  We propose a feasible scheme to implement a universal set of quantum gates
based on geometric phases and superadiabatic quantum control. Consolidating the
advantages of both strategies, the proposed quantum gates are robust and fast.
The diamond nitrogen-vacancy center system is adopted as a typical example to
illustrate the scheme. We show that these gates can be realized in a simple
two-level configuration by appropriately controlling the amplitude, phase, and
frequency of just one microwave field. The gate's robust and fast features are
confirmed by comparing the fidelity of the proposed superadiabatic geometric
phase (controlled-PHASE) gate with those of two other kinds of phase
(controlled-PHASE) gates.
