  Motivated for the fault tolerant quantum computation, quantum gate by
adiabatic geometric phase shift is extensively investigated. In this paper, we
demonstrate the nonadiabatic scheme for the geometric phase shift and
conditional geometric phase shift. Essentially, the new scheme is simply to add
an appropriate additional field. With this additional field, the state
evolution can be controlled exactly on a dynamical phase free path. Geometric
quantum gates for single qubit and the controlled NOT gate for two qubits are
given.
