Use a UCC-like ansatz with a VQE

When using a UCC-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 Hartree-Fock state).

1. We obtain an ElectronicStructureProblem which we want to solve:

from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(atom="H 0 0 0; H 0 0 0.735", basis="sto-3g")
problem = driver.run()

2. We setup our QubitMapper:

from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()

3. We setup our ansatz:

from qiskit_nature.second_q.circuit.library import UCCSD, HartreeFock
ansatz = UCCSD(
    problem.num_spatial_orbitals,
    problem.num_particles,
    mapper,
    initial_state=HartreeFock(
        problem.num_spatial_orbitals,
        problem.num_particles,
        mapper,
    ),
)

4. 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())

5. Now comes the key step: choosing the initial point. Since we picked the HartreeFock 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 HFInitialPoint like so:

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

This may seem like it is not adding a lot of benefit, but the key aspect here is that you can build your code on top of the InitialPoint interface based on which we also have the MP2InitialPoint which allows you to start from an MP2 starting point like so:

from qiskit_nature.second_q.algorithms.initial_points import MP2InitialPoint
initial_point = MP2InitialPoint()
initial_point.ansatz = ansatz
initial_point.problem = problem
vqe.initial_point = initial_point.to_numpy_array()

6. Finally, we can now actually solve our problem:

from qiskit_nature.second_q.algorithms import GroundStateEigensolver
solver = GroundStateEigensolver(mapper, vqe)
result = solver.solve(problem)

print(f"Total ground state energy = {result.total_energies[0]:.4f}")

Total ground state energy = -1.1373