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Observing rapid developments of both the number of qubits and quantum volume,especially with recent advances in ion-trap quantum computers, it is no doubtthat Fault-Tolerant-Quantum-Computer (FTQC) will be realized in the nearfuture. 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 untillarge-scale FTQC with more than 100 logical qubits are realized. Therefore, theVQE method must be improved with respect to both accuracy and time to solutionusing large resource of the near FTQC . In this paper, we proposeTangent-Vector VQE (TVVQE) method to manage these issues. The method optimizesthe norm of tangent vector of trial energy. We demonstrate the calculation ofenergy levels on Hydrogen molecule, Hubbard model, and Lithium Hydride moleculeand reveal that TVVQE has a potential to calculate ground and excited energylevels more accurately than other VQE methods.

Tangent Vector Variational Quantum Eigensolver: A Robust Variational Quantum Eigensolver against the inaccuracy of derivative