  Quantum simulators are widely seen as one of the most promising near-term
applications of quantum technologies. However, it remains unclear to what
extent a noisy device can output reliable results in the presence of
unavoidable imperfections. Here we propose a framework to characterize the
performance of quantum simulators by linking the robustness of measured quantum
expectation values to the spectral properties of the output observable, which
in turn can be associated with its macroscopic or microscopic character. We
show that, under general assumptions and on average over all states, imperfect
devices are able to reproduce the dynamics of macroscopic observables
accurately, while the relative error in the expectation value of microscopic
observables is much larger on average. We experimentally demonstrate the
universality of these features in a state-of-the-art quantum simulator and show
that the predicted behavior is generic for a highly accurate device, without
assuming any knowledge about the nature of the imperfections.
