Based on a recently developed notion of physical realizability for quantum
linear stochastic systems, we formulate a quantum LQG optimal control 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. Such a control
scheme is often referred to in the quantum control literature as "coherent
feedback control.'' It distinguishes the present work from previous works on
the quantum LQG problem where measurement is performed on the plant and the
measurement signals are used as input to a fully classical controller with no
quantum degrees of freedom. The difference in our formulation is the presence
of additional non-linear and linear constraints on the coefficients of the
sought after controller, rendering the problem as a type of constrained
controller design problem. Due to the presence of these constraints our problem
is inherently computationally hard and this also distinguishes it in an
important way from the standard LQG problem. We propose a numerical procedure
for solving this problem based on an alternating projections algorithm and, as
initial demonstration of the feasibility of this approach, we provide fully
quantum controller design examples in which numerical solutions to the problem
were successfully obtained. For comparison, we also consider the case of
classical linear controllers that use direct or indirect measurements, and show
that there exists a fully quantum linear controller which offers an improvement
in performance over the classical ones.

本文针对量子线性随机系统的物理可实现性，提出了一种可以完全量子化植物输出信号的量子 LQG 最优控制问题，区别于此前的传统控制方法，并提出了带有附加非线性和线性约束的控制器设计问题，为此提出了一种基于交替投影算法的数值方法，通过完全量子控制器设计示例，成功解决了这个问题。