{"paper":{"title":"Approximation algorithms for noncommutative CSPs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Eric Culf, Hamoon Mousavi, Taro Spirig","submitted_at":"2023-12-28T01:22:27Z","abstract_excerpt":"Noncommutative constraint satisfaction problems (NC-CSPs) are higher-dimensional operator extensions of classical CSPs. Despite their significance in quantum information, their approximability remains largely unexplored. A notable example of a noncommutative CSP that is not solvable in polynomial time is NC-Max-$3$-Cut. We present a $0.864$-approximation algorithm for this problem. Our approach extends to a broader class of both classical and noncommutative CSPs. We introduce three key concepts: approximate isometry, relative distribution, and $\\ast$-anticommutation, which may be of independen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16765","kind":"arxiv","version":2},"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/2312.16765/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"}