Bayesian and geometric analyses of power spectral densities of spin qubits in Si/SiGe quantum dot devices
Charge noise with a power-law spectrum poses a significant challenge to high-fidelity operation of spin qubits in semiconductor devices. Recently, considerable experimental work characterized this noise using qubits as spectrometers. It apparently arises from a collection of two-level fluctuating electric dipole systems (TLS). This suggests using the data to infer the positions, orientations, and other physical characteristics of the TLS. We identify a fundamental difficulty in this program: the inference of the TLS parameters is strongly undetermined, since the quantity of data is not sufficient to fix them uniquely. We describe two approaches to deal with this situation. The first approach is a qualitative method based on analytic calculations and simulations of small model systems that recognizes certain patterns. The second approach, more appropriate for detailed data analysis, is a Bayesian computation that assigns probabilities to candidate dipole configurations. We propose that the Brier score, a measure of confidence in the probabilities, can be used as a quantitative tool to judge the efficacy of experimental noise-measurement setups. Together, the analytical and computational Bayesian methods constrain, but do not fix, the density, the positions, the orientations, and the strengths of the dipole noise sources.