GKLS TUTORIAL FILES

[carlos-rib]

Summary

This is a tutorial file which goal is, by using the vectorization method, make a GKLS time evolution using Krylov method, as symbolic as possible.

Checklist

• I only changed files under docs/contributions/.
• New/updated files and folders under docs/contributions/ use kebab-case names.
• I ran npm run build locally and it succeeded.
• I verified links and references in the changed docs pages.
• I reviewed formatting and readability.

Notes for Reviewers

Since I dived the code in some utility layers and run layers, I hyperlinked the full code files in some part of the text for my own GitHub page. I don't know whether this is okay, but this is still a work in progress, just for the sake of visibility.

[AlexandreFoley]

Regarding you aleph scripts: for our own ability to make promises regarding long-term availability of your contribution we will have to bring copies, and link to those copies in the tutorial. You can always submit updates to it if you believe it is worth the hassle!

Overall, I think this is a really good tutorial, well written and clearly explained. The accompanying code is well organized.

The validations could be done using the aleph test framework. Its been made public fairly recently, so it probably wasn't available when you began working on this.
See https://docs.kotharcomputing.com/docs/aleph-101#testing .
Don't feel obligated to make that change.

So a few corrections and whatever is needed to make the ci pass afterwards (I'll help with that), and then it's good to go!

Thank you for sharing that with us!

[AlexandreFoley]

I would go further: the choice of row stacking is not even mathematically special; indeed, its just a choice of basis for the size $d^2$ vector space of quantum operators. One could change basis at any moment, using a unitary transform in that vector space.

As usual, the choice of basis can have great numerical consequences, especially with sparse numerical methods.

[carlos-rib]

Good point! I updated the note to say this is a basis choice in operator space, not something mathematically special, while keeping the warning about numerical consequences.

[AlexandreFoley]

I'm used to calling Liouvillian only the coherent part of the super-operator, and calling Lindbladian the Liouvillian augmented with dissipative term. But that may be because i'm not all that fluent in the domain of dissipative quantum systems.

[carlos-rib]

Thanks for that point! To make things more background-agnostic, I added a short convention note there. I’ll use “Liouvillian” for the full Liouville-space generator in this tutorial, but I now explicitly mention that “Lindbladian” is also used for the full GKLS generator, and that the coherent/Hamiltonian part can be separated when needed.

[carlos-rib]

Hey, Alexandre! Thanks a lot for the careful review, and also for the kind words about the tutorial and code organization. I’ll be going through the direct fixes now.

I’m also interested in the Aleph test framework point. I saw the test_section / test syntax in the docs, and I’d be happy to convert the validation layer to native Aleph tests either in this PR or in a follow-up, depending on what you think is cleaner for the contribution.

On the Born approximation comment: I see your point about the wording being confusing. I had in mind the usual weak-coupling/factorized-state step in the open-systems derivation, but I agree the way I phrased it mixes terminology too much. I’ll rewrite that part in safer language rather than trying to name the approximation too aggressively.

[AlexandreFoley]

I had to make quite a few changes to make the CI "build the webpage" part of the continuous integration test work.
The CI task themselves were untested it seems.
Those changes make the scope check test fail. That's normal and will have to be ignored this time.
Everything looks good as far as i'm concerned, but web development is much more alien to me than Lindbladians, So we'll wait on Julien to check that part.

[julienblin-kothar]

Thanks a lot @carlos-rib !

And sorry again about the missing files in the repo. You ended up being our guinea pig, and a great one at that.
I made a few small edits to the author format, and I’m approving and merging this now.

I’ll let you know as soon as it’s live on our official docs website.

[julienblin-kothar]

Great news @carlos-rib, your contribution is now live on our official docs website!

https://docs.kotharcomputing.com/docs/contributions/gkls-vec-tutorial

Thanks again for being our first external contributor. Really happy to have this up!