2026-08-18T04:29:48Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23719 2025-10-27T10:42:48Z ddc:004 open_access

Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products Golowich, Louis Guruswami, Venkatesan Quantum Error Correction Quantum LDPC Code Homological Product Iterative Construction The first linear-distance quantum LDPC codes were recently constructed by a line of breakthrough works (culminating in the result of Panteleev & Kalachev, 2021). All such constructions, even when allowing for almost-linear distance, are based on an operation called a balanced (or lifted) product, which is used in a one-shot manner to combine a pair of large classical codes possessing a group symmetry. We present a new construction of almost-linear distance quantum LDPC codes that is iterative in nature. Our construction is based on a more basic and widely used product, namely the homological product (i.e. the tensor product of chain complexes). Specifically, for every ε > 0, we obtain a family of [[N,N^{1-ε},N^{1-ε}]] (subsystem) quantum LDPC codes via repeated homological products of a constant-sized quantum locally testable code. Our key idea is to remove certain low-weight codewords using subsystem codes (while still maintaining constant stabilizer weight), in order to circumvent a particular obstruction that limited the distance of many prior homological product code constructions to at most Õ(√N). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Louis Golowich and Venkatesan Guruswami 2025 Is Part Of LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2025.25 urn:nbn:de:0030-drops-237196 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.25 eng https://creativecommons.org/licenses/by/4.0/legalcode