2026-07-22T00:05:11Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24053 2025-12-12T14:56:07Z ddc:004 open_access

Optimal Locality and Parameter Tradeoffs for Subsystem Codes Dai, Samuel Li, Ray Tang, Eugene Quantum Error Correcting Code Locality Subsystem Code Commuting Projector Code We study the tradeoffs between the locality and parameters of subsystem codes. We prove lower bounds on both the number and lengths of interactions in any D-dimensional embedding of a subsystem code. Specifically, we show that any embedding of a subsystem code with parameters [[n,k,d]] into R^D must have at least M^* interactions of length at least 𝓁^*, where M^* = Ω(max(k,d)), and 𝓁^* = Ω(max(d/(n^((D-1)/D)), ((kd^(1/(D-1))/n))^((D-1)/D))). We also give tradeoffs between the locality and parameters of commuting projector codes in D-dimensions, generalizing a result of Dai and Li [Dai and Li, 2025]. We provide explicit constructions of embedded codes that show our bounds are optimal in both the interaction count and interaction length. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Samuel Dai and Ray Li and Eugene Tang 2025 Is Part Of LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2025.4 urn:nbn:de:0030-drops-240539 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.4 eng https://creativecommons.org/licenses/by/4.0/legalcode