Effects of gate errors in digital quantum simulations of fermionic systems

TL;DR

This paper investigates how gate errors, especially stochastic over-rotations, affect digital quantum simulations of fermionic systems like the Hubbard model, highlighting limitations on simulation accuracy and system size.

Contribution

It analyzes the impact of gate errors on fermionic quantum simulations, establishing the relation between gate fidelity and simulation accuracy, and providing estimates for feasible Trotter steps and system sizes.

Findings

Gate errors can cause disordered or unphysical evolution.

A relation between gate fidelity and over-rotation strength is established.

Limits on Trotter steps and system size are derived.

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 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.