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Chinese Control Conference (CCC)

Coherent observer engineering for protecting quantum information

Yu Pan, Thien Nguyen, Zibo Miao, Nina H. Amini, Valery Ugrinovskii, M. R. James

Published Jul 1, 2016• 2 citations
Publisher

Abstract

In this paper, we extend the applicability of coherent quantum observers to enable the generation of decoherence free subsystem which can be used for quantum information storage. In particular, a general quantum linear passive system can be equipped with a decoherence free subsystem by placing some of its poles on the imaginary axis via engineered observer-based controller. The controller design for the case of optical cavity systems is illustrated in the context of examples.

DOI
10.1109/chicc.2016.7554812

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In this paper, we extend the applicability of coherent quantum observers to enable the generation of decoherence free subsystem which can be used for quantum information storage. In particular, a general quantum linear passive system can be equipped with a decoherence free subsystem by placing some of its poles on the imaginary axis via engineered observer-based controller. The controller design for the case of optical cavity systems is illustrated in the context of examples.
In this paper we extend our previous research on coherent observer-based pole placement approach to study the synthesis of robust decoherence-free (DF) modes for linear quantum passive systems, which is aimed at preservation of quantum information. In particular, DF modes can be generated by placing the poles on the imaginary axis via a coherent feedback design scheme, and these modes can further be simultaneously made robust against perturbations to the system parameters by minimizing the condition number associated with imaginary poles. We develop explicit algebraic conditions for the existence of such a coherent quantum controller, with the corresponding deign procedure provided. Examples are given to illustrate the process of tuning the DF modes towards perfect robustness via the proposed pole placement technique.
Abstract In this paper, the synthesis of robust memory modes for linear quantum passive systems in the presence of unknown inputs has been studied, aimed at facilitating secure storage and communication of quantum information. In particular, we can switch on decoherence-free (DF) modes in the storage stage by placing the poles on the imaginary axis via a coherent feedback control scheme, and these memory modes can further be simultaneously made robust against perturbations to the system parameters by minimizing the condition number associated with imaginary poles. The DF modes can also be switched off by tuning the controller parameters to place the poles in the left half of the complex plane in the writing/reading stage. We develop explicit algebraic conditions guiding the design of such a coherent quantum controller, which involves employing an augmented system model to counter the influence of unknown inputs. Examples are provided to illustrate the procedure of synthesizing robust memory modes for linear optical quantum systems.
We previously extended Luenberger's approach for observer design to the quantum case, and developed a class of coherent observers which tracks linear quantum stochastic systems in the sense of mean values. In light of the fact that the Luenberger observer is commonly and successfully applied in classical control, it is interesting to investigate the role of coherent observers in quantum feedback. As the first step in exploring observer-based coherent control, in this paper we study pole-placement techniques for quantum systems using coherent observers, and in such a fashion, poles of a closed-loop quantum system can be relocated at any desired locations. In comparison to classical feedback control design incorporating the Luenberger observer, here direct coupling between a quantum plant and the observer-based controller are allowed to enable a greater degree of freedom for the design of controller parameters. A separation principle is presented, and we show how to design the observer and feedback independently to be consistent with the laws of quantum mechanics. The proposed scheme is applicable to coherent feedback control of quantum systems, especially when the transient dynamic response is of interest, and this issue is illustrated in an example.
This paper provides a general theory for characterizing and constructing a decoherence-free (DF) subsystem for an infinite dimensional linear open quantum system. The main idea is that, based on the Heisenberg picture of the dynamics rather than the commonly-taken Schrödinger picture, the notions of controllability and observability in control theory are employed to characterize a DF subsystem. A particularly useful result is a general if and only if condition for a linear system to have a DF component; this condition is used to demonstrate how to actually construct a DF dynamics in some specific examples. It is also shown that, as in the finite dimensional case, we are able to do coherent manipulation and preservation of a state of a DF subsystem.
Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs.