Fermionic state preparation

[mrossinek]

What should we add?

#53 is laying the foundation of the qiskit_fermions.circuit and qiskit_fermions.transpiler modules (see also #5).

Another critical component we are missing is the ability to perform initial state preparation. There are some remaining questions for how to deal with this generally:

• not all F2Q encodings can actually map non-fermion-number-preserving (uneven) operators. So defining this gate based on fermion particle creation operators may not work in all settings.
• simply adding X gates to the circuit seems inelegant and prone to errors
• arbitrary Slater determinant preparation circuits require orbital rotations (OrbitalRotation gate #54) which may be decomposed more efficiently than via (Givens decompositon #48) if the initial occupation is known (i.e. the state is known to be prepared at the beginning of a circuit). This may be an optimization we wish to add.

[mrossinek]

#83 is going to add an early prototype implementation of a basic occupation-based InitializeModes gate. However, this still has some hard-coded assumptions which I would like to improve/generalize upon in the future. So for now, I'm leaving this issue open to reference those planned improvements.