{"id":"https://openalex.org/W3005044149","doi":"https://doi.org/10.22331/q-2021-03-15-410","title":"Hyper-optimized tensor network contraction","display_name":"Hyper-optimized tensor network contraction","publication_year":2021,"publication_date":"2021-03-15","ids":{"openalex":"https://openalex.org/W3005044149","doi":"https://doi.org/10.22331/q-2021-03-15-410","mag":"3005044149"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-03-15-410","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-410","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-410/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-03-15-410/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Johnnie Gray","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]},{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Johnnie Gray","raw_affiliation_strings":["Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom","Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA"],"affiliations":[{"raw_affiliation_string":"Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":null,"display_name":"Stefanos Kourtis","orcid":null},"institutions":[{"id":"https://openalex.org/I135117807","display_name":"Universit\u00e9 de Sherbrooke","ror":"https://ror.org/00kybxq39","country_code":"CA","type":"education","lineage":["https://openalex.org/I135117807"]},{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["CA","GB","US"],"is_corresponding":false,"raw_author_name":"Stefanos Kourtis","raw_affiliation_strings":["Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom","Department of Physics, Boston University, Boston, MA, 02215, USA","Institut quantique & D\u00e9partement de physique, Universit\u00e9 de Sherbrooke, Qu\u00e9bec J1K 2R1, Canada"],"affiliations":[{"raw_affiliation_string":"Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Department of Physics, Boston University, Boston, MA, 02215, USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Institut quantique & D\u00e9partement de physique, Universit\u00e9 de Sherbrooke, Qu\u00e9bec J1K 2R1, Canada","institution_ids":["https://openalex.org/I135117807"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I122411786","https://openalex.org/I47508984"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":18.3865,"has_fulltext":true,"cited_by_count":170,"citation_normalized_percentile":{"value":0.99575577,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"5","issue":null,"first_page":"410","last_page":"410"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.8675000071525574,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.8675000071525574,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.11230000108480453,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.004100000020116568,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6383000016212463},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5550000071525574},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5376999974250793},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.45320001244544983},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.42649999260902405},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4117000102996826},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.3968999981880188}],"concepts":[{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6383000016212463},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5550000071525574},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5376999974250793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4722000062465668},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.42649999260902405},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4117000102996826},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40310001373291016},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3968999981880188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39629998803138733},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.37540000677108765},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3555000126361847},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3224000036716461},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2962000072002411},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.2709999978542328},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2662000060081482}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.22331/q-2021-03-15-410","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-410","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-410/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.01935","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.01935","pdf_url":"https://arxiv.org/pdf/2002.01935","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:authors.library.caltech.edu:108992","is_oa":true,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20210506-130409930","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:e34116e28a084e43ba047d30dde71d26","is_oa":true,"landing_page_url":"https://doaj.org/article/e34116e28a084e43ba047d30dde71d26","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 