Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators
L. B. Shao, Z. D. Wang, D. Y. Xing · Physical Review A · 2007
We propose a 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 identical (or mod $2\ensuremath{\pi}$) while the corresponding geometric phases are nontrivial. We illustrate how this strategy works in a simple but typical NMR-type qubit system.