Function calcDistance

quest/src/api/calculations.cpp:331–364

qreal calcDistance(Qureg quregA, Qureg quregB) {
    validate_quregFields(quregA, __func__);
    validate_quregFields(quregB, __func__);
    validate_quregsCanBeProducted(quregA, quregB, __func__);

    bool isDensA = quregA.isDensityMatrix;
    bool isDensB = quregB.isDensityMatrix;

    // Hilbert-Schmidt = sqrt( Tr((A-B)(A-B)^dagger) = sqrt(sum_ij |A_ij - B_ij|^2)
    if (isDensA && isDensB) {
        qreal dif = localiser_densmatr_calcHilbertSchmidtDistance(quregA, quregB); // >= 0
        return std::sqrt(dif);
    }

    // Bures = sqrt(2 - 2 |<A|B>|) (even when unnormalised)
    if (!isDensA && !isDensB) {
        qcomp prod = localiser_statevec_calcInnerProduct(quregA, quregB);
        qreal mag = std::abs(prod); // >= 0

        validate_buresDistanceInnerProdIsNormalised(mag, __func__);
        mag = (mag > 1)? 1 : mag; // forgive eps error to avoid complex
        return std::sqrt(2 - 2 * mag);
    }

    // purified distance = sqrt(1 - <psi|rho|psi>)
    qcomp fid = (quregA.isDensityMatrix)?
        localiser_densmatr_calcFidelityWithPureState(quregA, quregB, false): // no conj
        localiser_densmatr_calcFidelityWithPureState(quregB, quregA, false); // no conj

    validate_purifiedDistanceIsNormalised(fid, __func__); 
    qreal re = std::real(fid);
    re = (re > 1)? 1 : re; // forgive eps error to avoid complex
    return std::sqrt(1 - re);
}