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Structure of 2D Topological Stabilizer Codes


By characterizing 2D topological stabilizer codes in terms of 'lattice groups' on infinite lattices, we show that they can all be characterized in terms of topological charges and string operators.  This is true either for subspace or subsystem codes, and it has direct applications for error correction, for example.  Subspace codes are directly connected to topologically ordered condensed matter systems, and we show that all 2D topological stabilizer codes are locally equivalent to several copies of one universal phase: Kitaev's topological code.