def _decompose_outside_control(
self, control: 'cirq.Qid', near_target: 'cirq.Qid', far_target: 'cirq.Qid'
) -> 'cirq.OP_TREE':
"""A decomposition assuming one of the targets is in the middle.
control: ───T──────@────────@───@────────────@────────────────
│ │ │ │
near: ─X─T──────X─@─T^-1─X─@─X────@─X^0.5─X─@─X^0.5────────
│ │ │ │ │
far: ─@─Y^-0.5─T─X─T──────X─T^-1─X─T^-1────X─S─────X^-0.5─
"""
a, b, c = control, near_target, far_target
t = common_gates.T
sweep_abc = [common_gates.CNOT(a, b), common_gates.CNOT(b, c)]
yield common_gates.CNOT(c, b)
yield pauli_gates.Y(c) ** -0.5
yield t(a), t(b), t(c)
yield sweep_abc
yield t(b) ** -1, t(c)
yield sweep_abc
yield t(c) ** -1
yield sweep_abc
yield t(c) ** -1
yield pauli_gates.X(b) ** 0.5
yield sweep_abc
yield common_gates.S(c)
yield pauli_gates.X(b) ** 0.5
yield pauli_gates.X(c) ** -0.5
def __pow__(self, exponent: int) -> 'LinearCombinationOfOperations':
if not isinstance(exponent, int):
return NotImplemented
if exponent < 0:
return NotImplemented
if len(self.qubits) != 1:
return NotImplemented
qubit = self.qubits[0]
i = identity.I(qubit)
x = pauli_gates.X(qubit)
y = pauli_gates.Y(qubit)
z = pauli_gates.Z(qubit)
pauli_basis = {i, x, y, z}
if not set(self.keys()).issubset(pauli_basis):
return NotImplemented
ai, ax, ay, az = self[i], self[x], self[y], self[z]
bi, bx, by, bz = operator_spaces.pow_pauli_combination(ai, ax, ay, az, exponent)
return LinearCombinationOfOperations({i: bi, x: bx, y: by, z: bz})
