  Conditional geometric phase shift gate, which is fault tolerate to certain
errors due to its geometric property, is made by NMR technique recently under
adiabatic condition. By the adiabatic requirement, the result is inexact unless
the Hamiltonian changes extremely slowly in the process. However, in quantum
computation, everything has to be completed within the decoherence time. High
running speed of every gate in quantum computation is demanded because the
power of quantum computer can be exponentially proportional to the maximum
number of logic gate operation that can be taken sequentially within the
decoherence time. Adiabatic condition makes any fast conditional Berry
phase(cyclic adiabatic geometric phase) shift gate impossible. Here we show
that by using a new designed sequence of simple operations with an additional
vertical magnetic field, the conditional geometric phase shift can be done
non-adiabatically. Therefore geometric quantum computation can be done in the
same speed level of usual quantum computation.
