Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems

TL;DR

This paper introduces a variational quantum algorithm designed to solve generalized eigenvalue problems in non-Hermitian systems, with applications demonstrated in ocean acoustics and robustness tested under noise conditions.

Contribution

It presents a novel variational quantum algorithm based on generalized Schur decomposition for non-Hermitian GEPs, including methods for evaluating loss and gradients on near-term devices.

Findings

Successfully solves non-Hermitian GEPs in simulations

Demonstrates application to ocean acoustics problems

Shows robustness under noise simulations

Abstract

Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for solving the GEPs in non-Hermitian systems. The algorithm transforms the generalized eigenvalue problem into a process of searching for unitary transformation matrices. We demonstrate a method for evaluating both the loss function and its gradients on near-term quantum devices. We validate numerically the algorithm's performance through simulations, and demonstrate its application to GEPs in ocean acoustics. The algorithm's robustness is further confirmed through noise simulations.