We consider the problem of estimating the state of a superconducting qubit, which is coupled to a microwave cavity via a continuous weak measurement. The quit is readout via homodyne detection on the cavity. Each possible measurement record corresponds to a particular realization of the quantum system and is necessarily random. We study the error bound of the state estimation from the measurement signal by using an optimal Kalman filter. We further tracking and stabilizing the Rabi frequency by using quantum feedback control to properly adjust the frequencies and amplitudes of the external drives.
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