{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0e59af04f42c8f435d29bbe10bc7a12f2beae27efed2b92e5aa5bc74ee44a0f7","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"20e216823a68bb6e3c218465e0be7dafe8d828644e06f760cb76014b049fd2ac","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":"1","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":null,"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":"171840612800a5fc54a3a1cbae538bc99ab2fa80a9901200da4096ec8477ba9b"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"0cf7dc74b6f5d37a1c4c4c2bd94a8e4a25dfd4151b7b59a5e369f1f172fd2b30","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"0e12963f96b24fb1044d388fe2681177c627f1bd9f6095fba477494b53b5b241","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ZaFhY-cBjw2rL7Zk1Pg8mT7tRu04QbNSE2RNARDS1_xh5EWakrWUc0kVfU_X6YaDQjil9rVmS_TBiqtDFjv8BA"},"schema":"pubphys.envelope/1"},"record_hash":"0cf7dc74b6f5d37a1c4c4c2bd94a8e4a25dfd4151b7b59a5e369f1f172fd2b30","leaf_index":2061}