Support different representations for `SuperOperator`

[ytdHuang]

In QuTiP, the superoperators have different representations:

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

Note that Kraus and Stinespring representations are just a list of Operators.

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 ChiSuperRepresentation <: AbstractSuperRepresentation end

struct SuperOperatorQuantumObject{T<:AbstractSuperRepresentation} <: QuantumObjectType
    superrep::T
end

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

const SuperOperator = SuperOperatorQuantumObject()
const ChoiSuperOperator = SuperOperatorQuantumObject(ChoiSuperRepresentation())
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.:(==)(::SuperOperatorQuantumObject{T1}, ::SuperOperatorQuantumObject{T2}) where {T1<:AbstractSuperRepresentation,T2<:AbstractSuperRepresentation}
    (T1 != T2) && @warn "warning message"
    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)

[ANUKOOL324]

allow me to look on this issue @ytdHuang

[ytdHuang]

@ANUKOOL324
Sure, but this issue was posted a long time before.

We now have modified the structure of QuantumObjectType, please refer to this source file.

Basically, we have already defined an

abstract SuperOperatorType <: QuantumObjectType

for different representation, and we currently only have

struct SuperOperator <: SuperOperatorType end

to represent the general superoperator representation.

I think you can start from defining

struct ChoiSuperOperator <: SuperOperatorType end
struct ChiSuperOperator <: SuperOperatorType end

[ytdHuang]

issue #270 is also the same topic