Description
Qudit systems are promising for quantum information processing by harnessing a larger Hilbert space. In atomic systems, qudits can naturally be encoded in the Zeeman sublevels of hyperfine manifolds. However, universal control of such hyperfine qudits is challenging due to spectral crowding of transitions within the Zeeman manifold. A potential solution uses quantum optimal control of RF-driven SU(2) rotations with engineered nonlinearities [1]. However, this approach becomes challenging for small Zeeman splittings and for single-ion addressing. Laser-based schemes are a promising alternative to overcome such challenges [2,3], but have yet to encorporate optimal control which could improve experimental complexity and gate fidelity.
Here, we investigate SU(d) optimal control of laser-driven Zeeman qudits. We consider a two-photon stimulated Raman transition with numerically optimised phase-modulations which gives universal control despite spectrally unresolved qudit transitions. As a concrete example, we apply our control scheme to a d = 15 qudit encoded in the F = 7 hyperfine manifold of a trapped Lutetium ion, and illustrate arbitrary qudit state preparation with fidelities exceeding 0.99 under realistic experimental parameters. Our protocol is broadly applicable to other atomic systems.
[1] Omanakuttan, Sivaprasad, Anupam Mitra, Michael J. Martin, and Ivan H. Deutsch. 2021. “Quantum Optimal Control of Ten-Level Nuclear Spin Qudits in Sr 87.” Physical Review A 104(6): L060401. doi:10.1103/PhysRevA.104.L060401.
[2] Ahmed, H. 2025. “Coherent Control Over the High-Dimensional Space of the Nuclear Spin of Alkaline-Earth Atoms.” PRX Quantum 6(2). doi:10.1103/PRXQuantum.6.020352.
[3] Gregory, Gabriel J., Evan R. Ritchie, Alex Quinn, Sean Brudney, David J. Wineland, David T. C. Allcock, and Jameson O’Reilly. 2026. “Four- and Six-Photon Stimulated Raman Transitions for Coherent Qubit and Qudit Operations.” doi:10.48550/arXiv.2602.18567.
| I am the presenting author | Yes |
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