  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
is achieved using quantum dot charge sensors, with its 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. Additionally, 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.
