Year: 2025
Type: article
Abstract: We present a modified version of the Bravyi-Terhal bound that applies to quantum codes defined by local parity-check constraints on aD-dimensional lattice quotient. Specifically, we consider a quotient ZD/Λ of ZDof cardinality ℓ, where Λ is someD-dimensional sublattice of ZD: we suppose that every vertex of this quotient indexesmqubits of a stabilizer codeC, which therefore has lengthn=mℓ. We prove that if all stabilizer generators act on qubits whose indices lie within a ball of radius ρ, then the minimum distancedof the code satisfiesd≤m√ γD( √D+ 4ρ)ℓD−1/D, where γDis theD-dimensional Hermite constant. We then apply this bound to derive an upper bound on the minimum distance of Abelian Two-Block Group Algebra (2BGA) codes whose parity-check matrices have the form [A|B] with each submatrix representing an element of a group algebra over a finite abelian group.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4415968791