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A hybrid quantum-classical filtering problem, where a qubit system isdisturbed by a classical stochastic process, is investigated. The strategy isto model the classical disturbance by using an optical cavity. Relationsbetween classical disturbances and the cavity analog system are analyzed. Thedynamics of the enlarged quantum network system, which includes a qubit systemand a cavity system, are derived. A stochastic master equation for thequbit-cavity hybrid system is given, based on which estimates for the state ofthe cavity system and the classical signal are obtained. The quantum extendedKalman filter is employed to achieve efficient computation. Numerical resultsare presented to illustrate the effectiveness of our methods.

Hybrid filtering for a class of nonlinear quantum systems subject to classical stochastic disturbances