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