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 137Ba+ ions for quantum information processing, achieving high-fidelity state preparation and readout of up to 25 internal levels, thus forming a 25-dimensional trapped-ion 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 trapped-ion. Our findings suggest that quantum computing architectures based on large-dimensional qudits hold significant promise. Similar content being viewed by others Acknowledgements This research was supported, in part, by the Natural Sciences and Engineering Research Council of Canada (NSERC), RGPIN-2018-05253 and the Canada First Research Excellence Fund (CFREF) (Transformative Quantum Technologies), CFREF-2015-00011. C.S. is also supported by a Canada Research Chair. Author information Authors and Affiliations Corresponding author Ethics declarations Competing interests The authors declare no competing interests. Additional information Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Supplementary information Rights and permissions Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article