A scheme for a single molecule phase-shift gate in a solid matrix.

We propose a feasible scheme to implement a phase-shift gate ((1 0) (0 eiγ)) based on a two-state single molecule in a solid matrix, where γ 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.