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Mathematics of Topological Quantum Computing

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arxiv 1705.06206 v2 pith:G7OKJEJO submitted 2017-05-17 math.QA cond-mat.str-elmath-phmath.MPquant-ph

Eric C. Rowell , Zhenghan Wang This is my paper · ORCID
classification math.QAcond-mat.str-elmath-phmath.MPquant-ph
keywords quantumtopologicalcomputingmathematicsaccuracybasicbeencomputer
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by experiments to an accuracy of $10^{-10}$, and harnessed to stabilize quantum memory. In this survey, we discuss the conceptual development of this interdisciplinary field at the juncture of mathematics, physics and computer science. Our focus is on computing and physical motivations, basic mathematical notions and results, open problems and future directions related to and/or inspired by topological quantum computing.

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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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