  Variational-Quantum-Eigensolver (VQE) method has been known as the method of
chemical calculation using quantum computers and classical computers. This
method also can derive the energy levels of excited states by
Variational-Quantum-Deflation (VQD) method. Although, parameter landscape of
excited state have many local minimums that the results are tend to be trapped
by them. Therefore, we apply Genetic Algorithms then Local Search (GA then LS)
as the classical optimizer of VQE method. We performed the calculation of
ground and excited states and their energies on hydrogen molecule by modified
GA then LS. Here we uses Powell, Broyden-Fletcher-Goldfarb-Shanno, Nelder-Mead
and Newton method as an optimizer of LS. We obtained the result that Newton
method can derive ground and excited states and their energies in higher
accuracy than others. We are predicting that newton method is more effective
for seed up and be more accurate.

Quantum Physics;Chemical Physics