The Controllability of Quantum-Classical Hybrid Systems

The classical noise is unavoided in the real world. In what way classical part impact quantum dynamics and whether classical part impact controllability of quantum system have become problems. To figure out these two problems, we focus on a specific hybrid system which is both quasi-free and Markov. Because of its quasi-free property, the hybrid system comprising an open quantum system and a classical stochastic process possesses a distinct transformation formula that determines its dynamical semigroup. All these discussions are described by Weyl operators which also constitue the observable space. The controllability of reduced quantum system is first discussed, given its likely Lindblad form. The drift term is consisted of both classical information and quantum information. By adding classical control term in drift term, the controllability is analyzed using LARC(Lie Algebra Rank Condition). We discover that the reduced quantum system is fully controllable under certain controls. When we take classical information as a control, the reduced quantum system is fully controllable without external input. And the same conclusions hold in hybrid system.