Nonadiabatic holonomic quantum gates in a decoherence-insensitive space

Nonadiabatic holonomic quantum computation (NHQC) has shown promise in mitigating control errors, but requires additional methods to further eliminate the effects of decoherence errors. Existing NHQC schemes capable of combating both types of errors often necessitate auxiliary qubits, thereby increasing qubit resource consumption. This paper proposes nonadiabatic holonomic quantum gates based on a three-level dressed state space, which have inherent insensitivity to decoherence and eliminate the need for auxiliary qubits. Through numerical simulations, the presented gates within the dressed-state framework display enhanced resistance to both control field errors and decoherence errors. Moreover, we discuss the implementation of our approach on the nitrogen-vacancy center in diamond, demonstrating its feasibility and potential for geometric quantum computation.