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arXiv:0707.1074 · IEEE Transactions on Automatic Control

Quantum Dissipative Systems and Feedback Control Design by Interconnection

M. R. James, John Edward Gough

Published Mar 24, 2010• 134 citations
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Abstract

The purpose of this paper is to extend J.C. Willems' theory of dissipative systems to open quantum systems described by quantum noise models. This theory, which combines ideas from quantum physics and control theory, provides useful methods for analysis and design of dissipative quantum systems. We describe the interaction of the plant and a class of external systems, called exosystems, in terms of feedback networks of interconnected open quantum systems. Our results include an infinitesimal characterization of the dissipation property, which generalizes the well-known Positive Real and Bounded Real Lemmas, and is used to study some properties of quantum dissipative systems. We also show how to formulate control design problems using network models for open quantum systems, which implements Willems' “control by interconnection” for open quantum systems. This control design formulation includes, for example, standard problems of stabilization, regulation, and robust control.

DOI
10.1109/tac.2010.2046067

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Control by dissipation, or environment engineering, constitutes an important class of quantum coherent control methods which was proposed to improve robustness and scalability of quantum control systems. This paper aims to develop the theory for engineering the dissipation based on a ground-state Lyapunov stability analysis of the open quantum systems via a Heisenberg-picture approach. In particular, expressing the Lyapunov conditions as operator inequalities allows a purely algebraic treatment of the quantum environment engineering problem, which facilitates the integration of large-scale quantum coherent networks and could be used to draw an explicit connection to the theory of quantum Markov semigroups.
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