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Stabilizer codes of less than two dimensions have constant distance

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arxiv 2503.17655 v1 pith:OPYH5NI3 submitted 2025-03-22 quant-ph

Stabilizer codes of less than two dimensions have constant distance

classification quant-ph
keywords codedimensionsdistancelessstabilisercodesconstantexist
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Introduces intrinsic locality dimension for stabilizer codes and uses it to prove general bounds on code parameters and fault-tolerant logical gates, generalizing prior topological code results.

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