Support different representations for SuperOperator

[ytdHuang]

In QuTiP, the superoperators have different representations:

• general representation
• Choi representation
• Kraus representation
• Stinespring representation
• Chi representation

Maybe we can make a new abstract type AbstractSuperRepresentation, and re-define the superoperator:

abstract type AbstractSuperRepresentation end

struct GeneralSuperRepresentation <: AbstractSuperRepresentation end
struct ChoiSuperRepresentation <: AbstractSuperRepresentation end
struct KrausSuperRepresentation <: AbstractSuperRepresentation end
struct StinespringSuperRepresentation <: AbstractSuperRepresentation end
struct ChiSuperRepresentation <: AbstractSuperRepresentation end

struct SuperOperatorQuantumObject <: QuantumObjectType
    superrep::AbstractSuperRepresentation
end

# default representation
SuperOperatorQuantumObject() = SuperOperatorQuantumObject(GeneralSuperRepresentation())

const SuperOperator = SuperOperatorQuantumObject()
const ChoiSuperOperator = SuperOperatorQuantumObject(ChoiSuperRepresentation())
const KrausSuperOperator = SuperOperatorQuantumObject(KrausSuperRepresentation())
const StinespringSuperOperator = SuperOperatorQuantumObject(StinespringSuperRepresentation())
const ChiSuperOperator = SuperOperatorQuantumObject(ChiSuperRepresentation())

When the users apply the basic operations (:+, :-, :*) between GeneralSuperRepresentation and other representation, it should work. However, if the users apply them on different representations, it should print a warning message just like qutip.

function Base.:(==)(S1::SuperOperatorQuantumObject, S2::SuperOperatorQuantumObject)
    if (S1 != S2)
        if !(S1 == SuperOperator || S2 == SuperOperator)
            # print warning
        end
    end
    return true
end

Also need to define some new functions same as qutip:

• superrep(Q) (return superrep of Qobj)
• to_super(Q)
• to_choi(Q)
• to_kraus(Q)
• to_stinespring(Q)
• to_chi(Q)
• iscp(Q)
• istp(Q)
• ishp(Q)
• iscptp(Q)