  We propose an experimentally feasible scheme to achieve quantum computation
based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase
is used to realize a set of universal quantum gates. Physical implementation of
this set of gates is designed for Josephson junctions and for NMR systems.
Interestingly, we find that the nonadiabatic phase shift may be independent of
the operation time under appropriate controllable conditions. A remarkable
feature of the present nonadiabatic geometric gates is that there is no
intrinsic limitation on the operation time, unlike adiabatic geometric gates.
Besides fundamental interest, our results may simplify the implementation of
geometric quantum computation based on solid state systems, where the
decoherence time may be very short.
