  Variational-Quantum-Eigensolver(VQE) method on a quantum computer is a
well-known hybrid algorithm to solve the eigenstates and eigenvalues that uses
both quantum and classical computers. This method has the potential to solve
quantum chemical simulation including polymer and complex optimization problems
that are never able to be solved in a realistic time. Though they are many
papers on VQE, there are many hurdles before practical application. Therefore,
we tried to evaluate VQE methods with Genetic Algorithms(GA). In this paper, we
propose the VQE method with GA. We selected ground and excited-state energy on
hydrogen molecules as the target because there are many local minimum values on
excited states though the molecular structure is extremely simple. Therefore it
is not easy to find the energy of states. We compared the GA method with other
methods from the viewpoint of log error of the ground, triplet, singlet, and
doubly excited state energy value. As a result, we denoted that the BFGS method
has the highest accuracy. We thought that rcGA used as an optimization for the
VQE method was proved disappointing. The rcGA does not show an advantage
compared to other methods. we suggest that the cause is due to initial
convergence. In the future, we want to try to introduce Genetic Algorithms then
local search.
