LQG feedback control of a class of linear non-Markovian quantum systems

TL;DR

This paper develops an LQG feedback control method for linear non-Markovian quantum systems, using a whitening filter based on an augmented Markovian model to improve control performance.

Contribution

It introduces a novel control strategy combining whitening quantum filtering with LQG control for non-Markovian quantum systems, enhancing performance over traditional Markovian approaches.

Findings

LQG controller with whitening filter outperforms Markovian filter in photon number minimization.

Simulation demonstrates improved control accuracy in non-Markovian quantum dynamics.

The approach effectively manages environmental noise via an augmented Markovian model.

Abstract

In this paper we present a linear quadratic Gaussian (LQG) feedback control strategy for a class of linear non-Markovian quantum systems. The feedback control law is designed based on the estimated states of a whitening quantum filter for an augmented Markovian model of the non-Markovian open quantum systems. In this augmented Markovian model, an ancillary system plays the role of internal modes of the environment converting white noise into Lorentzian noise and a principal system obeys non-Markovian dynamics due to the direct interaction with the ancillary system. The simulation results show the LQG controller with the whitening filter obtains a better control performance than that with a Markovian filter in the problem of minimizing the photon numbers of the principal system when the ancillary system is disturbed by thermal noise.