Fidelity Plateaux from Correlated Noise in Cold-Atom Quantum Simulators

We demonstrate that, in a quantum simulation protocol based on the Hubbard model, correlated noise in the Hubbard parameters leads to arbitrarily long plateaux in the state-preparation fidelity as a function of elapsed time. We argue that this correlated-noise scenario is the generic one in the cold-atom context, since all of the Hubbard-model parameters ultimately depend on the same set of lasers. We explain the formation of such a plateau using the Bloch-sphere representation, deriving analytical expressions for its start and end times and its height.