Topological order (TO) provides a natural platform for storing and manipulating quantum information. However, its stability to noise has only been systematically understood for Abelian TOs. In this Letter, we exploit the nondeterministic fusion of non-Abelian anyons to inform active error-correction and design decoders where the fusion products, instead of flag qubits, herald the noise. This intrinsic heralding offers improved thresholds over those of Abelian counterparts. Furthermore, we use Bayesian inference to obtain a statistical mechanics model for fixed-point non-Abelian TOs with perfect measurements under any noise model, which yields the optimal threshold conditioned on measuring anyon syndromes. We numerically illustrate these results for $D_4\cong {\mathbb{Z}}_4⋊{\mathbb{Z}}_2$ TO. In particular, for non-Abelian charge noise and perfect syndrome measurement, we find a conditioned optimal threshold $p_c=0.218(1)$, whereas an intrinsically heralded minimum-weight perfect matching (MWPM) decoder already gives $p_c=0.20842(2)$, outperforming standard honeycomb-lattice MWPM with $p_c=0.15860(1)$. Our Letter highlights how non-Abelian properties can enhance stability, rather than reduce it, and discusses potential generalizations for achieving fault tolerance.

Close

PrevNext

View figure in article

• Anyons
• Phase transitions
• Quantum error correction
• Topological order
• Topological quantum computing
• Finite-size scaling
• Monte Carlo methods