Use a UVCC-like ansatz with a VQE

When using a UVCC-style ansatz with a VQE one needs to pay particular attention to the initial_point attribute which indicates from which set of initial parameters the optimization routine should start. By default, VQE will start from a random initial point. In this how to we show how one can set a custom initial point instead (for example to guarantee that one starts from the VSCF state).

The basics of this how-to are identical to the UCC-like ansatz how-to (TODO: add link). Thus, here we will simply show how to use the VSCFInitialPoint like so:

1. Assuming we already have our VibrationalStructureProblem and QubitMapper:

from qiskit_nature.second_q.mappers import DirectMapper
from qiskit_nature.second_q.problems import VibrationalStructureProblem
problem: VibrationalStructureProblem = ...
num_modals = [2, 2, 2]  # some example of what problem.num_modals might yield
mapper = DirectMapper()

2. We setup our ansatz:

from qiskit_nature.second_q.circuit.library import UVCCSD, VSCF
ansatz = UVCCSD(
    num_modals,
    mapper,
    initial_state=VSCF(
        num_modals,
        mapper,
    ),
)

3. We setup a VQE:

import numpy as np
from qiskit_algorithms import VQE
from qiskit_algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
vqe = VQE(Estimator(), ansatz, SLSQP())

4. Now comes the key step: choosing the initial point. Since we picked the VSCF initial state before, in order to ensure we start from that, we need to initialize our initial_point with all-zero parameters. One way to do that is like so:

vqe.initial_point = np.zeros(ansatz.num_parameters)

Alternatively, one can also use VSCFInitialPoint like so:

from qiskit_nature.second_q.algorithms.initial_points import VSCFInitialPoint
initial_point = VSCFInitialPoint()
initial_point.ansatz = ansatz
initial_point.problem = problem
vqe.initial_point = initial_point.to_numpy_array()

Just like in the UCC-ansatz case, this is mostly useful when building more code on top of the InitialPoint interface.