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IEEE Conference on Decision and Control (CDC)

When do additional quantum noises affect controller performance?

Rebbecca TY Thien, Shanon L. Vuglar, Ian R. Petersen

Published Dec 14, 2020• 1 citation
Publisher

Abstract

The introduction of quantum noise in a system is necessary for realizing it as physical quantum system. In general, quantum noise can be detrimental to the performance of a coherent quantum feedback control system. This paper gives a necessary and sufficient condition for when a quantum system corresponding to a given Linear Time Invariant (LTI) controller can be made physically realizable in the presence of both direct feedthrough quantum vacuum noise and additional quantum vacuum noise such that the additional quantum noise has no effect on the controller output. Furthermore, an example is presented to illustrate our result.

DOI
10.1109/cdc42340.2020.9303833

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The introduction of quantum noise in a system is necessary for realizing it as physical quantum system. In general, quantum noise can be detrimental to the performance of a coherent quantum feedback control system. This paper gives a necessary and sufficient condition for when a quantum system corresponding to a given Linear Time Invariant (LTI) controller can be made physically realizable in the presence of both direct feedthrough quantum vacuum noise and additional quantum vacuum noise such that the additional quantum noise has no effect on the controller output. Furthermore, an example is presented to illustrate our result.
Additional noise in a quantum system can be detrimental to the performance of a quantum coherent feedback control system. This paper proposes a Linear Matrix Inequality (LMI) approach to construct an optimal quantum realization of a given Linear Time Invariant (LTI) system. The quantum realization problem is useful in designing coherent quantum feedback controllers. An optimal method is proposed for solving this problem in terms of a finite horizon quadratic performance index, which is related to the amount of quantum noise appearing at the system’s output. This cost function provides a measure of how much the additional quantum noise in the coherent controller will alter the feedback control system.
In M. R. James, H. I. Nurdin, and I. R. Petersen, “H∞ control of linear quantum stochastic systems,” IEEE Transactions on Automatic Control, vol. 53, no. 8, pp. 1787–1803, 2008, the authors showed that an arbitrary LTI system can be made physically realizable if additional quantum noise components are permitted in the implementation. However, incorporating additional noise is undesirable, and this paper refines their method in order to provide a concrete expression for the number of additional quantum noise components needed to guarantee physical realizability.
Physical Realizability addresses the question of whether it is possible to implement a given LTI system as a quantum system. It is in general not true that a given synthesized quantum controller described by a set of stochastic differential equations is equivalent to some physically meaningful quantum system. However, if additional quantum noises are permitted in the implementation it is always possible to implement an arbitrary LTI system as a quantum system. In this paper we give an expression for the exact number of noises required to implement a given LTI system as a quantum system. Furthermore, we focus our attention on proving that this is a minimum, that is, it is not possible to implement the system as a quantum system with a smaller number of additional quantum noises.