Renamings in circuit/library/data_encoding

[Cryoris]

Summary

Rename the module qiskit/circuit/library/data_encoding to data_preparation as this is more expressive. Also rename the contents to more descriptive names.

Details and comments

Suggestions (can be changed):

PauliExpansion -> PauliEvolutionFeatureMap
FirstOrderExpansion -> ZExpansionFeatureMap
SecondOrderExpansion -> ZZExpansionFeatureMap

Reasons:

• the circuits consist of time evolutions of Pauli strings and are known as "feature maps" in literature
• pauli_evolution would be nice because it is short, but these circuits do also the repetitions, entanglements and H-layers on top of the evolutions
• first-order expansion is the special case of the Pauli string Z
• second-order expansion is the special case of the Pauli strings ZZ and Z

[jaygambetta]

what about
PauliFeatureMap
LocalFeatureMap
TwoLocalFeatureMap

[Cryoris]

I'm fine with PauliFeatureMap 👍
Local and TwoLocal however might be a bit misleading since these classes don't accept arbitrary local and two local gates (for which you would use TwoLocal) but really only use exp(i*t*Z) and exp(i*t*ZZ). How about ZFeatureMap or PauliZFeatureMap instead?

[jaygambetta]

I'm good with ZFeatureMap and ZZFeatureMap. You are correct for some reason i was thinking i could make it X and XX but since we use the H at the start only Z makes sense.

[ajavadia]

only one of these we are going to call Ansatz?