Local-dimension-invariant low-density parity-check stabilizer codes

Abstract:The protection of quantum information in systems leveraging more than two basis states (qudits) is an ongoing challenge. A tool for transforming the plethora of qubit stabilizer codes into qudit stabilizer codes is the local-dimension-invariant (LDI) extension to the stabilizer formalism. A drawback of the LDI method is that generally in order to ensure the distance of the resultant code is at least preserved the newly selected local-dimension will need to be any prime bigger than a large cutoff value. In this work we consider the repercussions of this large cutoff value, then by focusing on quantum low-density parity-check (qLDPC) codes we are able to bring down this cutoff value. Notably, we are able to reduce it in some cases to the initial local-dimension and for arbitrary CSS qubit-derived codes to singly exponential in $d$ with no dependence on the number of logicals $k$. This reduces the size of the caveat in LDI forms in their distance preservation condition.

arXiv:2610.15893 [quant-ph]

(or arXiv:2610.15893v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.15893 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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