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arXiv:quant-ph/0703150

H-Infinity Control of Linear Quantum Stochastic Systems

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

Published Mar 16, 2007• 8 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0703150

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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.