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

Authors

Chitra Rangan, University of WindsorFollow
A.M. Bloch

Document Type

Article

Publication Date

2005

Publication Title

Journal of Mathematical Physics

Volume

46

Issue

3

First Page

032106-1

Last Page

032106-9

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.

Comments

This article was first published in the Journal of Mathematical Physics, Vol. 46 Iss. 3. Copyright (2012) American Physical Society (APS). It can be found here.

Recommended Citation

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.
https://scholar.uwindsor.ca/physicspub/6