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World Congress on Intelligent Control and Automation

Feedback tracking control of a class of non-Markovian quantum systems

Shibei Xue, Ian R. Petersen

Published Jun 1, 2016• 5 citations
Publisher

Abstract

In this paper, we propose a feedback tracking control scheme to reject Lorentzian noise in a linear non-Markovian quantum system. This non-Markovian quantum system is modelled as an augmented linear Markovian quantum system where a principal system represents the plant and an ancillary system represents the internal mode of the non-Markovian environment for generating Lorentzian noise. Based on this augmented system model, a whitening quantum filter can be constructed for continuously monitoring the dynamical variables of the principal system. To reject Lorentzian noise, a linear quadratic Gaussian (LQG) controller, using the estimate of the whitening filter and the dynamical variables of a reference system, can be designed to drive the principal system to track the reference system.

DOI
10.1109/wcica.2016.7578293

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In this paper, a quantum filter for estimating the states of a non-Markovian qubit system is presented in an augmented Markovian system framework including both the qubit system of interest and multi-ancillary systems for representing the internal modes of the non-Markovian environment. The colored noise generated by the multi-ancillary systems disturbs the qubit system via a direct interaction. The resulting non-Markovian dynamics of the qubit is determined by a memory kernel function arising from the dynamics of the ancillary system. In principle, colored noise with arbitrary power spectrum can be generated by a combination of Lorentzian noises. Hence, the quantum filter can be constructed for the qubit disturbed by arbitrary colored noise and the conditional state of the qubit system can be obtained by tracing out the multi-ancillary systems.