  We propose a new strategy to physically implement a universal set of quantum
gates based on geometric phases accumulated in the nondegenerate eigenstates of
a designated invariant operator in a periodic physical system. The system is
driven to evolve in such a way that the dynamical phase shifts of the invariant
operator eigenstates are the same (or {\it mod} $2\pi$) while the corresponding
geometric phases are nontrivial.
  We illustrate how this strategy to work in a simple but typical NMR-type
qubit system.
