Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum-Atom Optics Downunder (QAO)

H∞ Control of Linear Quantum Stochastic Systems

M. R. James, Hendra I. Nurdin, Ian R. Petersen

Published Jan 1, 2007• 242 citations
Publisher

Abstract

The purpose of this paper is to formulate and solve a H?controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H?control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements.

DOI
10.1364/qao.2007.qme32

Related papers

Control of Linear Quantum Stochastic Systems

Ian R. Petersen

The purpose of this paper is to formulate and solve a H∞ controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H∞ control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.

•Jan 1, 2008•2 citations

H-Infinity Control of Linear Quantum Stochastic Systems

M. R. James, H. I. Nurdin, Idar Petersen

The purpose of this paper is to formulate and solve a H-infinity controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H-infinity control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.

arXiv:quant-ph/0703150•Mar 16, 2007•8 citations

H∞ Control of Linear Quantum Systems

M. R. James, Ian R. Petersen

The purpose of this paper is to formulate and solve a H∞controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of the strict bounded real lemma is presented and from this, a quantum version of the two Riccati solution to the H∞control problem is derived

IEEE Conference on Decision and Control (CDC)•Dec 1, 2006•4 citations

$H^{\infty}$ Control of Linear Quantum Stochastic Systems

M. R. James, Hendra I. Nurdin, Ian R. Petersen

The purpose of this paper is to formulate and solve aHinfincontroller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived. This enables a quantum version of the two Riccati solution to theHinfincontrol problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.

IEEE Transactions on Automatic Control•Sep 1, 2008•452 citations

Coherent H∞ control for a class of linear complex quantum systems

Aline I. Maalouf, Ian R. Petersen

This paper considers a coherent Hinfincontrol problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a solution to the Hinfincontrol problem can be obtained in terms of a pair of complex Riccati equations. The paper also considers complex versions of the bounded real lemma, the strict bounded real lemma and the lossless bounded real lemma. For the class of quantum systems under consideration, the question of physical realizability is related to the bounded real and lossless bounded real properties.

Proceedings of the ... American Control Conference/Proceedings of the American Control Conference•Jan 1, 2009•54 citations

Coherent $H^{\infty }$ Control for a Class of Annihilation Operator Linear Quantum Systems

Aline I. Maalouf, Ian R. Petersen

This paper considers a coherent H∞control problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a solution to the H∞control problem can be obtained in terms of a pair of complex algebraic Riccati equations. In addition, the question of physical realizability of the resulting quantum controllers is related to a bounded real property.

IEEE Transactions on Automatic Control•Jul 21, 2010•86 citations
The purpose of this paper is to formulate and solve a H?controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H?control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements.
The purpose of this paper is to formulate and solve a H∞ controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H∞ control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.
The purpose of this paper is to formulate and solve a H-infinity controller synthesis problem for a class of non-commutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the Strict Bounded Real Lemma is derived. This enables a quantum version of the two Riccati solution to the H-infinity control problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.
H∞H^{\infty}H∞ Control of Linear Quantum Stochastic Systems
The purpose of this paper is to formulate and solve aHinfincontroller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology. The paper includes results on the class of such systems for which the quantum commutation relations are preserved (such a requirement must be satisfied in a physical quantum system). A quantum version of standard (classical) dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived. This enables a quantum version of the two Riccati solution to theHinfincontrol problem to be presented. This result leads to controllers which may be realized using purely quantum, purely classical or a mixture of quantum and classical elements. This issue of physical realizability of the controller is examined in detail, and necessary and sufficient conditions are given. Our results are constructive in the sense that we provide explicit formulas for the Hamiltonian function and coupling operator corresponding to the controller.
This paper considers a coherent Hinfincontrol problem for a class of linear quantum systems which can be defined by complex quantum stochastic differential equations in terms of annihilation operators only. For this class of quantum systems, a solution to the Hinfincontrol problem can be obtained in terms of a pair of complex Riccati equations. The paper also considers complex versions of the bounded real lemma, the strict bounded real lemma and the lossless bounded real lemma. For the class of quantum systems under consideration, the question of physical realizability is related to the bounded real and lossless bounded real properties.
Coherent H∞H^{\infty }H∞ Control for a Class of Annihilation Operator Linear Quantum Systems