  This paper is concerned with a risk-sensitive optimal control problem for a
feedback connection of a quantum plant with a measurement-based classical
controller. The plant is a multimode open quantum harmonic oscillator driven by
a multichannel quantum Wiener process, and the controller is a linear time
invariant system governed by a stochastic differential equation. The control
objective is to stabilize the closed-loop system and minimize the
infinite-horizon asymptotic growth rate of a quadratic-exponential functional
(QEF) which penalizes the plant variables and the controller output. We combine
a frequency-domain representation of the QEF growth rate, obtained recently,
with variational techniques and establish first-order necessary conditions of
optimality for the state-space matrices of the controller.

Quantum Physics;Systems and Control;Systems and Control;Optimization and Control