A prescreening method for variational quantum state eigensolver

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