Simulating the general dynamics of interacting many-body systems can be a notoriously hard problem, even for the most powerful classical supercomputers. The idea of quantum simulators is to map the dynamics of complex, interacting many-particle quantum systems of interest onto other, controlled quantum devices, to study their properties and time evolution in a more accessible and controlled way. This provides a promising route to study otherwise intractable interacting many-body systems from various fields ranging from condensed matter, quantum chemistry, to high-energy physics and potentially even biological systems where quantum effects might play a role. Furthermore, an open-system quantum simulator [1] enables the simulation of dynamics in open quantum systems, by engineering the coupling to a tailored environment. This opens new possibilities for the study of the competition of coherent and dissipative dynamics in driven, open many-body systems [2].

Recently, along this line of research we have been interested in developing new schemes for quantum simulation of topological many-body phases such as topological Mott insulators [3] and lattice gauge theories [4] and of models of interest in high-energy physics [5], using Rydberg atoms and trapped ions.