Efficient Implementation of a Quantum Algorithm with a Trapped Ion Qudit
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 (-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 single qudit gates and no entangling gates. This work highlights the potential of using qudits for efficient implementations of quantum algorithms.
Cite
@article{arxiv.2506.09371,
title = {Efficient Implementation of a Quantum Algorithm with a Trapped Ion Qudit},
author = {Xiaoyang Shi and Jasmine Sinanan-Singh and Timothy J. Burke and John Chiaverini and Isaac L. Chuang},
journal= {arXiv preprint arXiv:2506.09371},
year = {2025}
}