Phase diagram and observables of many-body localization in transmon circuit arrays

Disordered interacting quantum systems can undergo a phase transition from ergodic to many-body localized phase. Most of the previous theoretical studies on this subject concentrate on spin systems, and this phenomenon has been observed e.g. in optical lattices with ultra-cold atoms. In this work, we investigate the potential use of superconducting transmon circuits as a platform for experimental studies of the many-body localization [1]. We study numerically one-dimensional disordered arrays of up to 14 transmons, and find that the phase transition occurs at experimentally realizable values of disordered on-site potentials and is robust against experimentally relevant perturbations such as weak next-nearest neighbor and higher-order Kerr interactions. Based on the simulations of the system dynamics, we find that the temporal fluctuations of transmon occupations could be used as an observable for probing the many-body localization in transmon circuits.

[1] Roushan et al., Science 358, 1175 (2017).