Analyses of auto and cross power spectral densities of semiconductor spin qubits*

Charge noise is a major source of decoherence of spin qubits. This type of noise is not yet fully characterized, but fluctuating two-level systems (TLS) are generally thought to be responsible. Different spatial configurations and other variations between fluctuators lead to differences in their noise spectra. Experiments have been performed to probe the effects of qubit geometry, temperature, and other changing parameters. Here, we present techniques based on Monte Carlo simulations and Bayesian analysis to calculate qubit auto-power spectral density (APSD) and cross-power spectral density (CPSD). These are used to characterize the noise spectra generated from different theoretical TLS models. We find that both APSD and CPSD measurements can be used to constrain the identification of an unknown TLS. We also suggest some directions for future experiments to test these predictions.