  Quantum mechanical systems exhibit an inherently probabilistic nature upon
measurement. Using a quantum noise model to describe the stochastic evolution
of the open quantum system and working in parallel with classical
indeterministic control theory, we present the theory of nonlinear optimal
quantum feedback control. The resulting quantum Bellman equation is then
applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG)
problem which emphasizes many similarities with the corresponding classical
control problem.
