Quantum Feedback Networks and Control: A Brief Survey

The purpose of this paper is to provide a brief review of some recent developments in quantum feedback networks and control. A quantum feedback network (QFN) is an interconnected system consisting of open quantum systems linked by free fields and/or direct physical couplings. Basic network constructs, including series connections as well as feedback loops, are discussed. The quantum feedback network theory provides a natural framework for analysis and design. Basic properties such as dissipation, stability, passivity and gain of open quantum systems are discussed. Control system design is also discussed, primarily in the context of open linear quantum stochastic systems. The issue of physical realizability is discussed, and explicit criteria for stability, positive real lemma, and bounded real lemma are presented. Finally for linear quantum systems, coherent $H^\infty$ and LQG control are described.Comment: 29 pages, 11 figures. A new reference has been adde

Mixed quantum-classical linear systems synthesis and quantum feedback control designs

This thesis makes some theoretical contributions towards mixed quantum feedback network synthesis, quantum optical realization of classical linear stochastic systems and quantum feedback control designs. A mixed quantum-classical feedback network is an interconnected system consisting of a quantum system and a classical system connected by interfaces that convert quantum signals to classical signal (using homodyne detectors), and vice versa (using electro-optic modulators). In the area of mixed quantum-classical feedback networks, we present a network synthesis theory, which provides a natural framework for analysis and design for mixed linear systems. Physical realizability conditions are derived for linear stochastic differential equations to ensure that mixed systems can correspond to physical systems. The mixed network synthesis theory developed based on physical realizability conditions shows that how a classical of mixed quantum-classical systems described by linear stochastic differential equations can be built as a interconnection of linear quantum systems and linear classical systems using quantum optical devices as well as electrical and electric devices. However, an important practical problem for the implementation of mixed quantum-classical systems is the relatively slow speed of classical parts implemented with standard electrical and electronic devices, since a mixed system will not work correctly unless the electronic processing of classical devices is fast enough. Therefore, another interesting work is to show how classical linear stochastic systems build using electrical and electric devices can be physically implemented using quantum optical components. A complete procedure is proposed for a stable quantum linear stochastic system realizing a given stable classical linear stochastic system. The thesis explains how it may be possible to realize certain measurement feedback loops fully at the quantum level. In the area of quantum feedback control design, two numerical procedures based on extended linear matrix inequality (LMI) approach are proposed to design a coherent quantum controller in this thesis. The extended synthesis linear matrix inequalities are, in addition to new analysis tools, less conservative in comparison to the conventional counterparts since the optimization variables related to the system parameters in extended LMIs are independent of the symmetric Lyapunov matrix. These features may be useful in the optimal design of quantum optical networks. Time delays are frequently encountered in linear quantum feedback control systems such as long transmission lines between quantum plants and linear controllers, which may have an effect on the performance of closed-loop plant controller systems. Therefore, this thesis investigates the problem of linear quantum measurement-based feedback control systems subject to feedback-loop time delay described by linear stochastic differential equations. Several numerical procedures are proposed to design classical controllers that make quantum measurement-based feedback control systems with time delay stable and also guarantee that their desired control performance specifications are satisfied

Implementation of Classical Linear Stochastic Systems Using Quantum Optical Components

The purpose of this paper is to show how classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices, meaning faster response an