Control of finite-dimensional quantum systems: Application to a spin-12 particle coupled with a finite quantum harmonic oscillator

C. Rangan, A. M. Bloch
2005 Journal of Mathematical Physics  
In this paper, we consider the problem of the controllability of a finite-dimensional quantum system in both the Schrödinger 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
more » ... ion. We describe the control of the finite model obtained, under the right conditions, from the original infinite-dimensional system.
doi:10.1063/1.1852701 fatcat:keurdb4lrzba7dmtqo4ceqsdja