Structure of 2D Topological Stabilizer Codes

Details Structure of 2D Topological Stabilizer Codes Structure of 2D Topological Stabilizer Codes

2011-07-14

arxiv.org/abs/1107.2707v1

Physics

Quantum Physics

33 pages, 14 figures

Scientific paper

We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can be understood in terms of the homology of string operators that carry a certain topological charge. In the case of subspace codes, we prove that two codes are equivalent under a suitable set of local transformations if and only they have equivalent topological charges. Our approach emphasizes local properties of the codes over global ones.

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