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Computes non-negative integer power of single-qubit Pauli combination.
cirq.linalg.pow_pauli_combination(
ai: cirq.value.Scalar
,
ax: cirq.value.Scalar
,
ay: cirq.value.Scalar
,
az: cirq.value.Scalar
,
exponent: int
) -> Tuple[cirq.value.Scalar
, cirq.value.Scalar
, cirq.value.Scalar
, cirq.value.Scalar
]
Returns scalar coefficients bi, bx, by, bz such that
bi I + bx X + by Y + bz Z = (ai I + ax X + ay Y + az Z)^exponent
Correctness of the formulas below follows from the binomial expansion and the fact that for any real or complex vector (ax, ay, az) and any non-negative integer k:
[ax X + ay Y + az Z]^(2k) = (ax^2 + ay^2 + az^2)^k I