  Observing rapid developments of both the number of qubits and quantum volume,
especially with recent advances in ion-trap quantum computers, it is no doubt
that Fault-Tolerant-Quantum-Computer (FTQC) will be realized in the near
future. Since FTQC requires 10,000 physical qubits for every 100 logical ones,
it will be used as the first large-scale Noisy-Intermediate-Scale-Quantum
(NISQ) . The Variational Quantum Eigensolver (VQE) method will be used until
large-scale FTQC with more than 100 logical qubits are realized. Therefore, the
VQE method must be improved with respect to both accuracy and time to solution
using large resource of the near FTQC . In this paper, we propose
Tangent-Vector VQE (TVVQE) method to manage these issues. The method optimizes
the norm of tangent vector of trial energy. We demonstrate the calculation of
energy levels on Hydrogen molecule, Hubbard model, and Lithium Hydride molecule
and reveal that TVVQE has a potential to calculate ground and excited energy
levels more accurately than other VQE methods.
