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Australian Control Conference

Implementation of classical linear stochastic systems using quantum optical components

Shi Wang, Hendra I. Nurdin, Guofeng Zhang, M. R. James

Published Jan 1, 2011• 2 citations
OpenAlex

Abstract

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 and

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In the last decade, there has been a growing interest in the integration of photonic components into VLSI circuits that in the long term may drive the need for systematic mixed electronic-photonic circuit design methods. On the other hand, theoretical and experimental investigations of coherent-feedback quantum control, the feedback control of a quantum system with another quantum system, have led to the development of a network synthesis theory for linear quantum stochastic models that are commonly employed in (linear) quantum optics, modelling such devices as optical cavities and optical parametric amplifiers. This paper makes theoretical contributions towards connecting these two independent developments, and anticipates potential future interest in systematic design methods for mixed linear electronic-photonic circuits, by establishing a network synthesis theory for linear stochastic systems with mixed quantum and classical degrees of freedom. It is shown how a physically realizable mixed quantum-classical linear stochastic system can be realized as a circuit composed of a feedback interconnection of a fully quantum linear subsystem, that can be implemented by quantum optical devices, and a classical linear sub-system, that can be implemented with standard electrical and electronic devices, together with appropriate interfaces that convert quantum signals to classical signals, and vice-versa. Two feedback architectures are proposed, and a decomposition lemma is derived that shows the structure of linear transformations of bosonic quantum signals into classical signals.
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.
Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors. After developing the fundamental concepts in quantum optics and quantum information theory, the book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables. This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises.
The purpose of this paper is to study the response of linear quantum stochastic systems to continuous mode single photon input fields. Given multi-channel continuous-mode single-photon input fields interacting with a linear quantum optical system which may contain active components, two expressions for the corresponding mean steady state output intensity are derived. In the single channel case, a synthesis theorem is proposed for pulse shaping of single-photon wave packets by all-pass quantum optics networks. Moreover, for the all-pass case, the steady-state states of output fields are derived. Several examples illustrate the main results.