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

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.