Effects of gate errors in digital quantum simulations of fermionic systems

Abstract

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 for systems of interesting size, a non-vanishing error rate is inevitable. Here, 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 models a disordered fermionic system, or they may correspond to unphysical errors, e.g., violating 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. Based on this we provide estimates for the maximum number of gates which can be performed with sufficient accuracy. This in turn implies, apart from limitations on the maximum time of the simulation, also restrictions on the system size which can be handled with present-day technology.