Evaluation on Genetic Algorithms as an optimizer of Variational Quantum Eigensolver(VQE) method

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.