_arr[index]
output = []
if flip:
# 180 degree rotation
output.append((next_pauli, 2))
# 90 degree rotation about some axis
if self.pauli_tuple(next_pauli)[1]:
# Negative 90 degree rotation
output.append((pauli, -1))
else:
# Positive 90 degree rotation
output.append((pauli, 1))
return output
elif num_whole == 0:
# Gate is a 120 degree rotation
if x_rot[0] == pauli_gates.Y:
return [
(pauli_gates.X, -1 if y_rot[1] else 1),
(pauli_gates.Z, -1 if x_rot[1] else 1),
]
return [(pauli_gates.Z, 1 if y_rot[1] else -1), (pauli_gates.X, 1 if z_rot[1] else -1)]
# coverage: ignore
assert (
False
), 'Impossible condition where this gate only rotates one Pauli to a different Pauli.'
def decompose_rotation(self) -> Sequence[Tuple[Pauli, int]]:
"""Returns ((first_rotation_axis, first_rotation_quarter_turns), ...)
This is a sequence of zero, one, or two rotations."""
x_rot = self.transform(pauli_gates.X)
y_rot = self.transform(pauli_gates.Y)
z_rot = self.transform(pauli_gates.Z)
whole_arr = (
x_rot.to == pauli_gates.X,
y_rot.to == pauli_gates.Y,
z_rot.to == pauli_gates.Z,
)
num_whole = sum(whole_arr)
flip_arr = (x_rot.flip, y_rot.flip, z_rot.flip)
num_flip = sum(flip_arr)
if num_whole == 3:
if num_flip == 0:
# Gate is identity
return []
# 180 rotation about some axis
pauli = Pauli.by_index(flip_arr.index(False))
return [(pauli, 2)]
if num_whole == 1:
index = whole_arr.index(True)
pauli = Pauli.by_index(index)
next_pauli = Pauli.by_index(index + 1)
flip = flip_arr[index]
output = []
if flip:
# 180 degree rotation
output.append((next_pauli, 2))
# 90 degree rotation about some axis
if self.transform(next_pauli).flip:
# Negative 90 degree rotation
output.append((pauli, -1))
else:
# Positive 90 degree rotation
output.append((pauli, 1))
return output
elif num_whole == 0:
# Gate is a 120 degree rotation
if x_rot.to == pauli_gates.Y:
return [
(pauli_gates.X, -1 if y_rot.flip else 1),
(pauli_gates.Z, -1 if x_rot.flip else 1),
]
return [
(pauli_gates.Z, 1 if y_rot.flip else -1),
(pauli_gates.X, 1 if z_rot.flip else -1),
]
# coverage: ignore
assert (
False
), 'Impossible condition where this gate only rotates one Pauli to a different Pauli.'
