Quantum logic operations and algorithms in a single 25-level atomic qudit

TL;DR

This paper demonstrates high-fidelity control and operations on a 25-level atomic qudit using $^{137}$Ba$^+$ ions, exploring error scaling and implementing complex algorithms to advance high-dimensional quantum computing.

Contribution

It introduces experimental techniques for manipulating a 25-level atomic qudit and demonstrates high-dimensional quantum algorithms, highlighting the potential of large-dimensional qudits.

Findings

Achieved high-fidelity state preparation and readout of 25 levels.

Implemented a 3-qubit Bernstein-Vazirani algorithm.

Realized a 4-qubit Toffoli gate with a single ion.

Abstract

Scaling quantum computers remains a substantial scientific and technological challenge. Leveraging the full range of intrinsic degrees of freedom in quantum systems offers a promising route towards enhanced algorithmic performance and hardware efficiency. We experimentally study the use of $^{137}$Ba$^+$ ions for quantum information processing, achieving high-fidelity state preparation and readout of up to 25 internal levels, thus forming a 25-dimensional qudit. By probing superpositions of up to 24 states, we investigate how errors scale with qudit dimension $d$ and identify the primary error sources affecting quantum coherence. Additionally, we demonstrate high-dimensional qudit operations by implementing a 3-qubit Bernstein-Vazirani algorithm and a 4-qubit Toffoli gate with a single ion. Our findings suggest that quantum computing architectures based on large-dimensional qudits hold significant promise.