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Time optimal factorizations on compact Lie groups†

  1. G. Dirr,
  2. U. Helmke,
  3. M. Kleinsteuber

Article first published online: 27 DEC 2004

DOI: 10.1002/pamm.200410313

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PAMM

PAMM

Volume 4, Issue 1, pages 664–665, December 2004

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How to Cite

Dirr, G., Helmke, U. and Kleinsteuber, M. (2004), Time optimal factorizations on compact Lie groups. Proc. Appl. Math. Mech., 4: 664–665. doi: 10.1002/pamm.200410313

Author Information

  1. University of Würzburg, Department of Mathematics, 97074 Würzburg, Germany

  1. †

    This work was partially supported by the DAAD-Project: PPP Hong Kong, D/0122045

Publication History

  1. Issue published online: 27 DEC 2004
  2. Article first published online: 27 DEC 2004

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Keywords:

  • Euler angles;
  • compact Lie groups;
  • Cartan decomposition;
  • time optimal control;
  • quantum computing

Abstract

In this paper we study the relationship between factorization problems on SU(2n) or more generally on compact Lie groups G and time optimal control problems. Both types of problems naturally arise in physics, such as in quantum computing and in controlling coupled spin systems (NMR-spectroscopy). In the first part we show that certain factorization problems can be reformulated as time optimal control problems on G. In the second part a necessary condition for the existence of finite optimal factorizations is discussed. At the end we illustrate our results by an example on Euler angle factorizations. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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