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arXiv · 2007.12152

Minimal distances for certain quantum product codes and tensor products of chain complexes

Weilei Zeng·Leonid P. Pryadko
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Abstract

We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a complex are described by the K\"unneth theorem. We give an explicit expression for the distances when one of the complexes is a linear map between two spaces. The codes in the construction, subsystem product codes and their gauge-fixed variants, generalize several known families of quantum error-correcting codes.

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Weilei Zeng, Leonid P. Pryadko. 2020-07-23. Minimal distances for certain quantum product codes and tensor products of chain complexes. https://doi.org/10.1103/physreva.102.062402

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