Quantum gyroscope based on a Berry phase induced by three-dimensional rotation

Solid-spin defects in diamond provide long coherence times and room-temperature optical initialization and readout, making them an attractive platform for compact solid-state quantum gyroscopes. A central challenge for NV-based gyroscopes is that the rotation-induced signal is weak, while near-resonant operation, although enhancing the response, can induce nonadiabatic transitions that degrade the accumulated geometric phase and readout fidelity. Here we investigate a levitated diamond under three-dimensional rotation, in which intrinsic ${}^{14}\mathrm{N}$ nuclear spins associated with NV centers act as sensing qubits. We show that the rotation is encoded in a geometric (Berry) phase and identify a near-resonant regime with strongly enhanced phase response. To suppress the resulting nonadiabatic leakage, we introduce a counter-diabatic protocol derived from the Kato gauge potential. This enables robust geometric-phase accumulation and improves the sensitivity by four orders of magnitude relative to the conventional detuned protocol. We further evaluate the achievable sensitivity and the dominant experimental limitations, including decoherence and protocol overhead, thereby establishing a realistic route toward high-performance NV-based solid-state quantum gyroscopes.