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We propose a new strategy to physically implement a universal set of quantumgates based on geometric phases accumulated in the nondegenerate eigenstates ofa designated invariant operator in a periodic physical system. The system isdriven to evolve in such a way that the dynamical phase shifts of the invariantoperator eigenstates are the same (or {\it mod} $2\pi$) while the correspondinggeometric phases are nontrivial.  We illustrate how this strategy to work in a simple but typical NMR-typequbit system.Comment: 4 page

Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators