Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems

摘要

We propose an experimentally feasible scheme to achieve quantum computationbased on a pair of orthogonal cyclic states. In this scheme, quantum gates canbe implemented based on the total phase accumulated in cyclic evolutions. Inparticular, geometric quantum computation may be achieved by eliminating thedynamic phase accumulated in the whole evolution. Therefore, both dynamic andgeometric operations for quantum computation are workable in the presenttheory. Physical implementation of this set of gates is designed for NMRsystems. Also interestingly, we show that a set of universal geometric quantumgates in NMR systems may be realized in one cycle by simply choosing specificparameters of the external rotating magnetic fields. In addition, wedemonstrate explicitly a multiloop method to remove the dynamic phase ingeometric quantum gates. Our results may provide useful information for theexperimental implementation of quantum logical gates.