  We study a 2-qubit nuclear spin system for realizing an arbitrary geometric
quantum phase gate by means of non-adiabatic operation. A single magnetic pulse
with multi harmonic frequencies is applied to manipulate the quantum states of
2-qubit instantly. Using resonant transition approximation, the time dependent
Hamiltonian of two nuclear spins can be solved analytically. The time evolution
of the wave function is obtained without adiabatic approximation. The
parameters of magnetic pulse, such as the frequency, amplitude, phase of each
harmonic part as well as the time duration of the pulse, are determined for
achieving an arbitrary non-adiabatic geometric phase gate. The derivation of
non-adiabatic geometric controlled phase gates and A-A phase are also
addressed.
