Add an AdaptVQEUCCFactory

[mrossinek]

What should we add?

With the AdaptVQE algorithm being migrated to Terra (Qiskit/qiskit#7930), we should add a factory class to Nature which can leverage this algorithm in combination with the at-runtime constructed UCC ansatz. The same could be done for the UVCC case.

[Unathi-Skosana]

Hi @mrossinek, I would like to work on this. Just one question, do you expect the AdaptVQE factories to inherit from VQEUCCFactory and VQEUVCCFactory respectively or directly from the base MinimumEigensolverFactory?

[mrossinek]

I have some entirely new ideas on how to handle this kind of factories. I will update later next week 👍

[mrossinek]

I am putting this issue on hold for now, because the concept of the algorithm factories is a bit outdated. Now that all problem specific information is available before we pass it into the solver (i.e. it is in its final transformed form), the need for a factory to inject runtime information is not as high any more.

To be more specific: the data problem.num_particles, problem.num_spatial_orbitals is correctly known upfront and will not change under some transform.
The qubit_converter objects are still undergoing a refactoring so it is a bit hard to predict what these will look like in terms of their stateful contents (see #967).

However, there are still some aspects which could be usefully set on algorithms at runtime:

• the initial_point for variational algorithms
• potentially the ansatz bounds (see also Default bounds for UCC ansatz circuits #818)

With all that said, I would also like to point out that we do not want to start adding factories for every algorithm in Terra, especially not with all the combinatorial options for various ansatze. Maybe a new design needs to be found which supersedes this factory style, but until the QubitConverter refactoring is done, I am putting this on hold.