LQG feedback control of a class of linear non-Markovian quantum systems
Shibei Xue, Matthew R. James, Valery Ugrinovskii, Ian R. Petersen · 2016
In this paper we present a linear quadratic Gaussian (LQG) feedback control strategy for a class of linear non-Markovian quantum systems disturbed by Lorentzian noise. The feedback control law is designed based on the estimated dynamical variables of a whitening quantum filter for an augmented Markovian model of the non-Markovian quantum system. 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 cooling the principal system when the ancillary system is driven by thermal noise.