近日，中国科学院物理所的向涛课题组取得一项新进展。经过不懈努力，他们提出了一种并行的量子本征求解器，能够同时处理多个低能本征态。相关研究成果已于2023年5月30日在国际知名学术期刊《物理评论A》上发表。

该研究团队提出了一种量子算法，使用满足广义Rayleigh-Ritz变分原理的假设函数来对角化Hamiltonian。该算法采用了一种纯化技术，在一个量子电路中同时处理多个量子态，并实现对多个特征态的优化和确定。

此外，相对于现有算法，该算法的电路深度相对合理，并且能够对准确确定的特征子空间进行灵活的后处理。通过使用横向场伊辛模型，研究人员验证了该算法在迭代步骤中以高效且均匀的方式收敛的特征值，并通过模拟和IBM平台测量进行了测试。由于该算法所需的量子资源有限，因此在噪声韧性、性能改进和多样化应用方面具有巨大的潜力。

附：英文原文

Title: Concurrent quantum eigensolver for multiple low-energy eigenstates

Author: G. Xu, Y. B. Guo, X. Li, K. Wang, Z. Fan, Z. S. Zhou, H. J. Liao, T. Xiang

Issue&Volume: 2023/05/30

Abstract: We propose a quantum algorithm that diagonalizes a Hamiltonian by implementing an ansatz that satisfies the generalized Rayleigh-Ritz variational principle. This algorithm uses a purification technique to target many quantum states in one quantum circuit and allows multiple eigenstates to be optimized and determined simultaneously. Moreover, it requires a reasonable circuit depth compared to existing algorithms and enables flexible postprocessing on the accurately determined eigensubspace. Using the transverse-field Ising model, we confirm that the eigenvalues obtained with the algorithm converge efficiently and uniformly with the iteration steps, tested by both simulations and IBM platform measurements. As limited quantum resources are needed, this algorithm is promising for noise resilience, better performances, and versatile applications.

DOI: 10.1103/PhysRevA.107.052423

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.052423