Charge-state estimation in quantum dots using a Bayesian approach

Detection of single-electron charges in solid-state nanodevices is a key technique in semiconductor quantum bit readout for quantum information processing and probing electronic properties of nanostructures. This detection has been achieved using gate-based readouts and sensitive charge sensors including quantum dot charge sensors, with their detection speed enhanced by high-speed rf reflectometry. Recently, real-time processing of data from rf reflectometry has attracted much attention to quantum information processing. In this paper, we propose a sequential method based on Bayes' theorem for estimating the charge state and compare its performance with the averaging approach and threshold judgment. When the noise variance differs between the empty and occupied states, the Bayesian approach demonstrates a lower error score, facilitating the extraction of more data points in real-time charge state estimation. In addition, the Bayesian approach outperforms the averaging method and threshold judgment in terms of error rates for charge state estimation, even during charge transitions. This technique is broadly applicable to single-electron detection and holds substantial utility for quantum bit readout and the operation of nanoprobes that utilize single-electron detection.