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

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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.

© 2007 Optical Society of America

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