Characterizing local noise in QAOA circuits

Abstract

Recently Xue et al (2019 arXiv:1909.02196) demonstrated numerically that QAOA performance varies as a power law in the amount of noise under certain physical noise models. In this short note, we provide a deeper analysis of the origin of this behavior. In particular, we provide an approximate closed form equation for the fidelity and expected cost in terms of the noise rate, system size, and circuit depth. As an application, we show these equations accurately model the trade off between larger circuits which attain better expected cost values, at the expense of greater degradation due to noise.