  The main obstacles to the realization of high-fidelity quantum gates are the
control errors arising from inaccurate manipulation of a quantum system and the
decoherence caused by the interaction between the quantum system and its
environment. Nonadiabatic holonomic quantum computation allows for high-speed
implementation of whole-geometric quantum gates, making quantum computation
robust against control errors. Dynamical decoupling provides an effective
method to protect quantum gates against environment-induced decoherence,
regardless of collective decoherence or independent decoherence. In this paper,
we put forward a protocol of nonadiabatic holonomic quantum computation
protected by dynamical decoupling . Due to the combination of nonadiabatic
holonomic quantum computation and dynamical decoupling, our protocol not only
possesses the intrinsic robustness against control errors but also protects
quantum gates against environment-induced decoherence.
