Linear quadratic gaussian control of quantum linear stochastic systems with quantum mechanical controllers

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.