标题： 非厄米体系的广义本征值问题的变分量子算法 显示英文标题

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

摘要： 大多数用于广义特征值问题的量子算法集中在厄米特系统上，而很少适用于非厄米特系统。基于广义舒尔分解，我们提出了一种变分量子算法，用于解决非厄米特系统中的广义特征值问题。该算法将广义特征值问题转化为寻找酉变换矩阵的过程。此外，我们开发了一种在近期量子设备上评估损失函数及其梯度的方法。最后，我们通过仿真数值验证了该算法的性能，并展示了其在海洋声学中的广义特征值问题的应用。该算法的鲁棒性通过噪声仿真进一步得到确认。 显示英文摘要

摘要： Most quantum algorithms for generalized eigenvalue problems focus on Hermitian systems, and few are applicable to non-Hermitian systems. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for solving generalized eigenvalue problems in non-Hermitian systems. The algorithm transforms the generalized eigenvalue problem into a process of searching for unitary transformation matrices. Moreover, we develop a method for evaluating both the loss function and its gradients on near-term quantum devices. Finally, we numerically validate the algorithm's performance through simulations and demonstrate its application to generalized eigenvalue problems in ocean acoustics. The algorithm's robustness is further confirmed through noise simulations.