Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Error Correction

Background:

• Topological order (TO) offers a robust platform for quantum information processing.
• Stability of topological order against noise is well-understood for Abelian types but less so for non-Abelian types.

Purpose of the Study:

• To develop active error-correction strategies for non-Abelian topological order.
• To design novel decoders leveraging non-Abelian anyon properties for enhanced noise heralding.
• To investigate the potential of non-Abelian topological order for improved quantum information stability.

Main Methods:

• Exploiting nondeterministic fusion of non-Abelian anyons for intrinsic noise heralding.
• Developing Bayesian inference for a statistical mechanics model of fixed-point non-Abelian TOs.
• Numerical simulations for D_{4}≅Z_{4}⋊Z_{2} topological order under non-Abelian charge noise.

Main Results:

• Intrinsic heralding via fusion products offers improved error thresholds compared to Abelian topological orders.
• A conditioned optimal threshold of p_{c}=0.218(1) was found for non-Abelian charge noise with perfect syndrome measurement.
• An intrinsically heralded minimum-weight perfect matching (MWPM) decoder achieved p_{c}=0.20842(2), surpassing standard honeycomb-lattice MWPM (p_{c}=0.15860(1).

Conclusions:

• Non-Abelian topological order properties can enhance, not reduce, stability against noise.
• Intrinsic heralding provides a powerful mechanism for fault-tolerant quantum computation.
• The findings suggest potential generalizations for achieving robust quantum information processing.