Hybrid QAOA

[Dariusz Lasecki (dlasecki)]

This PR adds a library with the Quantum Approximate Optimization Algorithm (QAOA) written in Q#. It supports problems that can be encoded into 1-local and/or 2-local Hamiltonians. Additionally, it offers a hybrid QAOA algorithm in Q# and C# that uses a gradient-free Cobyla optimizer to choose optimal parameters for the QAOA in the form of a feedback loop. The hybrid QAOA supports interoperability with Python by a magic command. Values of parameters during the execution of the hybrid QAOA can be logged into a file.

[Guen Prawiroatmodjo (guenp)]

Thanks Dariusz Lasecki (@dlasecki), who did you email?

[Dariusz Lasecki (dlasecki)]

Thanks Dariusz Lasecki (@dlasecki), who did you email?

Yourself but not directly. :)

[Cassandra Granade (cgranade)]

Thanks for your patience as I complete my second round; I think it's a lot closer in its current state, so thank you for all of your changes! If there's anything I can do to help expand on or clarify comments, please let me know. Thank you so much!

[Dariusz Lasecki (dlasecki)]

Guen Prawiroatmodjo (@guenp) Was the document that I shared with you helpful?
In any case, I would be happy to join you all in a call to discuss the contribution, potential improvements or questions if you have any.

Regards,
Dariusz.

[Guen Prawiroatmodjo (guenp)]

Thanks, Dariusz Lasecki (@dlasecki) for this contribution! Linking the original issue: #209

We are currently following up internally how to move forward with this PR. Thanks for your patience.

[Dariusz Lasecki (dlasecki)]

Hi Guen Prawiroatmodjo (@guenp) Cassandra Granade (@cgranade),

I wanted to follow up on this PR and your internal discussions. Shall we discuss the big picture of how such optimization algorithms might be provided in Q# and possibly adjust/improve/extend this contribution to fit this vision or shall we think about delivering it to examples?