[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_256":257},"routes/_layout",{"_11":183},"routes/entity.$type.$id",{"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":22,"_23":24,"_25":26,"_27":28},"dehydratedState",{"_73":74,"_75":76},"type","paper","id","paper_W2170767514","section","technologies","entity",{"_15":16,"_29":30,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":38,"_39":-5,"_40":41,"_42":43,"_44":45,"_46":47,"_48":-5,"_49":50,"_51":30,"_52":53,"_54":55,"_56":57,"_58":59,"_60":61,"_62":-5,"_63":64,"_65":-5,"_66":67,"_68":30,"_69":-5},"canonical","https://www.hugmap.com/entity/paper/paper_W2170767514/technologies","siteBaseUrl","https://www.hugmap.com","sectionCount",1,"jsonLd","{\"@context\":\"https://schema.org\",\"@graph\":[{\"name\":\"P/NP, and the quantum field computer\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2170767514/technologies\",\"@type\":\"ScholarlyArticle\",\"headline\":\"P/NP, and the quantum field computer\",\"datePublished\":\"1998-01-06\",\"isPartOf\":{\"@type\":\"Periodical\",\"name\":\"Proceedings of the National Academy of Sciences\"}},{\"@type\":\"CollectionPage\",\"name\":\"P/NP, and the quantum field computer 相关技术\",\"description\":\"P/NP, and the quantum field computer 在 HugMap 中的相关技术，共 1 条，含结构化关联信息与详情链接。\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W2170767514/technologies\",\"inLanguage\":\"zh-CN\"},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"首页\",\"item\":\"https://www.hugmap.com/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"论文\",\"item\":\"https://www.hugmap.com/search?type=paper\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"P/NP, and the quantum field computer\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2170767514\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"相关技术\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W2170767514/technologies\"}]}]}","name","P/NP, and the quantum field computer","nameZh","aliases","description","descriptionZh","status","active","externalIds","{\"openalex\":\"W2170767514\",\"doi\":\"10.1073/pnas.95.1.98\"}","properties","source","openalex","createdAt","2026-05-23T04:44:40.206902116","updatedAt","2026-05-23T04:44:40.206904251","doi","10.1073/pnas.95.1.98","arxivId","openalexId","W2170767514","title","abstractText","The central problem in computer science is the conjecture that two complexity classes, P (polynomial time) and NP (nondeterministic polynomial time-roughly those decision problems for which a proposed solution can be checked in polynomial time), are distinct in the standard Turing model of computation: P not equal NP. As a generality, we propose that each physical theory supports computational models whose power is limited by the physical theory. It is well known that classical physics supports a multitude of implementation of the Turing machine. Non-Abelian topological quantum field theories exhibit the mathematical features necessary to support a model capable of solving all #P problems, a computationally intractable class, in polynomial time. Specifically, Witten [Witten, E. (1989) Commun. Math. Phys. 121, 351-391] has identified expectation values in a certain SU(2)-field theory with values of the Jones polynomial [Jones, V. (1985) Bull. Am. Math. Soc. 12, 103-111] that are #P-hard [Jaeger, F., Vertigen, D. & Welsh, D. (1990) Math. Proc. Comb. Philos. Soc. 108, 35-53]. This suggests that some physical system whose effective Lagrangian contains a non-Abelian topological term might be manipulated to serve as an analog computer capable of solving NP or even #P-hard problems in polynomial time. Defining such a system and addressing the accuracy issues inherent in preparation and measurement is a major unsolved problem.","publishedDate","1998-01-06","publishedYear",1998,"venue","Proceedings of the National Academy of Sciences","citationCount",225,"authors","keywords",[70,71,72],"pdfUrl","topVenue",false,"displayName","displayDescription","Quantum Computing Algorithms and Architecture","Quantum Information and Cryptography","Quantum Mechanics and Applications","mutations",[],"queries",[77],{"_78":79,"_80":81,"_82":83,"_84":85},"dehydratedAt",1780607271989,"state",{"_87":88,"_89":26,"_90":79,"_91":-5,"_92":93,"_94":93,"_95":93,"_96":-5,"_97":-5,"_98":67,"_35":99,"_100":101},"queryKey",[86,19,14,16],"queryHash","[\"portal\",\"entity\",\"paper\",\"paper_W2170767514\"]","portal","data",{"_19":20,"_102":103,"_104":105,"_106":107,"_108":109,"_18":110,"_62":111},"dataUpdateCount","dataUpdatedAt","error","errorUpdateCount",0,"errorUpdatedAt","fetchFailureCount","fetchFailureReason","fetchMeta","isInvalidated","success","fetchStatus","idle","entityType","Paper","taxonomies",[143,144,145,146],"events",[],"articles",[],[128],[112],{"_15":113,"_29":114,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":115,"_39":-5,"_40":41,"_42":116,"_44":117,"_118":119,"_51":-5,"_120":-5,"_121":-5,"_122":-5,"_60":-5,"_123":-5,"_124":-5,"_125":-5,"_126":-5,"_127":-5,"_68":114,"_69":-5},"person_A5064155719","Michael