Feature: Random superoperator (quantum channel)

[vprusso]

Add the ability to randomly generate a quantum channel (i.e. superoperator).

The following could be used as a reference that is implemented in MATLAB:
https://github.com/nathanieljohnston/QETLAB/blob/master/RandomSuperoperator.m

Related #849

[Shivansh20128]

Hi @vprusso ! Can I work on this? Also, it would be great if I could do this under KWOC 2024.
Thanks

[vprusso]

Hi @Shivansh20128 ,

You are welcome to work on it! Keep in mind that #848 would be needed as a prerequisite. There is currently a PR (in progress) up that I haven't had time to work on that attempts to implement this (#849). Hopefully, that's a helpful start!

[Shivansh20128]

Okay. I noticed that your PR is failing the tests. Shall I look into Sinkhorn Operator too if you need any help? Or should I wait for you before working on this?

[vprusso]

I likely won't have time to get to this one any time soon, so if you'd like to hijack that MR and fix the tests, that would likely be a prerequisite to being able to generate random quantum channels (as is done in the QETLAB code, for instance).

[Shivansh20128]

Okay, I will look into it. Is the OperatorSinkhorn function implemented correctly? If yes, then I won't look into it and directly move to the tests.

[vprusso]

I believe it does, but I think one would need to still thoroughly check whether this is the case. I would use what is on that PR more as a starting point, but a starting point to still be skeptical and thorough with just to ensure it's computing the right value.

It may also be worthwhile to concoct specific inputs from QETLAB and ensure that these are replicated in toqito as well to ensure that these are yielding consistent results.

[Shivansh20128]

Okay, I'll do that. Thank you.