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

TL;DR

This paper develops a hybrid quantum-classical filtering approach for nonlinear quantum systems affected by classical stochastic disturbances, modeling disturbances with an optical cavity and deriving a stochastic master equation for state estimation.

Contribution

It introduces a novel hybrid filtering framework combining quantum and classical models, including a cavity analog for disturbances and an extended Kalman filter for efficient estimation.

Findings

The method accurately estimates the quantum state and classical signals.

Numerical results demonstrate the effectiveness of the hybrid filtering approach.

Abstract

A hybrid quantum-classical filtering problem, where a qubit system is disturbed by a classical stochastic process, is investigated. The strategy is to model the classical disturbance by using an optical cavity. Relations between classical disturbances and the cavity analog system are analyzed. The dynamics of the enlarged quantum network system, which includes a qubit system and a cavity system, are derived. A stochastic master equation for the qubit-cavity hybrid system is given, based on which estimates for the state of the cavity system and the classical signal are obtained. The quantum extended Kalman filter is employed to achieve efficient computation. Numerical results are presented to illustrate the effectiveness of our methods.