Qeom refactoring and upgrades

[Anthony-Gandon]

Closes #769
Closes #415
Closes #403
Closes #52

Summary

Proposition for a modification to QEOM internals to :

• Make the code easier to follow
• Improve the potential for parallelism
• Improve the performances of the classical calculations by using a custom treatment of the tapering.

A new functionality is also added to compute excited state properties and transition amplitudes of arbitrary observables.

The typical interface to use it would be the following:

from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Estimator

from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.algorithms import VQEUCCFactory, GroundStateEigensolver
from qiskit_nature.second_q.algorithms.excited_states_solvers import QEOM
from qiskit_nature.second_q.circuit.library import UCCSD
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import QubitConverter
from qiskit_nature.second_q.mappers import JordanWignerMapper

import numpy as np

optimizer = COBYLA(maxiter=500,disp=False)
qubit_converter = QubitConverter(JordanWignerMapper(), z2symmetry_reduction=None, two_qubit_reduction=False)

new_driver = PySCFDriver(
    atom="H 0 0 0; H 0 0 1.735",
    basis="sto3g",
    charge=0,
    spin=0,
    unit=DistanceUnit.ANGSTROM,
)
new_es_problem = new_driver.run()
hamiltonian_op, _ = new_es_problem.second_q_ops()
aux_ops = {'hamiltonian':hamiltonian_op}

# Qeom results
vqe_solver = VQEUCCFactory(Estimator(), UCCSD(), optimizer)
me_gsc = GroundStateEigensolver(qubit_converter, vqe_solver)
qeom_solver = QEOM(me_gsc, estimator=Estimator(), excitations='sd', aux_eval_rules="all")
results_qeom = qeom_solver.solve(new_es_problem, aux_operators=aux_ops)

print("Aux QEOM")
for aux_op_eval in results_qeom.aux_operators_evaluated:
    print(aux_op_eval)

print("Transi QEOM")
for indice, value in results_qeom.raw_result.transition_amplitudes.items():
    print(indice, value)

Details and comments

The following guides details some of the changes that are proposed
QEOM_refactoring-3.pdf

[coveralls]

Pull Request Test Coverage Report for Build 3755972353

• 262 of 321 (81.62%) changed or added relevant lines in 5 files are covered.
• 19 unchanged lines in 4 files lost coverage.
• Overall coverage decreased (-0.04%) to 85.878%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit_nature/second_q/algorithms/excited_states_solvers/excited_states_eigensolver.py	2	3	66.67%
qiskit_nature/second_q/algorithms/excited_states_solvers/qeom_electronic_ops_builder.py	0	1	0.0%
qiskit_nature/second_q/mappers/qubit_converter.py	43	49	87.76%
qiskit_nature/second_q/algorithms/excited_states_solvers/qeom.py	213	264	80.68%

Files with Coverage Reduction	New Missed Lines	%
qiskit_nature/second_q/mappers/qubit_converter.py	1	89.83%
qiskit_nature/second_q/problems/vibrational_structure_result.py	2	55.77%
qiskit_nature/second_q/algorithms/excited_states_solvers/qeom.py	8	80.31%
qiskit_nature/second_q/problems/electronic_structure_result.py	8	89.45%

Totals
Change from base Build 3741697404:	-0.04%
Covered Lines:	17562
Relevant Lines:	20450

---

💛 - Coveralls

[mrossinek]

I think this PR is overall already in great shape. Thanks a lot Anthony for all the work here!

These are quite a few comments and I will need to do another pass of the actual QEOM code in a little bit more detail with some more time on my hands. But I figured I should post my review as it is now to give you time to work on these comments.

[mrossinek]

A few more comments from my side 👍

This is shaping up very nicely! I am skipping the changes done to the QubitConverter on purpose, since it will be refactored again as part of #967 at which point we can revert these unreleased changes and update the QEOM code accordingly. I would still like to get this long-standing PR out before the QubitConverter refactor hits because it allows us to do these two things largely in parallel 👍

(the above is just a comment for a potential other reviewer coming across this)

[mrossinek]

This is good, thank you 👍

@manoelmarques what would the deprecation strategy look like here, if I want to make these read-only properties of the result object. Doing this would allow us to put this computation logic into the property getters and ensure that the matrices stored in the result are always consistent (plus it simplifies the code here a bit).

[manoelmarques]

If you put the calculating logic in the init method, then you just need the deprecation msg in the setters. This way the user still can use the deprecated setter which would override the calculation done in the init.

[mrossinek]

Thanks, that's a good idea 👍 @Anthony-Gandon could you do that, please?

[Anthony-Gandon]

As discussed with @mrossinek , I could not put the calculating logic in the init method. I changed the getters instead.

[mrossinek]

This is looking very good, thanks a lot, Anthony!

I have a last round of comments, mostly on some docstring details 👍

[mrossinek]

Okay some final (minor) observations but other than that this looks good to me 👍
We will just need to keep in mind that, once we progress on #972 and #999, we should revert the public API changes (as much as possible) done to the QubitConverter in this PR.
We can see about the details of that as part of working on the epic mentioned above.

[Anthony-Gandon]

I'm not sure why we did not have a mypy error previously when

if isinstance(self.solver, MinimumEigensolverFactory):
    self._gsc._solver = self.solver.get_solver(problem, self.qubit_converter)

(because self._gscc is GroundStateSolver and does not have a _solver attribute, only GroundStateEigensolver has). Can we add a #type: ignore because anyway this part will be subject to changes in the near future.

[mrossinek]

I am tentatively approving this PR because I think it looks good as it is.

I am not quite sure what you meant in your last comment though, so I will hold off with merging until that is cleared up either here or offline.

EDIT: the questionable type ignore statement is already included in this PR and fine by me 👍

Thanks a lot for all your work, Anthony!