Qutrit toric code and parafermions in trapped ions

Mohsin Iqbal, Anasuya Lyons, Chiu Fan Bowen Lo, Nathanan Tantivasadakarn, Joan Dreiling, Cameron Foltz, Thomas M. Gatterman, Dan Gresh, Nathan Hewitt, Craig A. Holliman, Jacob Johansen, Brian Neyenhuis, Yohei Matsuoka, Michael Mills, Steven A. Moses, Peter Siegfried, Ashvin Vishwanath, Ruben Verresen and Henrik Dreyer ()
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Mohsin Iqbal: Quantinuum
Anasuya Lyons: Harvard University
Chiu Fan Bowen Lo: Harvard University
Nathanan Tantivasadakarn: California Institute of Technology
Joan Dreiling: Quantinuum
Cameron Foltz: Quantinuum
Thomas M. Gatterman: Quantinuum
Dan Gresh: Quantinuum
Nathan Hewitt: Quantinuum
Craig A. Holliman: Quantinuum
Jacob Johansen: Quantinuum
Brian Neyenhuis: Quantinuum
Yohei Matsuoka: Quantinuum
Michael Mills: Quantinuum
Steven A. Moses: Quantinuum
Peter Siegfried: Quantinuum
Ashvin Vishwanath: Harvard University
Ruben Verresen: Harvard University
Henrik Dreyer: Quantinuum

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: 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 $${{\mathbb{Z}}}_{3}$$ Z 3 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.

Date: 2025
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DOI: 10.1038/s41467-025-61391-z

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