  Considerable effort in experimental quantum computing is devoted to noisy
intermediate scale quantum computers (NISQ computers). Understanding the effect
of noise is important for various aspects of this endeavor including notable
claims for achieving quantum supremacy and attempts to demonstrate quantum
error correcting codes. In this paper we use Fourier methods combined with
statistical analysis to study the effect of noise. In particular, we use
Fourier analysis to refine the linear cross-entropy fidelity estimator. We use
both analytical methods and simulations to study the effect of readout and gate
errors, and we use our analysis to study the samples of Google's 2019 quantum
supremacy experiment.
