Document Type

Article

Publication Date

2007

Publication Title

Physical Review A - Atomic, Molecular, and Optical Physics

Volume

76

Issue

3

First Page

033401-1

Last Page

033401-6

Abstract

We study quantum systems with even numbers N of levels that are completely state controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1) 2 as discussed by Albertini and D'Allesandro [IEEE Trans. Autom. Control 48, 1399 (2003)]. These Lie algebras are smaller than the corresponding su(N) with dimension N2 -1. We show that this reduction constrains the field-free Hamiltonian to have symmetric energy levels. An example of such a system is an n -qubit system with state-independent interaction terms. Using Clifford's geometric algebra to represent the quantum wave function of a finite system, we present an explicit example of a two-qubit system that can be controlled by the elements of the Lie algebra sp(4) [isomorphic to spin(5) and so(5)] with dimension 10 rather than su(4) with dimension 15, but only if its field-free energy levels are symmetrically distributed about an average. These results enable one to envision more efficient algorithms for the design of fields for quantum-state engineering in certain quantum-computing applications, and provide more insight into the fundamental structure of quantum control.

Comments

This article was first published in PHYSICAL REVIEW A Vol. 76 Iss. 3, 2007. Copyright (2012) American Physical Society (APS). It can be found here.

Download

Included in

Physics Commons

Share

COinS