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

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