cirq.pow_pauli_combination

Computes non-negative integer power of single-qubit Pauli combination.

cirq.pow_pauli_combination(
    ai: cirq.TParamValComplex,
    ax: cirq.TParamValComplex,
    ay: cirq.TParamValComplex,
    az: cirq.TParamValComplex,
    exponent: int
) -> tuple[cirq.TParamValComplex, cirq.TParamValComplex, cirq.TParamValComplex,
    cirq.TParamValComplex]

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