B.I. Stepanov Institute of Physics, NAS of Belarus, Minsk, Belarus ,

Nitrogen-vacancy (NV) centers in diamond are a promising platform for quantum technologies, where the electron spin serves as an interface, while the nuclear spins of carbon-13 and nitrogen-14 act as long-lived quantum memory [1]. Extremely high spectral density of parasitic energy transitions and crosstalk caused by dipole–dipole interaction in a multi-qubit structure remains a central problem in pulse control of the nuclear subsystem. Conventional radio-frequency (RF) pulse control methods based on the rotating wave approximation fail to ensure selectivity of target excitation due to a strong dynamic Stark effect and off-resonant multiphoton transitions [2]. In this work, a nonperturbative method for optimal control of localized nuclear qubits is proposed, accounting for the exact quantum unitary dynamics of the spin register beyond the independent-level approximation. The evolution of the isolated system is modelled (using an electron–nuclear cluster truncated to effective nearest-neighbour isotopes within the C₅₁₀[NV]H₂₅₂ cluster [1]) via the fourth-order Magnus expansion within the self-consistent Kato–Floquet formalism [3]. The solution consists in employing quasi-adiabatic excitation pulses with synchronous continuous amplitude-and-frequency modulation, where automatic carrier frequency tuning dynamically compensates for the shifts of continuously evolving dressed states of the system. The system dynamics simulations confirm the possibility of suppressing the population leakage probability of target nitrogen-14 spin sublevels below the instrumental error thresholds. It is shown that controlling the nuclear subsystem under hyperfine hybridization with the electron shell near the ground-state level anti-crossing (GSLAC) points allows a substantial reduction of the Rabi oscillation half-period duration. The optimized amplitude-frequency control enables ultrafast (down to tens of microseconds) execution of nuclear quantum gates with fidelity exceeding 0.999, making the method suitable for high-speed selective manipulation of solid-state qubit registers. [1] Nizovtsev A. P. et al. Non-flipping 13C spins near an NV center in diamond: hyperfine and spatial characteristics by density functional theory simulation of the C510 [NV] H252 cluster //New Journal of Physics. – 2018. – Т. 20. – №. 2. – С. 023022. [2] Van Ommen H. B. et al. Improved electron-nuclear quantum gates for spin sensing and control //PRX Quantum. – 2025. – Т. 6. – №. 2. – С. 020309. [3] Schindler P. M., Bukov M. Geometric Floquet theory //Physical Review X. – 2025. – Т. 15. – №. 3. – С. 031037.