Quantum simulation of real-time dynamics in SU(2) lattice gauge theory

Gauge theories form the foundation of the Standard Model, providing the theoretical framework for describing nuclear and particle interactions. While classical computing has enabled significant insights into these systems, certain aspects—such as real-time dynamics—remain computationally intractable. Quantum simulation offers a promising alternative, but a key challenge lies in discretizing the continuous gauge degrees of freedom to make them compatible with qubit-based architectures. In this work, we analyze a set of recently introduced bases specifically designed for the quantum simulation of SU(2) lattice gauge theory and assess their performance across different regions of parameter space. We then present several strategies for implementing real-time evolution on quantum devices, detailing the corresponding circuit constructions. Finally, we demonstrate these approaches on real quantum hardware, investigating the time evolution of observables initialized from a product state.