Chiu Fan Bowen Lo, Anasuya Lyons, Ruben Verresen, Ashvin Vishwanath, Nathanan Tantivasadakarn (Feb 24 2025).
Abstract: Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with
S3 gauge symmetry was identified as a sweet spot -- simple enough to emerge from finite-depth adaptive circuits yet powerful enough to support a universal topological gate-set. In these notes, we review how anyon braiding and measurement in
S3 TO are primitives for topological quantum computation and we explicitly demonstrate universality. These topological operations are made concrete in the
S3 quantum double lattice model, aided by the introduction of a generalized ribbon operator. This provides a roadmap for near-term quantum platforms.
