Single Qudit Control in $^{87}$Sr via Optical Nuclear Electric Resonance

Optical nuclear electric resonance (ONER) was recently proposed as a fast and robust single-qubit gate mechanism in $^{87}$Sr. Here, we demonstrate through numerical simulations that ONER can be extended to single-qudit control, addressing multiple one-level hyperfine transitions within the ten-dimensional nuclear-spin manifold. We identify suitable operating regimes and show that ONER enables high-fidelity spin manipulations, with simulated $\pi$-gate fidelities exceeding 99.9\%, while maintaining coherence under realistic parameter fluctuations. These results establish a proof-of-principle for optical qudit control in $^{87}$Sr and delineate practical parameter ranges for future experiments, highlighting ONER as a promising pathway toward high-dimensional quantum information processing.