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Stabilizer codes of less than two dimensions have constant distance
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classification
quant-ph
keywords
codedimensionsdistancelessstabilisercodesconstantexist
abstract
The surface code is a two-dimensional stabiliser code with parameters $[[n,1,\Theta(\sqrt{n})]]$. To this day, no stabiliser code with growing distance is know to live in less than two dimensions. In this note we show that no such code can exist.
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