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Higher order topological superconductors as generators of quantum codes

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arxiv 1810.10556 v2 pith:UVFDHY6N submitted 2018-10-24 cond-mat.str-el cond-mat.mes-hallcond-mat.supr-conhep-th

Yizhi You , Daniel Litinski , Felix von Oppen This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hallcond-mat.supr-conhep-th
keywords hotsccodesquantumorderedtopologicaltopologicallydimensionsdrive
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We show that interactions can drive a class of higher order topological superconductors (HOTSC) into symmetry enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting HOTSC realize various topologically ordered surface and color codes. In three dimensions, interactions can drive HOTSC protected by subsystem symmetries into recently discovered fracton phases. We explicitly relate fermion parity operators underlying the gapless excitations of the HOTSC to the Wilson algebra of symmetry enriched quantum codes. Arrays of crossed Majorana wires provide an experimental platform for realizing fracton matter and for probing the quantum phase transition between HOTSC and topologically ordered phase.

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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. Higher-order topological phase without crystalline symmetry

    cond-mat.str-el 2019-08 conditional novelty 7.0 of 10

    Subsystem symmetries can protect gapless hinges and corners in interacting 3D models, yielding higher-order topological phases that require no crystalline symmetry.

  2. Anisotropic layer construction of anisotropic fracton models

    cond-mat.str-el 2019-08 accept novelty 5.0 of 10

    A coupled-layer construction from stacked 2D toric codes produces an exactly solvable anisotropic fracton model with lineon and planon excitations.

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