docs(notebooks): add QAOA transpiler guide

[a-matsuo]

Summary

Add a notebook that tells how to use a qaoa-specific transpiler which is useful for large QAOA circuits.

Details and comments

This notebook consists of the qaoa-specifc transpiler which is the swap strategy and initial mapping using SAT.

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[miamico]

Overall looking good! Some comments after a first read:

• Check that the notebook runs in a fresh virtual environment where only the packages specified by this repo's installation guide are installed (installing this repo from source) and qiskit 1.0
• Add a link to the Quantum Optimization Best Practices repo somewhere in the notebook
• The initial explanation of the Qiskit patterns (the 1,2,3,4 list at the beginning) is redundant, you are already providing the link and explaining them in the context of QAOA below. I think we can safely remove it

[a-matsuo]

Thank you for comments! I reflected those comments in the notebook. Could you please review it again?

[nathanearnestnoble]

Hello! Just did a closer read through!

• Very good structure, I think the patterns are clear!
• Appreciating showing how you can start from some qiskit functionality and then build from that with the q_opt_bestpractice repo! Great community contribution
• I personally like seeing a snapshot of the final sampled distribution, makes me see more of how hardware results translate to application results -- if others also likes seeing distributions, could be included as a '4.0 visualize final sampling'. Thoughts?
• I think many in the community would benefit from a strong 'state-of-the-art QAOA approach' example like this, lets try to publish on LP.

[nathanearnestnoble]

One more thought: The text is rather verbose when compared to some other published tutorials, but I think this is useful with respect to learning about the methods within. May be worth considering future updates to leave out edu content for tutorials and include this in other edu sections.

[miamico]

Taking a closer look at how we could resolve the current conflict due to the dependence on qopt_best_practices:

1. Add the code written for the SATMapper to our repo as a trasnpiler pass (similarly to what we've done for the twirling pass here )
2. Turn this tutorial into a how-to-guide showcasing the use of the SATMapper and SWAPstrategies to improve QAOA circuits. This boils down to Section 2.2 of the current notebook. This will allow us to avoid replicating tutorial content as the learning platform already hosts a tutorial on QAOA and Max-Cut. Additionally, we can define the problem as done in those notebook to avoid importing the definitions from qopt_best_practices

[eggerdj]

A few comments:

• regarding https://github.com/IBM-Quantum-Technical-Enablement/quantum-enablement/pull/13#issuecomment-2009877126 the SAT mapper is applied to a nx Graph, you could use a rustworkx instead or work with SparsePauliOp. Both would probably be fine. Also, I recommend having the SATMapper in a single place. If it has to move from qopt-best-practices to this repo that is fine. Note that wrapping the SATMapper into a transpiler pass might be tricky. Working on the circuit may be tricky. One way I could see this working is to have a transpiler pass that (i) extracts the cost_op from a QAOAAnsatz circuit instance and (ii) applies the SATMapper to that cost_op, then (iii) rebuilds the QAOAAnsatz circuit with the permuted cost_op. From there on, you can do the swap strategies as usual.
• This NB might be of interest for you: https://github.com/qiskit-community/qopt-best-practices/blob/main/demos/qiskit_patterns/2_qiskit_patterns.ipynb
• This NB may also help: https://github.com/qiskit-community/qopt-best-practices/pull/30

[miamico]

@a-matsuo I've made an example of how we could change this notebook to be approved and uploaded to the learning platform here. Please take a look and implement the same changes and any additional ones that you may think are needed.

[a-matsuo]

Hello everyone, I have removed the dependency on the qopt-best-practice repository from the notebook. Could you please review it again?

[miamico]

Also, please remove this notebook from the folder if redundant

[a-matsuo]

Thank you @miamico ! I fixed them. @pedrorrivero @nathanearnestnoble I have removed the dependency on the qopt-best-practice repository from the notebook. Could you please review it again?

[nathanearnestnoble]

Looks good -- good work @miamico and @a-matsuo !