  Non-adiabatic holonomic quantum computation has received increasing attention
due to its robustness against control errors. However, all the previous schemes
have to use at least two sequentially implemented gates to realize a general
one-qubit gate. In this paper, we put forward a novelty scheme by which one can
directly realize an arbitrary holonomic one-qubit gate with a single-shot
implementation, avoiding the extra work of combining two gates into one. Based
on a three-level model driven by laser pulses, we show that any single-qubit
holonomic gate can be realized by varying the detuning, amplitude, and phase of
lasers. Our scheme is compatible with previously proposed non-adiabatic
holonomic two-qubit gates, combining with which the arbitrary holonomic
one-qubit gates can play universal non-adiabatic holonomic quantum computation.
We also investigate the effects of some unavoidable realistic errors on our
scheme.
