arXiv Analytics

Sign in

arXiv:quant-ph/0608075AbstractReferencesReviewsResources

Finite Controllability of Infinite-Dimensional Quantum Systems

A. M. Bloch, R. W. Brockett, C. Rangan

Published 2006-08-09, updated 2009-09-07Version 2

Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is finite-dimensional and old results on controllability of systems defined on on Lie groups and quotient spaces provide most of what is needed insofar as controllability of non-dissipative systems is concerned. However, in an infinite-dimensional setting, controlling the evolution of quantum systems often presents difficulties, both conceptual and technical. In this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues. In particular, we analyze controllability for infinite-dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre-defined subspaces. This result, which we call the Finite Controllability Theorem, provides a set of sufficient conditions for controllability in an infinite-dimensional setting. We consider specific physical systems that are of interest for quantum computing, and provide insights into the types of quantum operations (gates) that may be developed.

Comments: This is a much improved version of the paper first submitted to the arxiv in 2006 that has been under review since 2005. A shortened version of this paper has been conditionally accepted for publication in IEEE Transactions in Automatic Control (2009)
Categories: quant-ph
Related articles: Most relevant | Search more
arXiv:1308.3287 [quant-ph] (Published 2013-08-15)
The CHSH-type inequalities for infinite-dimensional quantum systems
arXiv:1203.3933 [quant-ph] (Published 2012-03-18)
Concurrence for infinite-dimensional quantum systems
arXiv:1009.0116 [quant-ph] (Published 2010-09-01)
The RCCN criterion of separability for states in infinite-dimensional quantum systems