Hybrid Filtering for a Class of Quantum Systems with Classical Disturbances

TL;DR

This paper develops a hybrid quantum-classical filtering approach to estimate states of quantum systems disturbed by classical stochastic processes, using quantum filtering and Kalman filter techniques, validated through numerical simulations.

Contribution

It introduces a novel hybrid filtering method combining quantum filtering and Kalman filtering for quantum systems affected by classical disturbances.

Findings

Effective state estimation demonstrated through numerical results.

Hybrid filtering outperforms traditional methods in quantum systems with classical noise.

The approach successfully estimates both quantum states and classical disturbances.

Abstract

A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation, is modeled by a quantum cavity model. Then the hybrid quantum-classical system is described by a combined quantum system consisting of two quantum cavity subsystems. Quantum filtering theory and a quantum extended Kalman filter method are employed to estimate the states of the combined quantum system. An estimate of the classical stochastic process is derived from the estimate of the combined quantum system. The effectiveness and performance of the proposed methods are illustrated by numerical results.