Add Support for Rectangular SuperOperators

[Gavin-Rockwood]

Problem Description

In Qutip, I can create an $m \times n$ operator (such as a projection operator to project an $m$-dimensional state onto an $n$-dimensional subspace.

In order to do this currently, I need to extract the operator data, create a rectangular matrix, perform the necessary projections and then convert the final states / operators back into QuantumObjects.

Proposed Solution

The solution would be to allow the dim property to be either a 1D object for square operators or a pair of 1D objects for the left and right dimensions.

Alternate Solutions

No response

Additional Context

If sesolve/mesolve are extended to be able to evolve operators as a way to parallel evolve individual states, adding support for rectangular operators would allow for simultaneously evolving a handful of states as a single inplace ODE.

[albertomercurio]

Isn't this already working?

julia> data = rand(10, 8)
10×8 Matrix{Float64}:
 0.759253   0.513553   0.104768   0.605576    0.385391    0.0721597  0.180857   0.209894
 0.0934312  0.783052   0.50667    0.521443    0.663961    0.195585   0.208451   0.421421
 0.413533   0.608761   0.172731   0.789588    0.994341    0.96397    0.708587   0.520189
 0.877283   0.0212204  0.257026   0.189644    0.0187765   0.151057   0.0976282  0.638085
 0.745253   0.957868   0.020984   0.00592926  0.326993    0.967402   0.560682   0.254069
 0.658104   0.935406   0.515224   0.464243    0.00465439  0.529362   0.672316   0.873836
 0.0873381  0.902495   0.93655    0.0711005   0.194348    0.455316   0.845208   0.762882
 0.900537   0.591468   0.207572   0.728387    0.0314672   0.141946   0.69252    0.679833
 0.773779   0.5473     0.0763737  0.627195    0.16568     0.808949   0.0728314  0.778413
 0.0918927  0.257606   0.399639   0.603102    0.602523    0.756807   0.834671   0.894916

julia> QuantumObject(data)

Quantum Object:   type=Operator()   dims=[[10], [8]]   size=(10, 8)   ishermitian=false
10×8 Matrix{Float64}:
 0.759253   0.513553   0.104768   0.605576    0.385391    0.0721597  0.180857   0.209894
 0.0934312  0.783052   0.50667    0.521443    0.663961    0.195585   0.208451   0.421421
 0.413533   0.608761   0.172731   0.789588    0.994341    0.96397    0.708587   0.520189
 0.877283   0.0212204  0.257026   0.189644    0.0187765   0.151057   0.0976282  0.638085
 0.745253   0.957868   0.020984   0.00592926  0.326993    0.967402   0.560682   0.254069
 0.658104   0.935406   0.515224   0.464243    0.00465439  0.529362   0.672316   0.873836
 0.0873381  0.902495   0.93655    0.0711005   0.194348    0.455316   0.845208   0.762882
 0.900537   0.591468   0.207572   0.728387    0.0314672   0.141946   0.69252    0.679833
 0.773779   0.5473     0.0763737  0.627195    0.16568     0.808949   0.0728314  0.778413
 0.0918927  0.257606   0.399639   0.603102    0.602523    0.756807   0.834671   0.894916

[Gavin-Rockwood]

Oh sorry, my bad, this does't work SuperOperators (which i know is a bit niche). Qobj(rand(4,4), type = SuperOperator()) will produce a dim=2 4x4 SuperOperator. But I cannot create a $4\times n$ SuperOperator.

However, there was a few instances where I was working with rectangular operators and check_dimensions was called for an operation that should have gone through. I had to revert to doing all the operations with the data and then rebuilding the Qobj at the end. I am having issues reproducing the bug but if I get it working again I will post a minimal working model.

[albertomercurio]

I see, I agree that with superoperators it becomes harder.

It is something that I'm planning to do.