Methods of geometric control theory for quantum computations

The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. It is shown that these methods are very useful for the problem of constructing a universal set of gates for quantum computations. The well-known result that the set of all one-bit gates, together with no more than one two-bit gate, is universal is considered from the control theory viewpoint. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 27, Algebra and Geometry, 2005.