Optimal Thresholds and Decoders for Non-Abelian Topological Order

Non-Abelian anyons offer a fundamentally more powerful resource for quantum computation than their Abelian counterparts. However, the understanding of their error-correction problem remains at an early stage. In this talk, we develop a general theoretical framework for the optimal decoding of non-Abelian topological orders against arbitrary noise models, conditioned on anyon syndrome measurements. We demonstrate this framework on paradigmatic topological orders and numerically determine the corresponding optimal error-correction thresholds. Furthermore, we explore how to construct optimal decoders tailored to noise models relevant for near-term quantum devices.