Algorithms construct stabilizer models for boundaries and 0D defects in composite-dimensional twisted quantum double codes, with examples like Z4 double coupled to double semion phase and threshold comparisons to surface codes.
Universal topological phase of 2D stabilizer codes
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abstract
Two topological phases are equivalent if they are connected by a local unitary transformation. In this sense, classifying topological phases amounts to classifying long-range entanglement patterns. We show that all 2D topological stabilizer codes are equivalent to several copies of one universal phase: Kitaev's topological code. Error correction benefits from the corresponding local mappings.
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Composite-Dimensional Topological Codes with Boundaries and Defects
Algorithms construct stabilizer models for boundaries and 0D defects in composite-dimensional twisted quantum double codes, with examples like Z4 double coupled to double semion phase and threshold comparisons to surface codes.