Control of finite-dimensional quantum systems: Application to a spin-1/2 particle coupled with a finite quantum harmonic oscillator

Abstract

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 ion. We describe the control of the finite model obtained, under the right conditions, from the original infinite-dimensional system. © 2005 American Institute of Physics.