A universal quantum simulator is a controlled quantum device that reproduces the dynamics of any other many-particle quantum system with short-range interactions. This dynamics can refer to both coherent Hamiltonian and dissipative open-system evolution. While we first summarize the impressive progress with closed system quantum simulation with cold atoms and molecules, e.g. in optical lattices, we will focus here in particular on the engineering the open system dynamics of many particles by a controlled coupling to an environment. We will discuss both the basic theoretical concepts [1,2] as well as their physical implementation with cold Rydberg atoms [3] and ions [4].
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