Guaranteed Cost LQG Control of Uncertain Linear Stochastic Quantum Systems

Shaiju, A. J.; Petersen, Ian R.; James, Matthew R.

doi:10.1109/acc.2007.4282598

Cited by 20 publications

(25 citation statements)

References 15 publications

(40 reference statements)

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“…Under appropriate assumptions, some quantum optical systems can be approximately modeled by LQSDEs driven by quantum Wiener processes [56], [160]. This simplification provides an opportunity to develop quantum linear-quadratic-Gaussian (LQG) control to obtain an optimal feedback strategy [4], [69], [70], [73], [143], [160], [161], [162]. In LQG control, the goal is to find an optimal feedback control law for a stochastic linear system by optimizing a quadratic cost functional.…”

Section: Lqg Controlmentioning

confidence: 99%

“…In the quantum LQG control problem, the optimal control is also a linear feedback control law. The controller may be a classical controller [162] or a quantum controller [158], [159]. For classical controllers, it is straightforward to apply results in classical LQG control to quantum LQG problems.…”

Section: Lqg Controlmentioning

confidence: 99%

“…For classical controllers, it is straightforward to apply results in classical LQG control to quantum LQG problems. In fact, some results on quantum LQG control with classical controllers have been developed in [69], [73], [143], [160], [162]. For controllers which are themselves quantum systems, we must add some additional constraints on coefficient matrices to ensure that the controller is physically realizable.…”

Section: Lqg Controlmentioning

confidence: 99%

See 2 more Smart Citations

Quantum control theory and applications: a survey

Dong

Petersen

2010

IET Control Theory &Amp; Applications

Self Cite

527

392

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This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closedloop quantum control, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control.

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Section: Lqg Controlmentioning

confidence: 99%

Section: Lqg Controlmentioning

confidence: 99%

Section: Lqg Controlmentioning

confidence: 99%

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Quantum control theory and applications: a survey

Dong

Petersen

2010

IET Control Theory &Amp; Applications

Self Cite

527

392

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“…i.r.petersen@gmail.com possible platforms being investigated for future communication systems (see [30], [31]) and quantum computers (see [32], [33] and [34]). Feedback control of quantum systems aims to achieve closed loop properties such as stability [35], [36], robustness [11], [37], entanglement [18], [38], [39].…”

Section: Introductionmentioning

confidence: 99%

Quantum Linear Systems Theory

Petersen¹

2016

Open Autom. Control Syst. J.

106

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Abstract-This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics, take the specific form of a set of linear quantum stochastic differential equations (QSDEs). Such systems commonly arise in the area of quantum optics and related disciplines. Systems whose dynamics can be described or approximated by linear QSDEs include interconnections of optical cavities, beam-spitters, phase-shifters, optical parametric amplifiers, optical squeezers, and cavity quantum electrodynamic systems. With advances in quantum technology, the feedback control of such quantum systems is generating new challenges in the field of control theory. Potential applications of such quantum feedback control systems include quantum computing, quantum error correction, quantum communications, gravity wave detection, metrology, atom lasers, and superconducting quantum circuits.A recently emerging approach to the feedback control of quantum linear systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case. An important issue which arises both in the modelling of linear quantum systems and in the synthesis of linear coherent quantum controllers is the issue of physical realizability. This issue relates to the property of whether a given set of QSDEs corresponds to a physical quantum system satisfying the laws of quantum mechanics. The paper will cover recent results relating the question of physical realizability to notions occuring in linear systems theory such as lossless bounded real systems and dual J-J unitary systems.

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“…Some control methods involving coherent S. Wang feedback [4], [15] and measurement-based feedback [1] have been used for enhancing the performance of linear quantum optical systems with uncertainties. The design problems of robust controllers or observers have also been investigated for uncertain linear quantum stochastic systems [16], [17]. For example, Yamamoto [17] presented the result of robust observer design for linear quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Fault-Tolerant Control of Linear Quantum Stochastic Systems

Wang

Dong

2017

IEEE Trans. Automat. Contr.

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In quantum engineering, faults may occur in a quantum control system, which will cause the quantum control system unstable or deteriorate other relevant performance of the system. This note presents an estimator-based fault-tolerant control design approach for a class of linear quantum stochastic systems subject to fault signals. In this approach, the fault signals and some commutative components of the quantum system observables are estimated, and a fault-tolerant controller is designed to compensate the effect of the fault signals. Numerical procedures are developed for controller design and an example is presented to demonstrate the proposed design approach.Index Terms-Linear quantum stochastic system, quantum control, fault-tolerant control.

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Guaranteed Cost LQG Control of Uncertain Linear Stochastic Quantum Systems

Cited by 20 publications

References 15 publications

Quantum control theory and applications: a survey

Quantum control theory and applications: a survey

Quantum Linear Systems Theory

Fault-Tolerant Control of Linear Quantum Stochastic Systems

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