Recently, it is proposed to do quantum computation through the Berry's
phase(adiabatic cyclic geometric phase) shift with NMR (Jones et al, Nature,
403, 869(2000)). This geometric quantum gate is hopefully to be fault tolerant
to certain types of errors because of the geometric property of the Berry
phase. Here we give a scheme to realize the NMR C-NOT gate through
Aharonov-Anandan's phase(non-adiabatic cyclic phase) shift on the dynamic phase
free evolution loop.
In our scheme, the gate is run non-adiabatically, thus it is less affected by
the decoherence. And, in the scheme we have chosen the the zero dynamic phase
time evolution loop in obtaining the gepmetric phase shift, we need not take
any extra operation to cancel the dynamic phase.Comment: 5 pages, 1 figur