Efficient Implementation of a Quantum Algorithm with a Trapped Ion Qudit

TL;DR

This paper demonstrates the control of an eight-level trapped ion qudit and implements Grover's search algorithm on qudits of dimensions five and eight, showing high fidelity and efficiency advantages over qubit systems.

Contribution

It presents the first implementation of Grover's algorithm on high-dimensional qudits with multi-tone control, achieving high fidelity and reduced gate complexity.

Findings

Achieved 96.8% fidelity for 5-level qudit Grover search.

Achieved 69% fidelity for 8-level qudit Grover search.

Demonstrated efficient control requiring only O(d) single-qudit gates.

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 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.