Quantum simulators are special purpose devices designed to provide physical insight in a specific quantum problem that is hard to study in the laboratory and impossible on a computer. However, before they can be used they require calibration. For cold atomic systems, quantum Monte Carlo simulations have played a key role there. They established a few years ago that the thermodynamic properties of the experimental system are in one-to-one agreement with the simulations of the corresponding model. The synergy between the two approaches has dramatically progressed since then, to each other’s benefice: In the main part of this talk, I will focus on the dynamical properties of a U(1) critical system in (2+1) dimensions focusing on the existence of the amplitude mode or Higgs particle, and on the optical conductivity, which we compare against predictions from the AdS/CFT correspondence. Finally, I will discuss some open problems for this approach to quantum simulation.