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Braids, Motions and Topological Quantum Computing

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arxiv 2208.11762 v1 pith:JABQK7H3 submitted 2022-08-24 quant-ph math.QA

Eric C. Rowell This is my paper · ORCID
classification quant-phmath.QA
keywords topologicalbraidingbraidsmodelmotionsquantumwaysanyons
verification ladder T0 review T1 audit T2 compute T3 formal
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The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the mathematical study of braids is crucial for the theory. We provide some brief historical context as well, emphasizing ways that braiding appears in physical contexts. We also briefly discuss the 3-dimensional generalization of braiding: motions of knots.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta

    cond-mat.mes-hall 2025-05 conditional novelty 6.0 of 10

    Fractional quantum Hall anyons are re-derived from a non-Lagrangian flux quantization in 2-Cohomotopy, with new predictions for torus degeneracy and defect anyons.

  2. Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization

    hep-th 2024-11 conditional novelty 4.0 of 10

    Choosing equivariant twistorial Cohomotopy as the flux quantization law on single M5-probes wrapped on a Z2-orbifold yields abelian anyonic quantum states on the orbifold fixed locus.

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