Should the LUCJ ansatz be moved from ffsim to qiskit?

[kevinsung]

ffsim includes a qiskit module that you can use to construct LUCJ circuits. This function seems to be quite popular, even though it is somewhat tangential to ffsim's core functionality as a state vector simulation tool. The SQD tutorial on the learning platform depends on ffsim, only to use this function. Therefore, it might make sense to move the LUCJ circuit functionality into Qiskit. For an example of constructing an LUCJ circuit and sampling bitstrings from it using ffsim's implementation of the Sampler primitive, see this guide.

Here are some reasons we might not want to move the LUCJ code into Qiskit:

• It has a nontrivial dependency on the ffsim.linalg module, so it would not be a clean split, and there would end up being some duplication between Qiskit and ffsim.
• It has a soft dependency on a chemistry package such as PySCF because the ansatz is typically initialized using the output of a chemistry calculation (t2 amplitudes from, i.e., CCSD).
• It is application-specific. LUCJ is designed for quantum chemistry simulations.

It probably makes sense to resolve #13571 first.