  Noisy intermediate-scale quantum computers (NISQ) are in their childhood, but
showing high promise. One main concern for NISQ machines is their inherent
noisiness, as the qubit states are subject to disturbances with each
algorithmic operation applied. In this study, we conduct experiments on quantum
noise. Based on our data, we show that existing noise models fail to properly
capture the aggregation of noise effects over an algorithm's runtime. They are
underdispersed, meaning that observable frequencies scatter much more between
repeated experiments than what the standard assumptions of the binomial
distribution allow for. We develop noise model for the readout probabilities as
a function of the number of gate operations. The model is based on a continuous
random walk on the (Bloch) sphere, where the angular diffusion coefficient
characterizes the noisiness of gate operations. We superimpose a second random
walk at the scale of multiple readouts to account for overdispersion. The
interaction of these two random walks predicts theoretical, runtime-dependent
bounds for probabilities. Overall, it is a three-parameter distributional model
that fits the data better than the corresponding one-scale model (without
overdispersion). We demonstrate the fit and the plausibility of the predicted
bounds via Bayesian data-model analysis.
