Abstract
Demonstration of quantum advantage remains challenging due to the increased overhead of controlling large quantum systems. While significant effort has been devoted to qubit-based devices, qudits (d-level systems) offer potential advantages in both hardware efficiency and algorithmic performance. In this paper, we demonstrate multi-tone control of a single trapped ion qudit of up to eight levels, as well as the implementation of Grover’s search algorithm on a qudit with dimensions five and eight, achieving operation fidelity of 96.8(3)% and 69(6)%, respectively, which correspond to 99.9(1)% and 97.1(3) % squared statistical overlap, respectively, with the expected result for a single iteration of the Grover search algorithm. The performance is competitive when compared to qubit-based systems; moreover, the sequence requires only \({{{\mathcal{O}}}}(d)\) single-qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.
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The data generated in this study have been deposited in the Zenodo database under accession code https://doi.org/10.5281/zenodo.1747904659.
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The code for simulations is available upon request.
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Acknowledgements
I.L.C. acknowledges support by the NSF Center for Ultracold Atoms. This research was supported by the U.S. Army Research Office through grant W911NF-24-1-0379. This material is based upon work supported by the Department of Defense under Air Force Contract No. FA8702-15-D-0001. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the Department of Defense.
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X.S and T.B carried out experimental studies. X.S and J.S performed simulation and analysis. J.C and I.C supervised the work.
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Shi, X., Sinanan-Singh, J., Burke, T.J. et al. Efficient implementation of a quantum algorithm with a trapped ion qudit. Nat Commun (2026). https://doi.org/10.1038/s41467-026-68746-0
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DOI: https://doi.org/10.1038/s41467-026-68746-0
