  Nonadiabatic holonomic quantum computation in decoherence-free subspaces has
attracted increasing attention recently, as it allows for high-speed
implementation and combines both the robustness of holonomic gates and the
coherence stabilization of decoherence-free subspaces. Since the first protocol
of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a
number of schemes for its physical implementation have been put forward.
However, all previous schemes require two noncommuting gates to realize an
arbitrary one-qubit gate, which doubles the exposure time of gates to error
sources as well as the resource expenditure. In this paper, we propose an
alternative protocol for nonadiabatic holonomic quantum computation in
decoherence-free subspaces, in which an arbitrary one-qubit gate in
decoherence-free subspaces is realized by a single-shot implementation. The
present protocol not only maintains the merits of the original protocol, but
also avoids the extra work of combining two gates to implement an arbitrary
one-qubit gate and thereby reduces the exposure time to various error sources.
