Classification of 2D Homological Stabilizer Codes
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Microsoft Research331 тыс
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06.12.22 – 24756:03
27.10.22 – 40540:16Опубликовано 12 августа 2016, 0:03
The discovery of quantum error correction and fault-tolerance were major theoretical breakthroughs on the road towards building a full-fledged quantum computer. Since then thresholds have increased and geometric constraints on the underlying architecture have been added. Homological stabilizer codes provide a method for constructing stabilizer codes constrained to a 2D plane. In this talk I will define and proceed to classify all 2D homological stabilizer codes. I will show that Kitaev's toric code and the topological color codes arise naturally in this classification. I will finally show, up to a set of equivalence relations, that these are the only 2D homological stabilizer codes.
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