We propose a feasible scheme to implement a phase-shift gate ((1) (0) (ei gamma) (0)) based on a two-state single molecule in a solid matrix, where gamma is a geometric phase controlled through a fast on-resonant laser field and a slow off-resonant radio-frequency field. In our scheme, a non-Hermitian quantum model is employed to characterize the single molecule in a solid matrix including the spontaneous decay effect. By the coupling between the radio-frequency field and the two-state permanent dipole difference resulting from the solid matrix, the spontaneous decay fatal to the preservation of geometric phase can be effectively suppressed for a considerably long waiting time. (C) 2015 AIP Publishing LLC.
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