Nurdin, Hendra I.James, Matthew R.Petersen, Ian R.2026-07-032026-07-03ORCID:/0000-0003-4856-9450/work/219177681https://hdl.handle.net/1885/733812541We 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.en200784898990952