We propose an experimentally feasible scheme to achieve quantum computation
based on a pair of orthogonal cyclic states. In this scheme, quantum gates can
be implemented based on the total phase accumulated in cyclic evolutions. In
particular, geometric quantum computation may be achieved by eliminating the
dynamic phase accumulated in the whole evolution. Therefore, both dynamic and
geometric operations for quantum computation are workable in the present
theory. Physical implementation of this set of gates is designed for NMR
systems. Also interestingly, we show that a set of universal geometric quantum
gates in NMR systems may be realized in one cycle by simply choosing specific
parameters of the external rotating magnetic fields. In addition, we
demonstrate explicitly a multiloop method to remove the dynamic phase in
geometric quantum gates. Our results may provide useful information for the
experimental implementation of quantum logical gates.Comment: 9 pages, language revised, the publication versio