{"schema":"pubphys.bundle/1","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"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"0cf7dc74b6f5d37a1c4c4c2bd94a8e4a25dfd4151b7b59a5e369f1f172fd2b30","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"0e12963f96b24fb1044d388fe2681177c627f1bd9f6095fba477494b53b5b241","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ZaFhY-cBjw2rL7Zk1Pg8mT7tRu04QbNSE2RNARDS1_xh5EWakrWUc0kVfU_X6YaDQjil9rVmS_TBiqtDFjv8BA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIDhKWP5ayT7EETTiP4mgRd8Yn8b2fYJX7pHdJS1O1skHxIA3XiUMaq2bYLt_6MCezfJhH7mI1ge_RA5rRwsdXkSpYCPEgpbYMHnomkIcfn8T5HfVmoTCn7hZDpc85qHBesOeCsRAI8CAzUGG85iRkfZ9qicAyDlCNjlT-GPGNcE3zjTx6JErWhgjwIP10seudbYEWCGE08zfr-YA59zePPcDoxwdKpzxQxBAMCPEgoP3EgvSBso3EZLIOIU4CowLPrWkt9G2UIeerPxWxsGsI8SBdoK6aZzKVlKhSra2wrzOGdhkQ1ReNy8kFQWH11rSLFQjxIBButcXheltB9r5q_SiVaYiPmqtX1_20ZNerwgnGiSE_CPEgoIuFmZyvZNn9xG6qppiK_mJT40FHqHfjKvxdbYaYwQAI8CDTURm5psgkpndkZlRIia_PxrzHEbIi4fWR0w8YEe9YLAjwIMIc4xq7iJ2YP27EtWYUvEm4-TQD7cayDq2XvZh74n3BCPAg3v2QXfNkDO6Xzu9061umH0rhjRfHBKza3uG2nPQbpd8I8CCtNZgmApuKULvPC9nsMCaM05arV-F3o5FTlnJCnRvdMgjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xP8Ag9_jDS75DI4sK2h0dHBzOi8vYm9iLmJ0Yy5jYWxlbmRhci5vcGVudGltZXN0YW1wcy5vcmcI8CBXWeNiWFWltfHE0nkDXsVKIykUUwuObhsnN-2fvBt98gjwIM5Vf7j68sOFgVysYMc5S09Hho-fqxYW3oQ4oKUX7JpPCPAgaKHHQB3sdd9w1hu4NMh7vmb-p0X2r4uyVKKCj1G7S28I8SAW2Mg6Bzi9ygjrrjIYB7w90fwMcxH24SsqLmzPyAMGfwjwIMQ863zlveYIpNKWVrZaDOa4vowwoOg2CcTW8gXtxK3dCPEgrZxGGAf-t8jhz_eLMUyBN1IhNrdYDRcNHWvQcwNG9woI8CCVOUHG1YXudbaFIgUYvrCIevRWvb2ubhQAo-z0duD0rQjxIDBeKerVGkO3J2eXDwdraSioXbIWsdIPEN1s8pIwJIS2CPAgV2kB3n3JZ5HwBQjpRL1CWKnqvdCjZk3RcALk6N2wHigI8CB-wbljNlfqElD25uZkNg6taS81YDRU2vfMqGVQ420O9AjxWQEAAAABJM43UU6MLMRrPlCUqossvu1q_knons5yylyWTgxZzWUAAAAAAP7___8CLgABAAAAAAAWABQrYt3E7OllKRCEmL3FL589l78_5wAAAAAAAAAAImog8ATiyw4ACAjxILmbcIO7ixv3pCtwUMZ1VQGKus54F9lZ8-w5ECD5ZuiICAjwIG6ynCyFTLPE7Rgk-0ZGCtBDyqNQx8YvaSZNHy8D8p8jCAjwIMX8zoD2Be1YWvcx_bexVPRmBX0hK-do8b8t9SarimQVCAjxIG6XtpqIEclLlhzcK1LVjqoPGrjjmLnyno8tcETMzECECAjwIF6mlfXOFY51JhrK4eze8zQlKV75OYZYqbtyi8BWxmAsCAjwIKKUcJmVoz-u-geiRV_-ZHdF0VEPXaEPFWf_JX_0e7G2CAjxIGMeD0Z5QWNKBcAEpHht007FFIILW6aSJ8f3CMkKNsneCAjwIBFr6Je8rkB7kwhPGbq0yRgFwZsvW9JhY5sXDRtrq0QwCAjwIAHAwXaus-yUgKICJB5mVvx8VZuJgjwnpb0qWPg1pi6DCAjxIAJhb8cefkVHTAMymdsxa-_i-tUua62LcpALQnPG7R9_CAjwIDvsFqBhPfAL6TCtXZd7gBWmMpx6iiZ-Ug0Jf_LlcstgCAjwIDJRBX6Q0Vge-ra-k1_g76yJWTEp6WWF13I3JpTnsZPJCAjwILykZCbkC9VQgl5gytPKKir6T9nTvKR6y05iWSHBTQgzCAgABYiWDXPXGQED45c78Ah-sGbmQAwfZwjwEAYqxtHnZiPZnJEGPx_JvKsI8SDXkqDg17YsZIrEz5acRx7mBXCKW5mKNgRYnw_-U2cpDgjxBGrArDrwCEfK6Mono428_wCD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPAg10nyJ6Jn4kshQQQCKE0Lvj3hBC6nLRBVIzaPV4eh8VwI8CCQaAqWlxEbac_XOq1MOlf9iOKHEsxXspzbjK0vLpy8BwjwII3iRbRXUcDxrhAdkZmFlI15nySCSEZ7g922tF1Xln5DCPEgYYvZ1L4v4rPu_UqLfcHPtwSb2OH2GhPgVcVhhH6DpkQI8CDZCIoR20sC-uchP40oAmcLm9EJFV7xzwplj54AeVadXQjxILvLBjPFpCoz29m9Yf2qRnV7PI9GqxE8ozVQfk9QwCqrCPEgZXcMudvEoB_MJ8tqOW2PLTKAIeQBnE-1bfzptRc2gR8I8VkBAAAAAfXq-bmxWqOz7B5wKkwjzHGv2R4s7Y0Z76LqXWYNhmz0AAAAAAD-____Av0cAAAAAAAAFgAUl-skmdZDtn7Hnub6mF4HP2uVn7oAAAAAAAAAACJqIPAE4MsOAAgI8CBDmQsbEXc46Hu8DivhCBM1LGExa4TTM-wo7HpoCVjBTQgI8CCty5vkQtPHzzs8xqArOYhVSjgaDoG1ou3cojv5_P7wQQgI8SDQWB0kdXCTwbk-TqTt0QfRMyzDNLOtU1XXFgvGSRlW8wgI8CC2PKa_QCIBZtrXodq1GdEzppISMsMRDOnzr2gFjLKOAAgI8CCwQ_QF67bcFk_uJ2s0VCZmf5PGIjTmTCpt_qnVY5p_8AgI8SAbzyx7z-oxPMju6PvtQhzrJIQyH2ZAc9oyLuYemzbmZQgI8CC5bh7J74uUk91r8LwybHQFCNBC3PWeuwtMCCNFKWj19AgI8SAf4R2TUNPjaX_PWDUImpoITK0JoW89zaMKnD1wlEEi8AgI8SC2vNmdm7eyP5Ytl1yTzT0njliMdALl1ViKG-s3bG2zswgI8CCpbIVNz1GFVXdJk2zd82hBUoNFFemUPBt7IJdWEOciPwgI8CBtYdRQcrtX1FtCm1SxF7sx-5cO04U8KzbJh8fqBkyReAgI8CBHs2LGmX6gI-lV7yp1RrV7_tGfdiBAwnEFF6B6yXHzAQgI8CATotVmbXBMAixhZ-QKy5Q4lR0FusdA_wcIC1TbB7GmxAgIAAWIlg1z1xkBA-KXOw"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEI-HygGl2lKNU9nzkeLZUt2KspGiG283I2k6ZTCIlbhfzwIPiDBgDVP8Dnxw-AJa56FmJLwma3_67NAR-4z7SG0dJhCPEgTBTccWyQ76xKhCaJwzc74y6awE7cbsgvhQu3IxqADZ0I8SDVn8vpS8jHK0VT94-8WB2toL6PZLTtLsn9tkXgzQ31OwjwIFUKWOJGFE4dLjAqZoimlQsf4uMO6GF5JfdBXBBAYzBkCPEgWIx0uvtEGVwIUcH3hpddUnylrquUUn-Kl9rzmeVhbesI8CCaVvGFcFjWuGlxcE3iF0dvk0TcN-e8_-WkY_vxMeYSCQjwII1OGo6m_8GpiiXK1pC7312jTWia9PNuWF9nWxoSLBVxCPAgwaB6v5-rgNtbRovqByHYFx5vLPaMlAE1dmQXdsyW6UQI8SDWlL7IzfO_cwYxfadaDmoPVp0tptPmw2XmYaU4JMe_wgj_8Ah24IVYDhTLjQjwED2StpR20zKnAmFKLczkHJkI8CCe67kSLOh57nysQqZi1IHlJdGlLtKL-P9z6nKaUvm3XQjxICOd9Lx83cM_96PY2EN1mm5UmleuFn5-z5m8uVi8iPgNCPEEasCsO_AISExe0692tcT_AIPf4w0u-QyOLCtodHRwczovL2JvYi5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3JnCPAgV1njYlhVpbXxxNJ5A17FSiMpFFMLjm4bJzftn7wbffII8CDOVX-4-vLDhYFcrGDHOUtPR4aPn6sWFt6EOKClF-yaTwjwIGihx0Ad7HXfcNYbuDTIe75m_qdF9q-LslSigo9Ru0tvCPEgFtjIOgc4vcoI664yGAe8PdH8DHMR9uErKi5sz8gDBn8I8CDEPOt85b3mCKTSlla2WgzmuL6MMKDoNgnE1vIF7cSt3QjxIK2cRhgH_rfI4c_3izFMgTdSITa3WA0XDR1r0HMDRvcKCPAglTlBxtWF7nW2hSIFGL6wiHr0Vr29rm4UAKPs9Hbg9K0I8SAwXinq1RpDtydnlw8Ha2koqF2yFrHSDxDdbPKSMCSEtgjwIFdpAd59yWeR8AUI6US9Qlip6r3Qo2ZN0XAC5OjdsB4oCPAgfsG5YzZX6hJQ9ubmZDYOrWkvNWA0VNr3zKhlUONtDvQI8VkBAAAAASTON1FOjCzEaz5QlKqLLL7tav5J6J7Ocspclk4MWc1lAAAAAAD-____Ai4AAQAAAAAAFgAUK2LdxOzpZSkQhJi9xS-fPZe_P-cAAAAAAAAAACJqIPAE4ssOAAgI8SC5m3CDu4sb96QrcFDGdVUBirrOeBfZWfPsORAg-WboiAgI8CBuspwshUyzxO0YJPtGRgrQQ8qjUMfGL2kmTR8vA_KfIwgI8CDF_M6A9gXtWFr3Mf23sVT0ZgV9ISvnaPG_LfUmq4pkFQgI8SBul7aaiBHJS5Yc3CtS1Y6qDxq445i58p6PLXBEzMxAhAgI8CBeppX1zhWOdSYayuHs3vM0JSle-TmGWKm7covAVsZgLAgI8CCilHCZlaM_rvoHokVf_mR3RdFRD12hDxVn_yV_9HuxtggI8SBjHg9GeUFjSgXABKR4bdNOxRSCC1umkifH9wjJCjbJ3ggI8CARa-iXvK5Ae5MITxm6tMkYBcGbL1vSYWObFw0ba6tEMAgI8CABwMF2rrPslICiAiQeZlb8fFWbiYI8J6W9Klj4NaYugwgI8SACYW_HHn5FR0wDMpnbMWvv4vrVLmuti3KQC0Jzxu0ffwgI8CA77BagYT3wC-kwrV2Xe4AVpjKceoomflINCX_y5XLLYAgI8CAyUQV-kNFYHvq2vpNf4O-siVkxKellhddyNyaU57GTyQgI8CC8pGQm5AvVUIJeYMrTyioq-k_Z07ykestOYlkhwU0IMwgIAAWIlg1z1xkBA-OXO_AIfrBm5kAMH2cI8BAGKsbR52Yj2ZyRBj8fybyrCPEg15Kg4Ne2LGSKxM-WnEce5gVwiluZijYEWJ8P_lNnKQ4I8QRqwKw68AhHyujKJ6ONvP