Optimal control of two-level quantum systems

Author

Alessandro, Domenico D. ; Dahleh, Mohammed

Author_Institution

Dept. of Math., Iowa State Univ., Ames, IA, USA

Volume

46

Issue

6

fYear

2001

fDate

6/1/2001 12:00:00 AM

Firstpage

866

Lastpage

876

Abstract

We study the manipulation of two-level quantum systems. This research is motivated by the design of quantum mechanical logic gates which perform prescribed logic operations on a two-level quantum system, a quantum bit. We consider the problem of driving the evolution operator to a desired state, while minimizing an energy-type cost. Mathematically, this problem translates into an optimal control problem for systems varying on the Lie group of special unitary matrices of dimension two, with cost that is quadratic in the control. We develop a comprehensive theory of optimal control for two-level quantum systems. This includes, in particular, a classification of normal and abnormal extremals and a proof of regularity of the optimal control functions. The impact of the results of the paper on nuclear magnetic resonance experiments and quantum computation is discussed

Keywords

Hilbert spaces; Lie groups; controllability; maximum principle; nuclear magnetic resonance; quantum gates; Hilbert space; Lie group; controllability; logic gates; maximum principle; nuclear magnetic resonance; optimal control; quantum mechanics; two-level quantum systems; Control systems; Cost function; Energy states; Logic design; Masers; Mechanical systems; Nuclear magnetic resonance; Optimal control; Quantum computing; Quantum mechanics;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.928587

Filename

928587