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

• URL: http://arxiv.org/abs/2007.12152v3
• Date: Fri, 25 Jun 2021 03:30:48 GMT
• Title: Minimal distances for certain quantum product codes and tensor products of chain complexes
• Authors: Weilei Zeng and Leonid P. Pryadko
• Abstract summary: We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances. The codes in the construction, subsystem product codes and their gauge-fixed variants, generalize several known families of quantum error-correcting codes.
• Score: 0.5076419064097732
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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