Exploring Hilbert-Space Fragmentation on a Superconducting Processor

Isolated interacting quantum systems generally thermalize, yet there are several examples for the breakdown of ergodicity, such as many-body localization and quantum scars. Recently, ergodicity breaking has been observed in systems subjected to linear potentials, termed Stark many-body localization. This phenomenon is closely associated with Hilbert-space fragmentation, characterized by a strong dependence of dynamics on initial conditions. Here, we explore initial-state dependent dynamics using a ladder-type superconducting processor with up to 24 qubits, which enables precise control of the qubit frequency and initial state preparation. In systems with linear potentials, we experimentally observe distinct non-equilibrium dynamics for initial states with the same quantum numbers and energy, but with varying domain wall numbers. Accompanied by the numerical simulation for systems with larger sizes, we reveal that this distinction becomes increasingly pronounced as the system size grows, in contrast with weakly disordered interacting systems. Our results provide convincing experimental evidence of the fragmentation in Stark systems, enriching our understanding of the weak breakdown of ergodicity.