Overdispersion in gate tomography: Experiments and continuous, two-scale random walk model on the Bloch sphere

TL;DR

This paper investigates noise in NISQ quantum computers, revealing that existing models underestimate variability, and introduces a novel two-scale random walk model on the Bloch sphere that better captures overdispersion in gate tomography.

Contribution

It develops a new continuous, two-scale random walk model on the Bloch sphere that accurately describes overdispersion in quantum gate noise, improving upon existing models.

Findings

Existing noise models are underdispersed and fail to capture experimental variability.

The proposed three-parameter model fits experimental data better than traditional models.

The model provides runtime-dependent bounds for readout probabilities, validated by Bayesian analysis.

Abstract

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.