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Quantum Stabilizer Codes, Lattices, And Cfts, Anatoly Dymarsky, Alfred D. Shapere
Quantum Stabilizer Codes, Lattices, And Cfts, Anatoly Dymarsky, Alfred D. Shapere
Physics and Astronomy Faculty Publications
There is a rich connection between classical error-correcting codes, Euclidean lattices, and chiral conformal field theories. Here we show that quantum error-correcting codes, those of the stabilizer type, are related to Lorentzian lattices and non-chiral CFTs. More specifically, real self-dual stabilizer codes can be associated with even self-dual Lorentzian lattices, and thus define Narain CFTs. We dub the resulting theories code CFTs and study their properties. T-duality transformations of a code CFT, at the level of the underlying code, reduce to code equivalences. By means of such equivalences, any stabilizer code can be reduced to a graph code. We can …