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjwINdJ8ieiZ-JLIUEEAihNC7494QQupy0QVSM2j1eHofFcCPAgkGgKlpcRG2nP1zqtTDpX_YjihxLMV7Kc24ytLy6cvAcI8CCN4kW0V1HA8a4QHZGZhZSNeZ8kgkhGe4PdtrRdV5Z-QwjxIGGL2dS-L-Kz7v1Ki33Bz7cEm9jh9hoT4FXFYYR-g6ZECPAg2QiKEdtLAvrnIT-NKAJnC5vRCRVe8c8KZY-eAHlWnV0I8SC7ywYzxaQqM9vZvWH9qkZ1ezyPRqsRPKM1UH5PUMAqqwjxIGV3DLnbxKAfzCfLajltjy0ygCHkAZxPtW386bUXNoEfCPFZAQAAAAH16vm5sVqjs-wecCpMI8xxr9keLO2NGe-i6l1mDYZs9AAAAAAA_v___wL9HAAAAAAAABYAFJfrJJnWQ7Z-x57m-pheBz9rlZ-6AAAAAAAAAAAiaiDwBODLDgAICPAgQ5kLGxF3OOh7vA4r4QgTNSxhMWuE0zPsKOx6aAlYwU0ICPAgrcub5ELTx887PMagKzmIVUo4Gg6BtaLt3KI7-fz-8EEICPEg0FgdJHVwk8G5Pk6k7dEH0TMswzSzrVNV1xYLxkkZVvMICPAgtjymv0AiAWba16HatRnRM6aSEjLDEQzp869oBYyyjgAICPAgsEP0Beu23BZP7idrNFQmZn-TxiI05kwqbf6p1WOaf_AICPEgG88se8_qMTzI7uj77UIc6ySEMh9mQHPaMi7mHps25mUICPAguW4eye-LlJPda_C8Mmx0BQjQQtz1nrsLTAgjRSlo9fQICPEgH-Edk1DT42l_z1g1CJqaCEytCaFvPc2jCpw9cJRBIvAICPEgtrzZnZu3sj-WLZdck809J45YjHQC5dVYihvrN2xts7MICPAgqWyFTc9RhVV3SZNs3fNoQVKDRRXplDwbeyCXVhDnIj8ICPAgbWHUUHK7V9RbQptUsRe7MfuXDtOFPCs2yYfH6gZMkXgICPAgR7Nixpl-oCPpVe8qdUa1e_7Rn3YgQMJxBRegeslx8wEICPAgE6LVZm1wTAIsYWfkCsuUOJUdBbrHQP8HCAtU2wexpsQICAAFiJYNc9cZAQPilzs"]},"log":{"leaf_index":"2061","tree_size":"2123","proof":["8c914e6ed5486b651e41f751291f90f9b7629b04389a6e5148f9da92a72ab8c0","00f2f161092d8acca62b7ebd68fd7abde46ad2486ef1f6d5f81072e8c46e56db","2ffe19499cd8ba9343687418fada545678c5f220eef5c1b96a3185ad5d4169da","0b65473a463e9395f9df008984f0f5874980ad4ab3ff8d4d22ccc6dad5fa485e","e4a9a5131ce23a060ef3aace87a0ad8c371d77273bd260f210379d90b5c6e387","9e2eab6351497bb7630c20edf604158f6e0b1888784eae40ff069205cc38e5c4","e6fe28a74db11e411f7b825398eaff5c6a5c1228133acc9bc663eaf6ba57e637","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n2123\npXVcluz7BF4vgChQs6lShuU0386gCH0RxrC1sxyE3rI=\n\n— pubphys.com/log/v1 JFPwIOLzsUD22XoTVyTfk/FMVj/u3f3DxZk4V/Ws10KVSS+8WQSwhunQ//EAhyS9Td5CyM0E++85GMezmKd8240j9Q8=\n","promise":null},"orcid_key_evidence":[],"attesting":null}