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

TL;DR

This paper introduces the Tangent-Vector VQE (TVVQE), a novel method designed to improve the accuracy and efficiency of quantum eigensolvers, especially in the context of near-term quantum computers and large-scale fault-tolerant quantum computing.

Contribution

The paper proposes the TVVQE method that optimizes the tangent vector norm to enhance accuracy and robustness of energy level calculations in quantum systems.

Findings

TVVQE achieves more accurate energy calculations for molecules and models.

Demonstrated on Hydrogen, Hubbard, and Lithium Hydride systems.

Potential to outperform existing VQE methods in accuracy.

Abstract

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.