Narrow Results

We study a 2-qubit spin model for the possibility of realizing an arbitrary geometric quantum phase gate in terms of a single coherent magnetic pulse with multi-harmonic frequency. Using resonant transition approximation, the time-dependent Hamiltonian of two coupled 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 requirement of materials for realizing such a gate is analyzed. As a result, the non-adiabatic geometric controlled phase gates and A–A phase are also addressed.