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Structure of 2D Topological Stabilizer Codes

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Abstract

We provide a detailed study of the general structure of translationally invariant two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. We show that they can be understood in terms of the homology of string operators that carry a certain topological charge. In subsystem codes, two dual kinds of charges appear. We prove that two non-chiral codes are equivalent under local transformations iff they have isomorphic topological charges. Our approach emphasizes local properties over global ones.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5, Canada

    Héctor Bombín

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  1. Héctor Bombín
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Correspondence to Héctor Bombín.

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Communicated by M. B. Ruskai

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Bombín, H. Structure of 2D Topological Stabilizer Codes. Commun. Math. Phys. 327, 387–432 (2014). https://doi.org/10.1007/s00220-014-1893-4

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  • DOI: https://doi.org/10.1007/s00220-014-1893-4

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