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

TL;DR

This paper introduces a novel approach combining SU(2) symmetry-aware quantum circuits with Dynamic Mode Decomposition to efficiently simulate larger quantum systems without retraining, promising scalable modeling of strongly correlated materials.

Contribution

It develops a method that uses DMD to extrapolate variational quantum circuit parameters, enabling larger Trotter steps without additional training, integrating symmetry and spectral prediction techniques.

Findings

Effective extrapolation of quantum states beyond initial training range

Comparable accuracy to classical Trotterization methods

Potential for scalable simulation of complex quantum systems

Abstract

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.