Prescreening method for Variational Quantum State Eigensolver

The development of Fault-Tolerant Quantum Computer (FTQC) gradually raised the possibility of the Quantum Phase Estimation (QPE) algorithm. However, QPE can work only for normalized systems. This requires the minimum and maximum of eigenvalues of Hamiltonian. Variational Quantum Eigensolver (VQE) well developed in the Noisy Intermediate Scale Quantum (NISQ) era is necessary for preparing initial eigenvectors close to exact states. In this paper, we propose a method to derive all of the states in high accuracy using the Variational Quantum State Eigensolver (VQSE) method and Subspace-Search VQE (SSVQE) method for processing. We show that VQSE and SSVQE prescreening methods capable to derive all the states correctly on hydrogen molecules.