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We study a 2-qubit nuclear spin system for realizing an arbitrary geometricquantum phase gate by means of non-adiabatic operation. A single magnetic pulsewith multi harmonic frequencies is applied to manipulate the quantum states of2-qubit instantly. Using resonant transition approximation, the time dependentHamiltonian of two nuclear spins can be solved analytically. The time evolutionof the wave function is obtained without adiabatic approximation. Theparameters of magnetic pulse, such as the frequency, amplitude, phase of eachharmonic part as well as the time duration of the pulse, are determined forachieving an arbitrary non-adiabatic geometric phase gate. The derivation ofnon-adiabatic geometric controlled phase gates and A-A phase are alsoaddressed.Comment: 7 pages, 1 figur

NON-ADIABATIC ARBITRARY GEOMETRIC PHASE GATE IN 2-QUBIT SPIN MODEL