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Mathematics of Topological Quantum Computing

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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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hep-th 1

years

2024 1

verdicts

CONDITIONAL 1

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  • Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization hep-th · 2024-11-25 · conditional · none · ref 64 · internal anchor

    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.