Model-based Qubit Noise Spectroscopy

Model-based approaches to classical spectral density estimation have a number of potential benefits over nonparametric approaches, including reduced estimation error and super-resolution, the ability to resolve spectra below the nominal frequency resolution. These benefits are achieved by exploiting assumptions about the spectral content, such as a particular parametric form or the number of signal components. Classically, model-based techniques are well studied, but they have not yet been employed in qubit noise spectroscopy (QNS). In this work, we show how such approaches can be adapted to standard gate-based QNS procedures; moreover, we demonstrate that the recently introduced Schrödinger Wave Autoregressive Moving Average (SchWARMA) models can be used in a spectrum estimation technique that can resolve an injected noise tone to numerical precision in frequency. These results continue to expand the role of classical statistical signal processing in advancing quantum characterization, verification, and validation, and furthermore will have applications in quantum sensing of classical signals from radar to magnetic resonance imaging.