Qutrit Toric Code and Parafermions in Trapped Ions

• Main Authors: Iqbal, Mohsin, Lyons, Anasuya, Lo, Chiu Fan Bowen, Tantivasadakarn, Nathanan, Dreiling, Joan, Foltz, Cameron, Gatterman, Thomas M, Gresh, Dan, Hewitt, Nathan, Holliman, Craig A, Johansen, Jacob, Neyenhuis, Brian, Matsuoka, Yohei, Mills, Michael, Moses, Steven A, Siegfried, Peter, Vishwanath, Ashvin, Verresen, Ruben, Dreyer, Henrik
• Format: Journal Article
• Language: English
• Published: 06-11-2024
• Subjects: Physics - Quantum Physics; Physics - Strongly Correlated Electrons
• DOI: 10.48550/arxiv.2411.04185

The development of programmable quantum devices can be measured by the
complexity of manybody 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 realisations have thus far been
limited to lattice models of qubits. Here, we prepare a ground state of the Z3
toric code state on 24 qutrits 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.