GEOMETRIC PHASE AND TOPOLOGY QUANTUM GATES USING PARALLEL TRANSPORTATION

Abstract

We present a novel evolution method to obtain pure geometric phase with orthogonal superposed initial state method (OGSM). As examples we illustrate in detail the geometric evolution both in NMR and superconducting Josephson junction systems, which may be further designed to construct fault-tolerant geometric quantum gates. In the end we also propose a simple way to construct topological quantum gates based on OGSM.