Support OperatorBraQuantumObject and OperatorKetQuantumObject

[ytdHuang]

Solve #37

TODO list (I definitely miss something, let me know and I will add to the list):

• define abstract type OperatorBraQuantumObject <: QuantumObjectType end (8994e7d)
• define abstract type OperatorKetQuantumObject <: QuantumObjectType end (8994e7d)
• method show for above new types (8994e7d)
• define isoperbra() (8994e7d)
• define isoperket() (8994e7d)
• QuantumObject constructors for OperatorKet and OperatorBra (0060fff)
• check if the basic operations still works: :(+), :(-), :(*) (0060fff)
• make mat2vec(Operator) -> OperatorKet (0096192)
• make vec2mat(OperatorKet) -> Operator (0096192)
• make adjoint(OperatorKet) -> OperatorBra (0060fff)
• make adjoint(OperatorBra) -> OperatorKet (0060fff)
• support Base.conj() for all QuantumObjectType (0060fff)
• support SuperOperator * Operator -> Operator (0060fff)
• support SuperOperator * OperatorKet -> OperatorKet (0060fff)
• support OperatorBra * SuperOperator -> OperatorBra (0060fff)
• support OperatorBra * OperatorKet -> Number (0060fff)
• support dot(OperatorKet, OperatorKet) -> Number (0060fff)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 89.23%. Comparing base (7cd969c) to head (0060fff).

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #44      +/-   ##
==========================================
+ Coverage   89.03%   89.23%   +0.19%     
==========================================
  Files          18       18              
  Lines        1660     1690      +30     
==========================================
+ Hits         1478     1508      +30     
  Misses        182      182              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[albertomercurio]

Why don't we include also the met2vec and vec2mat functionalities? I think this should be easy to implement, am I right? Aside from that, everything seems great.

[ytdHuang]

Ahh, I was thinking cause the origin mat2vec and vec2mat only support standard matrices but not QuantumObject.

Maybe we can keep the origin methods, but also add new methods for just QuantumObject:

mat2vec(A::QuantumObject{<:AbstractArray{T},OperatorQuantumObject}) where {T} = QuantumObject(mat2vec(A.data), OperatorKetQuantumObject, A.dims)

vec2mat(A::QuantumObject{<:AbstractArray{T},OperatorKetQuantumObject}) where {T} = QuantumObject(vec2mat(A.data), OperatorQuantumObject, A.dims)

I will add this and also the corresponding runtests

[albertomercurio]

Yes, that's what I had in mind.