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

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.

The Variational Quantum Eigensolver: a review of methods and best practices

“…While this can be used for ground state energies, it is also combined with VQD to compute excited states. While the method is shown to provide improved accuracy compared to a UCC based VQE on simple models (Hubbard, H 2 , LiH), it is reported to require a run time on average five times more important than VQE [590].…”

“…6.3.1). Wakaura and Suksomo [590] propose an adaptation of the VQE cost function to minimize the norm of the tangent vector to the energy rather than just the energy, dubbed Tangent-Vector VQE (TVVQE). While this can be used for ground state energies, it is also combined with VQD to compute excited states.…”