Exploring Hilbert-Space Fragmentation on a Superconducting Processor

TL;DR

This paper demonstrates experimentally how Hilbert-space fragmentation causes initial-state dependent dynamics in a superconducting qubit system with linear potentials, revealing non-ergodic behavior in Stark many-body localization.

Contribution

It provides the first experimental evidence of Hilbert-space fragmentation effects in a superconducting processor with up to 24 qubits, highlighting size-dependent non-ergodic dynamics.

Findings

Distinct non-equilibrium dynamics observed for states with same quantum numbers.

Fragmentation effects become more pronounced as system size increases.

Experimental results align with numerical simulations for larger systems.

Abstract

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.