Generalized Color Codes Supporting Non-Abelian Anyons

Abstract

We propose a generalization of the color codes based on finite groups $G$. For non-abelian groups, the resulting model supports non-abelian anyonic quasiparticles and topological order. We examine the properties of these models such as their relationship to Kitaev quantum double models, quasiparticle spectrum, and boundary structure.

17 pages, 8 figures; references added, typos removed

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Cited by in corpus (8)

• Continuous symmetries and approximate quantum error correction
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• Qudit Colour Codes and Gauge Colour Codes in All Spatial Dimensions
• Generalized Cluster States Based on Finite Groups
• Comparison of memory thresholds for planar qudit geometries
• A bilayer Double Semion Model with Symmetry-Enriched Topological Order
• Quantum computation with charge-and-color permuting twists in qudit color codes
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective