Operating a geometric quantum gate by external controllable parameters

A scheme to perfectly preserve an initial qubit state ingeometric quantum computation is proposed for a single-qubit geometricquantum gate in a nuclear magnetic resonance system. At first, byadjusting some magnetic field parameters, one can let the dynamicphase be proportional to the geometric phase. Then, by controllingthe azimuthal angle in the initial state, we may realize ageometric quantum gate whose fidelity is equal to one undercyclic evolution. This means that the quantum information is nodistortion in the process of geometric quantum computation.