{"schema":"pubphys.bundle/1","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},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"bcd0354708925d64044c0fb2afa86acba4ec63913a1ea7b78106e30213ae13d9","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"5bb2d68f69732bcd2bd37c7ca7f5f765be0fdab8509d5891cbc4cbec1087ffda","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"meiZZ1fHvHtEVD5EYpBk1biqiYNQk-Q6PcUMGOoK0II9qVzq4KNzS8KNBME4vNR8htg0g9JdMlbdC6j7UEuvDg"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIW7LWj2lzK80r03x8p_X3Zb4P2rhQnViRy8TL7BCH_9rwIFu2w-R11-2KrBmFy7ozQHiDMd03qS0FzI1b-ZtUTKmFCPAgP5N4f_l2iRM5IRB8jajFl2e0cPcgwb-lt1w9kCt6gQAI8SAfCziBmt_lrjZ-PdRSMSWGygkLubprm5qURbSCUk7v1gjxINfcDf_eSWiqFJdWG_NvBg93LN5Epf-4l3c2cmtkqIGvCPEgzGLVA_dcRrfOxoSUrDpZ-GYDvSMP6pJzbvl9n2QrrpQI8SAylZSZZiM5R0YQooag5o-y5mvKzVJ_BtW_iylPECNAogjwIEYgJ6hBg9UaSbcZ5P0xO88jG54rlgan_Jhx1rNZQm7iCPEg-b8Lkm9aIcNajW2D_tonI2BpSvWgXJkN2LygUbv3ObsI8CCFjG9pSMiq3eVzHAmZsjRKj0iAZic3nIa3eyIChZggbAjwIOv_x0B6HyZ6WMHKeIf_d_EUIvwPGdZeVY-hXN3RLDM5CPEgHd9u6OIGCvUV12A1B1xdiOprSJ-4w0cqwfe7CzVX5HsI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIqBWv9ZcLawoXtnBfyFLtwVkj1RJfWRPmPt5ModalbS7wIKg8N2GCOEXM5ibj0rjyO6mF3pw1AHNwbk_PnS-Zjqd2CPAgtomGPwXzQfoYK3ZTqprOuaO8AuKqKID5yMFHfXlRj7MI8CCjcO3aObYlWdxmdobOzGuT-Vhr5ieFAKp2Xf23ggO-zwjxIP9IWCwUb48Qr-e9UrCwFSBkRst2_c21ldiF6tlKkSyZCPEgRMWmQyRLtOQxrsj6xIglgOBbi5vlSdQclgK2xgPFtl8I8SA2egp0G2ge8pnr1JRslpoPLLFcM41Ju0LnbChmXPjjngjwIHExvyo7F9qj3z61fSDvdyatlouUDqqU4ATffdHOplJWCPEgXBC-vhHz95oq2yKKi3ggahpIP6-CNOC1MPNshHV0yjUI8CDKr-9A1x_uMQhhNTqvWvXpPsAsdseP-4IejtAraE3u4AjwIIgwugvlgSNOmTWMhquqetKjeLf0x7d1a1MH4KU52JbFCPAg3mczMYDKOd7Nhf3ojA9ZvuTsN66Y1NnyYTp9j8GKQNwI8SCvAiiN-Hrv7IEejd8wdUihoozu5KOvpoBFJ0vg3UnGAQj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"]},"log":{"leaf_index":"3766","tree_size":"3804","proof":["00a8c7ac7c1a262fc15caae3df5bdb81bc45695c44789f0580eb704033929eea","7040e242cc21456141ce7f7a52a49e50aad60b61a7164627e26cd031489dbc27","af46eda8ac78fe2f3fed28b7c56cb1711c695344b1685165f0b097eb01b81393","81b3359265d7b3d637358d7a753a4d4cf09cc95f4a5a2c2c4279bf5ffa7fae3f","fe5ebd14312db8db85f73cb4b2f82846a874b0225bd76cea074e3f2d1949f96b","7108e7001c9b1ec2f42d2dee6929c25df3fc216659083a58f27049458363f88e","17c91a7812aa72cd79b13c02f19c3226fff2624c8ff753f84916b2fa345baaf3","0455d4faa8c1028929d27c21062fe4bb47127ac22b5867e956f5c4f72c680cf1","e55158332fc5066d8199fad50d3929c561e805c1a4826619f59cd2254d322eb8","af34d80d0065c0ab502282775e865492e2cb49c9493f4594d63ba5577922854a","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\n1e2b339a7f49cb1734efcc5b7e6ac273615ecce55f8b43dce12ec2ee25a59541\n3766\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwIBMy7YLvqt+HfudO1DX70C6scgENzKpXb7knSgtCTQidzTBU70nL/7gYqDb1diFWLRnFYEh6AsjhwpQK8j325gc=\n"},"orcid_key_evidence":[],"attesting":null}