Related papers: Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition

Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition

URL: http://arxiv.org/abs/2502.14974v1
Date: Thu, 20 Feb 2025 19:07:31 GMT
Title: Universal Quantum Computation with the $S_3$ Quantum Double: A Pedagogical Exposition
Authors: Chiu Fan Bowen Lo, Anasuya Lyons, Ruben Verresen, Ashvin Vishwanath, Nathanan Tantivasadakarn,
Abstract summary: We show how anyon braiding and measurement in $S_3$ TO are primitives for topological quantum computation.<n>This provides a roadmap for near-term quantum platforms.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ 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 $S_3$ TO are primitives for topological quantum computation and we explicitly demonstrate universality. These topological operations are made concrete in the $S_3$ quantum double lattice model, aided by the introduction of a generalized ribbon operator. This provides a roadmap for near-term quantum platforms.

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