Add falqon algorithm to qiskit-terra

[tpecyna]

Summary

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

Details and comments

I had to close the previous issue #8751 for some reason. I've implemented into the algorithm the Estimator primitive and the MinimumEigensolver interface. Now I have the following questions:

1. Falqon algorithm works in a simple iteration loop, in which it measures an ansatz with some commutator operator, then it multiplies the expval by $-1$ and finally uses the result as one of the parameters of the next circuit of length $i+1$. For longer circuits it takes more time to run them so there is a high probability that users will always want to track the intermediate results:
   a) should this main loop remain to be implemented inside the falqon class and handling of the intermediate results be left to a callback function implemented by users,
   b) or should the simple loop be left for implementation by the users, and the class would then only contain building ansatz and making measurements?
2. In case of QAOA we pass Sampler, and then DiagonalEstimator is created, so we can have both the eigenvalue and the eigenstate. In Falqon we can't use the DiagonalEstimator because the commutator Hamiltonian is not diagonal. How to manage that? Should the class constructor ask for both Sampler and Estimator?

Thanks

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[woodsp-ibm]

Thank you for your interest in contributing to Qiskit. It has however been decided that the algorithms are to be moved out of Qiskit (see #10406) and the plan is a new community repository that will contain these going forwards. As such I am going to close this PR as it stands.

If you still have interest in pursuing this then might I suggest a community project in the ecosystem for this. See https://qiskit.org/ecosystem/ and follow/click the "Join the ecosystem" for more information on what that would entail.