  A unifying framework for the control of quantum systems with non-Abelian
holonomy is presented. It is shown that, from a control theoretic point of
view, holonomic quantum computation can be treated as a control system evolving
on a principal fiber bundle. An extension of methods developed for these
classical systems may be applied to quantum holonomic systems to obtain insight
into the control properties of such systems and to construct control algorithms
for two established examples of the computing paradigm.
