近日，中国工程物理研究院Xiaosi Xu及其研究团队取得一项新进展。经过不懈努力，他们提出核壳层模型激发态的量子增强格林函数蒙特卡罗算法。相关研究成果已于2024年10月21日在国际知名学术期刊《物理评论A》上发表。

该研究团队提出一种混合量子-经典格林函数蒙特卡洛（GFMC）算法，用于估算核壳层模型的激发态。传统GFMC方法虽广泛应用于求解量子多体系统的基态，但受符号问题困扰，导致随着系统规模和演化时间的增长，方差呈指数级增加。

通常通过施加经典约束来缓解这一问题，但代价是引入了偏差。该研究的方法采用量子计算机上的量子子空间对角化（QSD）来制备量子试探态，以替代GFMC过程中的经典试探态。

此外，研究人员在实施QSD时融入了改良的经典阴影技术，以优化量子资源的利用。另外，研究人员还扩展了混合GFMC算法，以求解给定量子系统的激发态。数值结果表明，这一方法在确定激发态能量方面显著提高了准确性，相较于传统方法有所改进。

附：英文原文

Title: Quantum-enhanced Green's function Monte Carlo algorithm for excited states of the nuclear shell model

Author: Yongdan Yang, Ruyu Yang, Xiaosi Xu

Issue&Volume: 2024/10/21

Abstract: We present a hybrid quantum-classical Green's function Monte Carlo (GFMC) algorithm for estimating the excited states of the nuclear shell model. The conventional GFMC method, widely used to find the ground state of a quantum many-body system, is plagued by the sign problem, which leads to an exponentially increasing variance with the growth of system size and evolution time. This issue is typically mitigated by applying classical constraints but at the cost of introducing bias. Our approach uses quantum subspace diagonalization (QSD) on a quantum computer to prepare a quantum trial state, replacing the classical trial state in the GFMC process. We also incorporated a modified classical shadow technique in the implementation of QSD to optimize quantum resource utilization. Besides, we extend our hybrid GFMC algorithm to find the excited states of a given quantum system. Numerical results suggest our method largely enhances accuracy in determining excited-state energies, offering an improvement over the conventional method.

DOI: 10.1103/PhysRevA.110.042623

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.042623