Qutrit toric code and parafermions in trapped ions

Creators: Iqbal, Mohsin¹; Lyons, Anasuya²; Lo, Chiu Fan Bowen²; Tantivasadakarn, Nathanan³; Dreiling, Joan⁴; Foltz, Cameron⁴; Gatterman, Thomas M.⁴; Gresh, Dan⁴; Hewitt, Nathan⁴; Holliman, Craig A.⁴; Johansen, Jacob⁴; Neyenhuis, Brian⁴; Matsuoka, Yohei⁴; Mills, Michael⁴; Moses, Steven A.⁴; Siegfried, Peter⁴; Vishwanath, Ashvin²; Verresen, Ruben^{2, 5}; Dreyer, Henrik¹

1. Quantinuum, Leopoldstrasse 180, Munich, Germany
2. Harvard University
3. California Institute of Technology
4. Quantinuum, 303 S Technology Ct, Broomfield, CO, USA
5. University of Chicago

Abstract

The development of programmable quantum devices can be measured by the complexity of many-body states that they are able to prepare. Among the most significant are topologically ordered states of matter, which enable robust quantum information storage and processing. While topological orders are more readily accessible with qudits, experimental realizations have thus far been limited to lattice models of qubits. Here, we prepare and measure a ground state of the ℤ₃ toric code state on 24 qutrits (obtained by encoding one qutrit into two qubits) in a trapped ion quantum processor with fidelity per qutrit exceeding 96.5(3)%. We manipulate two types of defects which go beyond the conventional qubit toric code: a parafermion, and its bound state which is related to charge conjugation symmetry. We further demonstrate defect fusion and the transfer of entanglement between anyons and defects, which we use to control topological qutrits. Our work opens up the space of long-range entangled states with qudit degrees of freedom for use in quantum simulation and universal error-correcting codes.

Copyright and License

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, 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 changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Acknowledgement

We thank the broader team at Quantinuum for comments. N.T. is supported by the Walter Burke Institute for Theoretical Physics at Caltech. A.V. and R.V. are supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (618615, A.V.). A.L. and C.F.B.L. acknowledge support from the National Science Foundation Graduate Research Fellowship Program (NSF GRFP). This work is in part supported by the DARPA MeasQuIT program. The experimental data in this work were produced by the Quantinuum H2 trapped ion quantum computer, powered by Honeywell, in 2024.

Data Availability

The data generated in this study have been deposited in the Zenodo repository https://doi.org/10.5281/zenodo.14007593 database under open access.

Code Availability

The code used for numerical simulations is available from from Zenodo repository https://doi.org/10.5281/zenodo.14007593.

Conflict of Interest

H.D. is a shareholder of Quantinuum. All other authors declare no competing interests.

Supplemental Material

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