Fix parameter order in VQE, if the ansatz is resized

[Cryoris]

Summary

Fix a bug in VQE where the parameters of the ansatz were
still explicitly ASCII-sorted by their name if the ansatz was resized. That led to a
mismatching order of the optimized values in the optimal_point attribute of the result
object.

This should have been included in #7099, where the sorting was removed, but was missed.

Details and comments

For example, this led to a wrong optimal circuit if a user tried to construct it using VQEResult.optimal_point.

from qiskit.algorithms import VQE
from qiskit.circuit.library import RealAmplitudes
from qiskit.opflow import Z, I
from qiskit.providers.aer import AerSimulator
from qiskit.quantum_info import Statevector

# Hamiltonian that will lead to more than 11 parameters.
# The default ansatz is RealAmplitudes with 4 rotation layers, hence this will
# produce  a 12-parameter ansatz.
hamiltonian = Z ^ Z ^ Z

sim = AerSimulator(method="statevector")
vqe = VQE(quantum_instance=sim)  # don't set the ansatz but let VQE use the default
result = vqe.compute_minimum_eigenvalue(hamiltonian)

ansatz = RealAmplitudes(hamiltonian.num_qubits)
reconstructed_state  = Statevector(ansatz.bind_parameters(result.optimal_point))
print("Reconstructed state from optimal parameters:")
print(reconstructed_state)
print("State from VQE result:")
print(result.eigenstate)

Instead of the same statevectors, this yields

Optimal circuit using optimal values as list
Statevector([ 0.64431664+0.j, -0.2110578 +0.j,  0.38441563+0.j,
             -0.17266969+0.j, -0.26513136+0.j,  0.02009964+0.j,
              0.50885393+0.j, -0.18190522+0.j],
            dims=(2, 2, 2))
[ 2.81202210e-04+0.j  2.24955744e-01+0.j -1.10683555e-01+0.j
  1.51121930e-04+0.j  7.54507043e-01+0.j  6.74747145e-05+0.j
  9.33921914e-05+0.j -6.06517165e-01+0.j]

With this PR, these vectors are the same.

[Cryoris]

Note that I had to change the TestVQE.test_max_evals_grouped test slightly since in the tests, the ansatz was resized and thus the parameters ASCII-sorted. Now they are sorted by vector, which leads to a slightly different optimization, in particular for stochastic optimizers (since the params are in a different order).

[coveralls]

Pull Request Test Coverage Report for Build 1692405590

• 4 of 4 (100.0%) changed or added relevant lines in 1 file are covered.
• 1 unchanged line in 1 file lost coverage.
• Overall coverage decreased (-0.0008%) to 83.101%

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Files with Coverage Reduction	New Missed Lines	%
qiskit/algorithms/minimum_eigen_solvers/vqe.py	1	91.27%

Totals
Change from base Build 1687988160:	-0.0008%
Covered Lines:	51984
Relevant Lines:	62555

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💛 - Coveralls

[mrossinek]

Merging this PR caused our nightly scheduled CI of Qiskit Nature to break: https://github.com/Qiskit/qiskit-nature/actions/runs/1695769065

I verified locally that this is indeed the offending commit. I assume this has to do with the fact that this fixes a bug related to using the optimal_point? If so, then likely the expected values in our unittests were simply wrong (by a small margin as you can see from the CI output above) since the BopesSampler leverages the optimal_point when applying bootstrapping.

Tagging some more people who are not already involved in this discussion:

• @pbark regarding BopesSampler
• @manoelmarques regarding Qiskit Nature CI failure