Find ground state energy using AdaptVQE

This guide outlines how the AdaptVQE algorithm can be used to find the ground state solutions of natural science problems.

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 StatevectorEstimator
vqe = VQE(StatevectorEstimator(), ansatz, SLSQP())
vqe.initial_point = np.zeros(ansatz.num_parameters)

5. We setup the AdaptVQE:

from qiskit_algorithms import AdaptVQE
adapt_vqe = AdaptVQE(vqe)
adapt_vqe.supports_aux_operators = lambda: True  # temporary fix

6. We wrap everything in a GroundStateEigensolver:

from qiskit_nature.second_q.algorithms import GroundStateEigensolver
solver = GroundStateEigensolver(mapper, adapt_vqe)

7. We solve the problem:

result = solver.solve(problem)

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

Total ground state energy = -1.1373