support required for complex Hamiltonian in particle_hole_transformation about qiskit-nature

[woodsp-ibm]

I transferred from Aqua as Chemistry has been moved here for the next release with Aqua being deprecated.

[mrossinek]

Hi @HNK-coder! Thanks for raising this issue!
As you may have noticed, we are actively working on a larger refactoring of the code during which your issue has been migrated to a new repository. Last week @pbark and I were looking into the migration of the particle-hole transformation (see also #86).
For the upcoming release we do not plan to support the particle-hole transformation because (as you also raised this issue) there are some problems with the old implementation. You can also find an overview of some of our thoughts on this topic in this gist (also linked to in the PR I mentioned above).

If you do indeed need to use the particle-hole transformation, you should be able to achieve a similar effect as to what it did by adding an energy shift to the all-unity (e.g. IIII) term of your operator. I shortly mention this in the gist above.

I hope this helps! We will definitely revisit this issue when we look into implementing the particle-hole transformation in a future release. However, for the time being, I will put this on hold.

[HNK-coder]

Years ago, I was also disappointed to notice that the normal order operation resulted in just a shift in the amplitude of the identity operator in Pauli space. Classical optimization gets faster, as you mentioned, but nothing else. I thought that there must have been an advantage even in Pauli space.
Anyway I will manege by myself.
Take your time.