Year: 2026
Type: preprint
Abstract: Maximum likelihood (ML) decoders perform quantum error correction by measuring a set of syndromes, classically computing an optimal recovery based on these syndromes and the noise model, and then performing that recovery. ML decoders are well understood for the toric code and generalize straightforwardly to other surface codes with Abelian anyons, where they can saturate information-theoretic decoding thresholds. On the other hand, codes with non-Abelian anyons have become increasingly relevant because they can support transversal or constant-depth non-Clifford gates and admit efficient preparation protocols in modern quantum devices. However, they present new challenges for decoding: non-Abelian anyons cannot in general be deterministically annihilated, and the logical operators cannot be classified by Abelian homology. In this work, we show that refined syndrome sets, including measurements that resolve non-Abelian anyon fusion outcomes, systematically improve the performance of ML decoders. We demonstrate this concretely by constructing explicit decoders for the $D_4$ quantum double model under charge noise, and obtaining numerical results for thresholds via mappings to classical statistical-mechanics models. We show that there is a nonzero noise threshold below which the entire logical qudit can be recovered with a single round of measurements.
Source: arXiv (Cornell University)
Institutions: Harvard University, Purdue University West Lafayette, New York University, State University of New York, Stony Brook University, National Institute of Standards and Technology, Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, University of Oklahoma, University of British Columbia
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Isaac Newton Institute for Mathematical Sciences (INI), G2259086438, G2595738051, QuEST: Quantum Education for Students and Teachers, QLCI-CI: NSF Quantum Leap Challenge Institute for Robust Quantum Simulation, G4373780718, Kavli Institute for Theoretical Physics, Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics
OpenAlex ID: W7220744149