Comparisons

Functions for comparing multiple quantum states. More...

Functions
qreal	calcDistance (Qureg qureg1, Qureg qureg2)
qreal	calcFidelity (Qureg qureg, Qureg other)
qcomp	calcInnerProduct (Qureg qureg1, Qureg qureg2)

Detailed Description

Functions for comparing multiple quantum states.

Function Documentation

calcDistance()

qreal calcDistance	(	Qureg	qureg1,
		Qureg	qureg2 )

Note

Documentation for this function or struct is under construction!

Attention

This function's input validation has not yet been tested, so erroneous usage may produce unexpected output. Please use with caution!

Definition at line 326 of file calculations.cpp.

                                               {
    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);
        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);
 
        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);
}

Referenced by TEST_CASE().

calcFidelity()

qreal calcFidelity	(	Qureg	qureg,
		Qureg	other )

Note

Documentation for this function or struct is under construction!

Attention

This function's input validation has not yet been tested, so erroneous usage may produce unexpected output. Please use with caution!

Definition at line 298 of file calculations.cpp.

                                               {
    validate_quregFields(quregA, __func__);
    validate_quregFields(quregB, __func__);
    validate_quregsCanBeProducted(quregA, quregB, __func__);
 
    bool isDensA = quregA.isDensityMatrix;
    bool isDensB = quregB.isDensityMatrix;
 
    // F(rho,sigma) not yet supported
    if (isDensA && isDensB)
        validate_throwErrorBecauseCalcFidOfDensMatrNotYetImplemented(__func__);
 
    // |<A|B>|^2
    if (!isDensA && !isDensB) {
        qcomp prod = localiser_statevec_calcInnerProduct(quregA, quregB);
        return std::norm(prod);
    }
 
    // Re[<B|A|B>] or Re[<A|B|A>]
    qcomp fid = (quregA.isDensityMatrix)?
        localiser_densmatr_calcFidelityWithPureState(quregA, quregB, false): // no conj
        localiser_densmatr_calcFidelityWithPureState(quregB, quregA, false); // no conj
 
    validate_fidelityIsReal(fid, __func__);
    return std::real(fid);
}

Referenced by TEST_CASE(), and TEST_CASE().

calcInnerProduct()

qcomp calcInnerProduct	(	Qureg	qureg1,
		Qureg	qureg2 )

Note

Documentation for this function or struct is under construction!

Attention

This function's input validation has not yet been tested, so erroneous usage may produce unexpected output. Please use with caution!

Definition at line 44 of file calculations.cpp.

                                                   {
    validate_quregFields(quregA, __func__);
    validate_quregFields(quregB, __func__);
    validate_quregsCanBeProducted(quregA, quregB, __func__);
 
    // <A|B> or Tr(A^dagger B) = <<A|B>>
    if (quregA.isDensityMatrix == quregB.isDensityMatrix)
        return localiser_statevec_calcInnerProduct(quregA, quregB);
 
    return (quregA.isDensityMatrix)?
        localiser_densmatr_calcFidelityWithPureState(quregA, quregB, true):  // <B|A^dagger|B>
        localiser_densmatr_calcFidelityWithPureState(quregB, quregA, false); // <A|B|A>
}

Referenced by TEST_CASE(), and TEST_CASE().