Function calcExpecFullStateDiagMatrPower

quest/src/api/calculations.cpp:185–215

qreal calcExpecFullStateDiagMatrPower(Qureg qureg, FullStateDiagMatr matrix, qreal exponent) {
    validate_quregFields(qureg, __func__);
    validate_matrixFields(matrix, __func__);
    validate_matrixAndQuregAreCompatible(matrix, qureg, true, __func__);
    validate_matrixExpIsHermitian(matrix, exponent, __func__);

    // the backend can use either the pow(qcomp,qcomp) or pow(qreal,qreal) overload;
    // the former is significantly less accurate when the base is real & negative and
    // the exponent is real, because complex pow(a,b) = exp(i b Arg(a)) = exp(i b 2 pi),
    // and the numerical error in pi is compounded by the exponent and the exp(). Because
    // this function assumes approx/intended Hermiticity, it will always use the real-pow
    // overload, discarding the imaginary components of 'matrix' during computation - this
    // is a behaviour unique to this function (other functions collect the erroneous
    // imaginary components before a final validation and discarding).
    const bool useRealPow = true;

    qcomp value = (qureg.isDensityMatrix)?
        localiser_densmatr_calcExpecFullStateDiagMatr(qureg, matrix, exponent, useRealPow):
        localiser_statevec_calcExpecFullStateDiagMatr(qureg, matrix, exponent, useRealPow);

    // is it impossible for the statevector routine to produce non-zero
    // imaginary components because of our use of real-pow, the result of
    // which is multiplied by abs(amp). Alas, density matrices multiply the
    // result with a complex scalar and can accrue erroneous imaginary
    // components when the density matrix is non-Hermitian, or due to rounding
    // errors. As such, we only post-validate density matrix values.
    if (qureg.isDensityMatrix)
        validate_densMatrExpecDiagMatrValueIsReal(value, exponent, __func__);

    return std::real(value);
}