{"paper":{"title":"Approximability limits for bounded-degree max-LINSAT and implications for decoded quantum interferometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Carsten Schubert, Jens Eisert, Maximilian J. Kramer","submitted_at":"2026-06-11T16:59:12Z","abstract_excerpt":"For general max-k-XORSAT with $k \\geq 3$, no polynomial-time algorithm can do substantially better than random guessing on worst-case instances unless $\\mathsf{P} = \\mathsf{NP}$: approximating beyond the random-assignment value of $1/2$ is $\\mathsf{NP}$-hard. The picture changes when each variable appears in at most $D$ constraints. In that bounded-degree setting, polynomial-time algorithms can provably beat the random baseline by an additive amount of order $1/\\sqrt{D}$. For Boolean instances, this scaling is known to be optimal: the matching hardness result is due to Trevisan, while the corr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13570","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.13570/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}