Uwe Helmke

Mathematical Institute

University of Wuerzberg

**Control Theoretic Aspects of Matrix Factorizations**

We discuss control theoretic aspects of factorizing elements in a compact Lie group via a given set of generators of the Lie algebra.

Such problems naturally arise in quantum computing and the control of spin systems in nuclear magnetic resonance spectroscopy. We begin with a short introduction on Lie groups and Lie algebras, we discuss relevant controllability issues on Lie groups. The main part of the talk is then devoted to time optimal control and, in particular, to computing time optimal pulse sequences for the control of 2 spin systems.

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