{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"65f84de4322e4a5746335c239911a1a8b510ee4cfa5db5656bd94c3088ec6b1f","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["0cf7dc74b6f5d37a1c4c4c2bd94a8e4a25dfd4151b7b59a5e369f1f172fd2b30","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"0f0704e69960cd10cfa9876e24827ee47a01ad379f9cfe379675405033d9c33f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.useful-advantage.dqi-optimization-speedup","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Most quantum methods for hard optimization problems give only modest speedups. A quantum method called decoded quantum interferometry finds better approximate solutions to a structured problem than any known classical method, and it is open whether a classical method can catch up.","posed_since":"2024","precise":"Optimal Polynomial Intersection (OPI): given a prime $p$, points $x_{1}..x_{m}$ in $F_{p}$ and subsets $S_{i}$ of $F_{p}$, find a polynomial $Q$ over $F_{p}$ of $\\mathrm{degree}<n$ maximizing the number of $i$ with $Q(x_{i})$ in $S_{i}$. For the parameter families of Jordan et al. (Nature 646, 831, 2025, arXiv:2408.08292), decoded quantum interferometry reaches a satisfied fraction (given by a semicircle-law formula) above that of every known polynomial-time classical algorithm. Answer: a classical polynomial-time algorithm achieving the same fraction, or a hardness proof under a standard complexity assumption.","problem_ref":"0cf7dc74b6f5d37a1c4c4c2bd94a8e4a25dfd4151b7b59a5e369f1f172fd2b30","references":"","settled_by":"A classical algorithm matching the DQI fraction on the stated OPI families, or a reduction showing that doing so would break a standard assumption.","status_note":"2025-2026 work gave faster DQI implementations and inapproximability results for related max-LINSAT problems; no classical match for OPI has been reported.","title":"Can classical algorithms match decoded quantum interferometry on polynomial intersection?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"bcd0354708925d64044c0fb2afa86acba4ec63913a1ea7b78106e30213ae13d9","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"5bb2d68f69732bcd2bd37c7ca7f5f765be0fdab8509d5891cbc4cbec1087ffda","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"meiZZ1fHvHtEVD5EYpBk1biqiYNQk-Q6PcUMGOoK0II9qVzq4KNzS8KNBME4vNR8htg0g9JdMlbdC6j7UEuvDg"},"schema":"pubphys.envelope/1"},"record_hash":"bcd0354708925d64044c0fb2afa86acba4ec63913a1ea7b78106e30213ae13d9","leaf_index":3766}