Add falqon algorithm to qiskit-terra

[tpecyna]

Summary

To add the Feedback-based quantum optimization (falqon) algorithm (arxiv.)

Details and comments

I lack the falqon algorithm in qiskit. I've written my own little version based on other implementations and I would like to adjust it so I can contribute do qiskit-terra. I am asking for suggestions on the next steps to be taken.

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[woodsp-ibm]

Hi. At present the existing algorithms in Qiskit Terra are being refactored to use the primitives (samplers and estimators) that have been introduced to Qiskit (existing algorithms are all being marked pending deprecation and will later be deprecated and removed). For instance VQE, QAOA are refactored here #8702 and #8669 and you might like to take a look to see if/how this algorithm you have implemented can be done using such primitives. Also as a minimum eigen solver the algorithm should implement the MinimumEigensolver interface to allow any upper level applications to use the algorithm in a standard way via that interface. You can see this in the referenced PRs where VQE etc implement this interface and pass back a given result type, although they can extend the result class and add algorithm result specifics.