  Recently Xue et al. [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 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 cost values, at the expense of
greater degradation due to noise.
