  Digital quantum simulations offer exciting perspectives for the study of
fermionic systems such as molecules or lattice models. However, with quantum
error correction still being out of reach with present-day technology, a
non-vanishing error rate is inevitable. We study the influence of gate errors
on simulations of the Trotterized time evolution of the quantum system with
focus on the fermionic Hubbard model. Specifically, we consider the effect of
stochastic over-rotations in the applied gates. Depending on the particular
algorithm implemented such gate errors may lead to a time evolution that
corresponds to a disordered fermionic system, or they may correspond to
unphysical errors, e.g., violate particle number conservation. We substantiate
our analysis by numerical simulations of model systems. In addition we
establish the relation between the gate fidelity and the strength of the
over-rotations in a Trotterized quantum simulation. Based on this we provide
estimates for the maximum number of Trotter steps which can be performed with
sufficient accuracy for a given algorithm. This in turn implies, apart from
obvious limitations on the maximum time of the simulation, also limits on the
system size which can be handled.
