  Non-Abelian holonomy in dynamical systems may arise in adiabatic transport of
energetically degenerate sets of states. We examine such a holonomy structure
for mixtures of energetically degenerate quantal states. We demonstrate that
this structure has a natural interpretation in terms of the standard
Wilczek-Zee holonomy associated with a certain class of Hamiltonians that
couple the system to an ancilla. The mixed state holonomy is analysed for
holonomic quantum computation using ion traps.
