Find excited state energies using the NumPyEigensolver

In order to ensure a physically meaningful excited states of a hamiltonian are found when using the NumPyEigensolver one needs to set the filter_criterion attribute of the solver.

Subclasses of BaseProblem in Qiskit Nature provide the get_default_filter_criterion() method which provides a default implementation of such a filter criterion for commonly encountered cases.

Below we show how you can use this setting.

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 NumPyEigensolver:

from qiskit_algorithms import NumPyEigensolver
algo = NumPyEigensolver(k=100)
algo.filter_criterion = problem.get_default_filter_criterion()

4. We wrap everything in a ExcitedStatesEigensolver:

from qiskit_nature.second_q.algorithms import ExcitedStatesEigensolver
solver = ExcitedStatesEigensolver(mapper, algo)

5. We solve the problem:

result = solver.solve(problem)

print(f"Total ground state energy = {result.total_energies[0]:.4f}")
print(f"Total first excited state energy = {result.total_energies[1]:.3f}")
print(f"Total second excited state energy = {result.total_energies[2]:.3f}")

Total ground state energy = -1.1373
Total first excited state energy = -0.163
Total second excited state energy = 0.495