A conditional geometric phase shift gate, which is fault tolerant to certai
n types of errors due to its geometric nature, was realized recently via nu
clear magnetic resonance (NMR) under adiabatic conditions. However, in quan
tum computation, everything must be completed within the decoherence time.
The adiabatic condition makes any fast conditional Berry phase (cyclic adia
batic geometric phase) shift gate impossible. Here we show that by using a
newly designed sequence of simple operations with an additional vertical ma
gnetic field, the conditional geometric phase shift gate can be run nonadia
batically. Therefore geometric quantum computation can be done at the same
rate as usual quantum computation.