Probing quantum information propagation with out-of-time-ordered correlators

Interacting many-body quantum systems show a rich array of physical phenomena and dynamical properties, but are notoriously difficult to study: they challenging analytically exponentially simulate on classical computers. Small-scale information processors hold the promise efficiently emulate these systems, characterizing their dynamics is experimentally challenging, requiring probes beyond simple correlation functions multi-body tomographic methods. Here, we demonstrate measurement out-of-time-ordered correlators (OTOCs), one most effective tools for studying system evolution processes like thermalization. We implement 3x3 two-dimensional hard-core Bose-Hubbard lattice with superconducting circuit, study its time-reversibility by performing Loschmidt echo, measure OTOCs that enable us observe propagation information. A central requirement our experiments ability coherently reverse time evolution, which achieve digital-analog simulation scheme. In presence frequency disorder, localization can partially be overcome more particles present, possible signature in two dimensions.