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Quantum-Atom Optics Downunder (QAO)

Linear Quadratic Gaussian Control of Quantum Linear Stochastic Systems with Quantum Mechanical Controllers

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

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We formulate a (sub-optimal) quantum Linear Quadratic Gaussian (LQG) problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum. Our problem may be viewed as a polynomial matrix programming problem and we show that by utilizing a non-linear change of variables, it can be systematically converted to a Linear Matrix Inequality (LMI) rank constrained problem. As an initial demonstration of the feasibility of this approach, we provide a fully quantum controller design example in which a numerical solution to the problem was successfully obtained.

DOI
10.1364/qao.2007.qme33

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A coherent quantum controller is itself a quantum system that is required to be physically realizable. Thus, additional non-linear and linear constraints must be imposed on the coefficients of a physically realizable quantum controller, which differs the quantum Linear Quadratic Gaussian (LQG) design from the standard LQG problem. The purpose of this paper is to propose one numerical procedure based on extended linear matrix inequality (LMI) approach and new physical realizability conditions proposed in [14] to design a coherent quantum controller. 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. For comparison, we apply our numerical procedure to the same example given in [9].