Journal of Mathematical Physics
In this paper, we consider the problem of the controllability of a finite-dimensional quantum system in both the SchrÃ¶dinger and interaction pictures. Introducing a Quantum Transfer Graph, we elucidate the role of Lie algebra rank conditions and the complex nature of the control matrices. We analyze the example of a sequentially coupled N-level system: a spin-1/2 particle coupled to a finite quantum harmonic oscillator. This models an important physical paradigm of quantum computers - the trapped ion. We describe the control of the finite model obtained, under the right conditions, from the original infinite-dimensional system.
Rangan, Chitra and Bloch, A.M.. (2005). Control of finite-dimensional quantum systems: Application to a spin-1/2 particle coupled with a finite quantum harmonic oscillator. Journal of Mathematical Physics, 46 (3), 032106-1-032106-9.