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