  Classical control noise is ubiquitous in qubit devices, making its accurate
spectral characterization essential for designing optimized error suppression
strategies at the physical level. Here, we focus on multiplicative Gaussian
amplitude control noise on a driven qubit sensor and show that sensing
protocols using optimally band-limited Slepian modulation offer substantial
benefit in realistic scenarios. Special emphasis is given to laying out the
theoretical framework necessary for extending non-parametric multitaper
spectral estimation to the quantum setting by highlighting key points of
contact and differences with respect to the classical formulation. In
particular, we introduce and analyze two approaches (adaptive vs.
single-setting) to quantum multitaper estimation, and show how they provide a
practical means to both identify fine spectral features not otherwise
detectable by existing protocols and to obtain reliable prior estimates for use
in subsequent parametric estimation, including high-resolution Bayesian
techniques. We quantitatively characterize the performance of both single- and
multitaper Slepian estimation protocols by numerically reconstructing
representative spectral densities, and demonstrate their advantage over
dynamical-decoupling noise spectroscopy approaches in reducing bias from
spectral leakage as well as in compensating for aliasing effects while
maintaining a desired sampling resolution.
