Nonadiabatic holonomic single-qubit gates in off-resonant $\mathrm{\Lambda }$ systems

We generalize nonadiabatic holonomic quantum computation in a resonant $\mathrm{\Lambda }$ configuration proposed in [New J. Phys. 14 (2012) 103035] to the case of off-resonant driving lasers. We show that any single-qubit holonomic gate can be realized by separately varying the detuning, amplitude, and phase of the lasers.