Minimal distances for certain quantum product codes and tensor products of chain complexes
arXiv:2007.12152 · doi:10.1103/PhysRevA.102.062402
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 Künneth 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.
arXiv comment16 pages, no figures. An erratum is posted to fix Lemma.1. No other result is affected
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