Freedman","{\"openalex\":\"A5064155719\",\"orcid\":\"0000-0001-8664-3485\"}","2026-05-14T07:05:42.417711449","2026-05-23T04:44:40.212952663","orcid","0000-0001-8664-3485","affiliation","researchArea","paperCount","homepage","linkedin","twitter","github","hindex",{"_15":129,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":130,"_39":-5,"_40":131,"_42":132,"_44":133,"_134":135,"_136":137,"_138":-5,"_139":140,"_141":-5,"_122":-5,"_142":-5,"_68":70,"_69":-5},"tech_oa_T10682","{\"taxonomy_id\":\"tax_rd_T10682\"}","openalex_topics","2026-05-17T09:00:16.315436236","2026-05-17T09:00:16.315439876","techType","architecture","domain","Physical Sciences","proposedYear","maturityLevel","growing","wikipediaUrl","patentCount",{"_15":176,"_29":177,"_31":-5,"_32":-5,"_33":178,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":182,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":177,"_69":178},{"_15":170,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":171,"_39":-5,"_40":41,"_42":172,"_44":173,"_151":152,"_153":-5,"_154":155,"_156":174,"_158":175,"_160":93,"_161":162,"_163":93,"_164":-5,"_68":72,"_69":-5},{"_15":165,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":166,"_39":-5,"_40":41,"_42":167,"_44":168,"_151":152,"_153":-5,"_154":155,"_156":157,"_158":169,"_160":93,"_161":162,"_163":93,"_164":-5,"_68":70,"_69":-5},{"_15":147,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":148,"_39":-5,"_40":41,"_42":149,"_44":150,"_151":152,"_153":-5,"_154":155,"_156":157,"_158":159,"_160":93,"_161":162,"_163":93,"_164":-5,"_68":71,"_69":-5},"tax_rd_T10020","{\"openalex_topic\":\"T10020\"}","2026-05-14T00:38:04.322811986","2026-05-23T12:41:03.247863187","taxonomyType","RESEARCH_DOMAIN","code","level",3,"parentId","tax_rd_1702","path","Physical Sciences/Computer Science/Artificial Intelligence/Quantum Information and Cryptography","sortOrder","isLeaf",true,"entityCount","children","tax_rd_T10682","{\"openalex_topic\":\"T10682\"}","2026-05-14T00:30:39.395658458","2026-05-23T12:41:03.272911456","Physical Sciences/Computer Science/Artificial Intelligence/Quantum Computing Algorithms and Architecture","tax_rd_T10622","{\"openalex_topic\":\"T10622\"}","2026-05-14T00:30:39.36852586","2026-05-23T12:41:03.259661709","tax_rd_3107","Physical Sciences/Physics and Astronomy/Atomic and Molecular Physics, and Optics/Quantum Mechanics and Applications","tax_ind_security","网络安全","Cybersecurity","manual","INDUSTRY","tax_ind_root","科技行业/网络安全",{"_73":184,"_75":185},[],[186],{"_78":187,"_80":188,"_82":189,"_84":190},1780607269976,{"_87":192,"_89":26,"_90":187,"_91":-5,"_92":93,"_94":93,"_95":93,"_96":-5,"_97":-5,"_98":67,"_35":99,"_100":101},[86,191],"[\"portal\",\"industries\"]","industries",[193,194,195,196,197,198,199,200,201,202,203,204],{"_15":249,"_29":250,"_31":-5,"_32":251,"_33":252,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":253,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":250,"_69":252},{"_15":245,"_29":246,"_31":-5,"_32":-5,"_33":247,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":248,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":246,"_69":247},{"_15":239,"_29":240,"_31":-5,"_32":241,"_33":242,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":243,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":240,"_69":242},{"_15":176,"_29":177,"_31":-5,"_32":-5,"_33":178,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":182,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":177,"_69":178},{"_15":235,"_29":236,"_31":-5,"_32":-5,"_33":237,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":238,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":236,"_69":237},{"_15":229,"_29":230,"_31":-5,"_32":231,"_33":232,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":233,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":230,"_69":232},{"_15":225,"_29":226,"_31":-5,"_32":-5,"_33":227,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":228,"_160":93,"_161":162,"_163":93,"_164":-5,"_68":226,"_69":227},{"_15":221,"_29":222,"_31":-5,"_32":-5,"_33":223,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":224,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":222,"_69":223},{"_15":217,"_29":218,"_31":-5,"_32":-5,"_33":219,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":220,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":218,"_69":219},{"_15":213,"_29":214,"_31":-5,"_32":-5,"_33":215,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":216,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":214,"_69":215},{"_15":209,"_29":210,"_31":-5,"_32":-5,"_33":211,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":212,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":210,"_69":211},{"_15":205,"_29":206,"_31":-5,"_32":-5,"_33":207,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":179,"_42":-5,"_44":-5,"_151":180,"_153":-5,"_154":26,"_156":181,"_158":208,"_160":93,"_161":67,"_163":93,"_164":-5,"_68":206,"_69":207},"tax_ind_smartphone","智能手机","Smartphone","科技行业/智能手机","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算","tax_ind_blockchain","区块链",[234],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_semi","半导体",[244],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[254,255],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_258":24},"SITE_BASE_URL"]

<i>P/NP</i>, and the quantum field computer 论文

<i>P/NP</i>, and the quantum field computer · 相关技术

相关技术