Fusion-assisted decoding of non-Abelian topological order
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 D4 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.
Related
- Climbing the Fusion Tree: Center Ordering and Decoding Hierarchy in Non-Abelian Mixed States
- Strong subadditivity of topological entropy on the torus: Rényi order and non-Abelian structure
- Provable circuit-level thresholds for non-abelian topological phases
- Torus Berry Data Determine All-Genus Abelian Topological Orders
- The topological non-Abelian string in the extended SU(N) ⊗ U(1) gauge sector
BibTeX
@misc{sajith2026fusionassisted,
title = {{Fusion-assisted decoding of non-Abelian topological order}},
author = {Rohith Sajith and Yabo Li and Zijian Song and Tsung-Cheng Lu and Carolyn Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05901},
eprint = {2610.05901},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05901},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fusion-assisted decoding of non-Abelian topological order
AU - Rohith Sajith
AU - Yabo Li
AU - Zijian Song
AU - Tsung-Cheng Lu
AU - Carolyn Zhang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05901
UR - https://arxiv.org/abs/2610.05901
AB - 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.
ER -