Fast arbitrary qutrit gates for NV centers in the low-field regime

Abstract The ground state of the negatively charged NV center forms a spin–1 manifold providing a versatile platform for sensing and information processing. Here we present a scheme for implementing fast arbitrary qutrit gates in the low–field regime using monochromatic microwave pulses of constant intensity tuned to the zero–field transition. By concatenating pulses with appropriate phases and durations, the NV-ERC scheme is extended from SU(2) operations in the double-quantum subspace to the full three–level structure. We show that arbitrary SU(3) operations can be decomposed into rotations in the double-quantum subspace together with effective implementations of the generators related to $\hat{\lambda }_{5}$ λ ˆ 5 and $\hat{\lambda }_{8}$ λ ˆ 8 . We further analyze the nontrivial $\hat{\lambda }_{5}$ λ ˆ 5 operation under pure dephasing, finding low average gate infidelities throughout the regime studied. We illustrate the SU(3) decomposition with a use case: performing quantum state tomography of the complete three-level density matrix.