{"paper":{"title":"Efficient Exact Quantum Sampling from the Sun-Wootters Distribution for Optimal Polynomial Intersection","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Sunghyeon Jo","submitted_at":"2026-07-17T22:33:06Z","abstract_excerpt":"Optimal Polynomial Intersection (OPI) is a structured optimization problem for which Decoded Quantum Interferometry (DQI) attains a satisfaction guarantee governed by the semicircle law. Sun and Wootters recently showed that, for balanced OPI over prime fields, a Fourier-defined distribution $P_u$ gives a strict worst-case improvement from limiting rate $0.6225$ onward and asymptotically perfect solutions from rate $0.7496$ onward, and asked whether $P_u$ can be sampled efficiently. We answer this question for Reed--Solomon OPI parameters satisfying their exponent condition strictly below the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16541","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/2607.16541/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"}