Bayesian estimation of correlation functions

Spatial noise correlations beyond nearest-neighbor in ${}^{28}$Si/SiGe spin qubits

“…Second, these correlations have a well-defined phase relation, with a sharp transition from positive to negative at around 0.06 Hz. The estimating distributions in the plots provide us with confidence on the measured results [58]. All this confirms the correlations are beyond coincidence, proving that the resonant frequencies of these two qubits are correlated.…”

“…We calculated the auto-PSD for each qubit using Bayesian estimation of correlation functions [58], from which we are able to extract not only the values of the PSDs but also the confidence level of the estimations, the results are plotted in Fig. 2a.…”

“…This highlights the importance of providing a level of confidence when reporting noise spectra and is the reason why we use the Bayesian estimation of correlation functions from Ref. [58]. Since the frequency switchings are independent from one another, noise at the lowest-frequencies (< 10 −3 Hz) appears to be close to uncorrelated, but we cannot quantify the degree of correlation with reasonable confidence unless we cover a much longer time span with our measurement.…”

“…First, despite the large separation between qubits we find finite spatial noise correlations that In all panels, the color gradient represents the estimating distribution of the corresponding quantity at each frequency with the maximum likelihood estimator marked as points (details are discussed in Ref. [58]); the continuous lines are calculated from the distribution in Fig. 3.…”

“…Inset: sample time traces of each qubit frequency showing a 2-level switching behavior; the color code follows that of the main panel. (b) and (c) correlation coefficient amplitude and phase, respectively.In all panels, the color gradient represents the estimating distribution of the corresponding quantity at each frequency with the maximum likelihood estimator marked as points (details are discussed in Ref [58]…”