Attribute functions operating on Qobj

[ytdHuang]

close #148

This PR supports most of the attribute functions in Python qutip.Qobj class.

Summary of this PR:

• add missing @doc raw in front of each docstirings.
• add missing docstrings for several LinearAlgebra functions
• always throw DimensionMismatch exception if A.dims != B.dims
• introduce isherm (same as LinearAlgebra.ishermitian)
• support generalized LinearAlgebra.dot(i, A, j): returns $\langle i | A | j \rangle$
  • if A is in the type of Operator, i and j need to be Ket
  • if A is in the type of SuperOperator, i and j need to be OperatorKet
• introduce matrix_element(i, A, j) (same as LinearAlgebra.dot(i, A, j))
• introduce trans (same as LinearAlgebra.transpose)
• introduce dag (same as LinearAlgebra.adjoint)
• introduce unit (same as LinearAlgebra.normalize)
• allow normalize(A, p) and normalize!(A, p) to normalize the QuantumObject so that p-norm of A equals to unity. Support for the following types of QuantumObject:
  • If A is Ket or Bra, default p = 2
  • If A is Operator, default p = 1
• introduce expm (same as LinearAlgebra.exp)
• support LinearAlgebra.sin and LinearAlgebra.cos
• only support exp, expm, sin, sinm, cos, cosm for Operator and SuperOperator types of QuantumObject as input
• introduce LinearAlgebra.diag
• introduce LinearAlgebra.log and logm (same as LinearAlgebra.log)
• introduce purity: $\textrm{Tr}(\rho^2)$
• introduce proj: the projector of a Ket or Bra

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.89%. Comparing base (ce251c5) to head (ea57987).
Report is 3 commits behind head on main.

Additional details and impacted files

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+ Coverage   92.68%   92.89%   +0.21%     
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  Files          26       27       +1     
  Lines        1913     1956      +43     
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+ Hits         1773     1817      +44     
+ Misses        140      139       -1     

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[albertomercurio]

Can you convert also sinm and cosm to LinearAlgebra.sinandLinearAlgebra.cosand them putsinmandcosm` as synonyms?

[ytdHuang]

Ohh, I didn't notice that there is also matrix sin and cos in LinearAlgebra.
Will implement it right away !

[ytdHuang]

This could be more efficient compared to the original way

[albertomercurio]

No I don’t think that it will work with the LinearAlgebra functions, because we have sparse matrices, and (at least at the time) there wasn’t an implementation for such functions. That’s why I implemented the exp function by myself. When SparseArrays will export their exp sin cos functions, we can delete our definition of exp function.

What I mean here is to do the same as the exp case also for sin and cos, and then define sinm and cosm as synonyms.

[ytdHuang]

Okay, just to make sure I understand correctly, you mean:

LinearAlgebra.sin(A::QuantumObject) = (exp(1im * A) - exp(-1im * A)) / 2im
sinm(A::QuantumObject) = sin(A)

[albertomercurio]

I think that also isherm should be moved here

[ytdHuang]

sure, thanks for the reminder