Interacting many-body quantum systems show a rich array of physical phenomena and dynamical properties, but are notoriously difficult to study: they are analytically challenging and exponentially hard to simulate on classical computers. Small-scale quantum information processors hold the promise to efficiently emulate these systems, but characterizing their dynamics is experimentally difficult, requiring probes beyond simple correlation functions and multi-body tomographic methods. Here we demonstrate the measurement of out-of-time-ordered correlators—one of the most effective tools for studying quantum system evolution and processes like quantum thermalization. We implement a 3 × 3 two-dimensional hard-core Bose–Hubbard lattice with a superconducting circuit, study its time reversibility by performing a Loschmidt echo, and measure out-of-time-ordered correlators that enable us to observe the propagation of quantum information. A central requirement for our experiments is the ability to coherently reverse time evolution, which was achieved with a digital–analogue simulation scheme. In the presence of frequency disorder, we observe that localization can partially be overcome with more particles present—a possible signature of many-body localization in two dimensions.
The complexity of many-body quantum states makes their evolution difficult to simulate with classical computers. Experiments on a 2D nine-qubit device demonstrate that the key properties of quantum lattices can be accessed by measuring out-of-time-ordered correlators.