All-Optical Universal Control of Hyperfine Qudits in Trapped Neutral Atoms

Quantum systems with more than two levels $-$ so-called qudits $-$ offer increased computational density and reduced circuit complexity compared to qubit-based architectures, but achieving universal and scalable control remains challenging. We propose an all-optical scheme for universal qudit control in trapped neutral atoms in moderate to high magnetic fields, focusing on the fermionic isotope $^{173}$Yb ($I=5/2$). The strong hyperfine interaction in the $^3P_1$ manifold enables fast and selective Raman transitions between nuclear-spin states in the $^1S_0$ ground-state manifold using a single linearly polarized laser. For each neighboring transition in the qudit manifold, we identify a magic polarization angle that enables coherent, state-selective control while suppressing off-resonant excitations, with operation frequencies exceeding 100~kHz. Combined with phase-shift operations, this provides universal control of the full single-qudit space. We further discuss compatible two-qudit gates based on the Rydberg blockade mechanism, completing a universal gate set, and analyze state-selective readout schemes compatible with the proposed protocol. Our results identify $^{173}$Yb as a promising platform for high-fidelity, all-optical qudit-based quantum information processing.