Noisy quantum simulators: theory of random perturbations and characterization of robust observables*

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 study the effect of weak random perturbations of various kinds in the performance of a dynamical quantum simulator and establish a framework that links the robustness of the resulting expectation values to the spectral properties of the output observable. These properties, in turn, can be associated with the macroscopic or microscopic character of the observable. We then show that, under general assumptions and on average over all states, imperfect simulators 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 some 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 detailed knowledge about the nature of the imperfections.