标题： 利用 SU(2) 对称性对量子系统进行高效模拟 显示英文标题

标题： Utilization of SU(2) Symmetry for Efficient Simulation of Quantum Systems

摘要： 这项工作研究了用于模拟具有内部 SU(2) 对称性的量子系统的变分编译方法。 研究的核心组成部分是将动态模式分解（DMD）方法应用于将训练好的变分电路参数外推到初始优化范围之外。 提出了一种方法，使用外推参数预测具有更多 Trotter 步数的变分编译量子态，从而无需重新训练。 通过与经典 Trotter 化方法和变分训练结果进行比较，验证了该方法的效率。 所提出的方法展示了对称性一致的量子电路架构与谱预测技术的有效结合。 该方法在强关联系统的可扩展建模方面显示出前景，特别是在凝聚态物理问题中，如 Kagome 晶格上的 Heisenberg 模型。 显示英文摘要

摘要： This work investigates variational compilation methods for simulating quantum systems with internal SU(2) symmetry. The central component of the research is the application of the Dynamic Mode Decomposition (DMD) method to extrapolate trained variational circuit parameters beyond the initial optimization range. An approach is proposed for predicting variationally compiled quantum states with a larger number of Trotter steps using extrapolated parameters, eliminating the need for retraining. The efficiency of the method is validated by comparing it with classical Trotterization and the results of variational training. The proposed method demonstrates an effective integration of symmetry-consistent quantum circuit architecture with spectral prediction techniques. The methodology shows promise for scalable modeling of strongly correlated systems, particularly in condensed matter physics problems, such as the Heisenberg model on Kagome lattices.