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 first implementation of Grover's search algorithm on a qudit with dimension 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 (SSO), 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.

DOI: 10.48550/arxiv.2506.09371

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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

\%

and 69(6)

\%

\mathcal{O}(d)

single qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.

{{{\mathcal{O}}}}(d)

single-qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms. The authors demonstrate high-fidelity multi-tone electronic control of trapped-ion qudits up to d=8 levels, enabling efficient SU(d) operations and showcasing advantage by implementing Grover’s search algorithm using encoding in a single qudit, rather than in multiple qubits.