410 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-03-15-410","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-410","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-410/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6116963495","display_name":null,"funder_award_id":"Global Research Partnership","funder_id":"https://openalex.org/F4320315121","funder_display_name":"Samsung Advanced Institute of Technology"},{"id":"https://openalex.org/G8937612496","display_name":null,"funder_award_id":"Canada First Research Excellence Fund","funder_id":"https://openalex.org/F4320319880","funder_display_name":"Government of Canada"}],"funders":[{"id":"https://openalex.org/F4320315121","display_name":"Samsung Advanced Institute of Technology","ror":null},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3005044149.pdf","grobid_xml":"https://content.openalex.org/works/W3005044149.grobid-xml"},"referenced_works_count":71,"referenced_works":["https://openalex.org/W1531177993","https://openalex.org/W1546864018","https://openalex.org/W1659514373","https://openalex.org/W1904663217","https://openalex.org/W1930886120","https://openalex.org/W1971421925","https://openalex.org/W1975277392","https://openalex.org/W1981426329","https://openalex.org/W1987188265","https://openalex.org/W1995703916","https://openalex.org/W2006912660","https://openalex.org/W2008014812","https://openalex.org/W2012917738","https://openalex.org/W2033368244","https://openalex.org/W2036463035","https://openalex.org/W2049446489","https://openalex.org/W2069280326","https://openalex.org/W2072969317","https://openalex.org/W2074814947","https://openalex.org/W2075431083","https://openalex.org/W2088160021","https://openalex.org/W2096391265","https://openalex.org/W2097100165","https://openalex.org/W2114267503","https://openalex.org/W2127048411","https://openalex.org/W2145503356","https://openalex.org/W2147560177","https://openalex.org/W2168101857","https://openalex.org/W2192203593","https://openalex.org/W2203759264","https://openalex.org/W2269557952","https://openalex.org/W2293506269","https://openalex.org/W2482126025","https://openalex.org/W2516041031","https://openalex.org/W2545038605","https://openalex.org/W2570248857","https://openalex.org/W2593174005","https://openalex.org/W2611715903","https://openalex.org/W2617994470","https://openalex.org/W2754727929","https://openalex.org/W2769838435","https://openalex.org/W2782213776","https://openalex.org/W2798663460","https://openalex.org/W2809993672","https://openalex.org/W2810421208","https://openalex.org/W2826166138","https://openalex.org/W2891143562","https://openalex.org/W2897579646","https://openalex.org/W2913798276","https://openalex.org/W2943659715","https://openalex.org/W2945613423","https://openalex.org/W2946158922","https://openalex.org/W2946972079","https://openalex.org/W2950267153","https://openalex.org/W2951043472","https://openalex.org/W2953072660","https://openalex.org/W2963489471","https://openalex.org/W2963809597","https://openalex.org/W2980017474","https://openalex.org/W2982169647","https://openalex.org/W2994702301","https://openalex.org/W3083123017","https://openalex.org/W3167560924","https://openalex.org/W4211049957","https://openalex.org/W4213390282","https://openalex.org/W6600213211","https://openalex.org/W6600514347","https://openalex.org/W6601187393","https://openalex.org/W6604950735","https://openalex.org/W6629866355","https://openalex.org/W6637414577"],"related_works":[],"abstract_inverted_index":{"Tensor":[0],"networks":[1,31,43],"represent":[2],"the":[3,12,36,89,103,120,139,149,165,174,190,194,198],"state-of-the-art":[4],"in":[5,154],"computational":[6],"methods":[7,82],"across":[8],"many":[9,114],"disciplines,":[10],"including":[11,88],"classical":[13,195],"simulation":[14,166,196],"of":[15,24,86,156,167,176,185,197],"quantum":[16,20,91,98,168,178],"many-body":[17,169],"systems":[18,170],"and":[19,55,75,112,142,171],"circuits.":[21,201],"Several":[22],"applications":[23],"current":[25],"interest":[26],"give":[27],"rise":[28],"to":[29,110,189],"tensor":[30,77],"with":[32,48],"irregular":[33],"geometries.":[34],"Finding":[35],"best":[37],"possible":[38],"contraction":[39,71,157],"path":[40,150],"for":[41,73,164,173,193],"such":[42],"is":[44],"a":[45,84,134,183],"central":[46],"problem,":[47],"an":[49],"exponential":[50],"effect":[51],"on":[52,83,96],"computation":[53],"time":[54],"memory":[56],"footprint.":[57],"In":[58],"this":[59],"work,":[60],"we":[61,131,181],"implement":[62],"new":[63,177],"randomized":[64],"protocols":[65],"that":[66,102],"find":[67,101],"very":[68,108],"high":[69],"quality":[70,155],"paths":[72,104],"arbitrary":[74],"large":[76],"networks.":[78],"We":[79,100],"test":[80],"our":[81],"variety":[85],"benchmarks,":[87],"random":[90],"circuit":[92],"instances":[93],"recently":[94],"implemented":[95],"Google":[97],"chips.":[99,179],"obtained":[105],"can":[106],"be":[107],"close":[109],"optimal,":[111],"often":[113],"orders":[115],"or":[116],"magnitude":[117],"better":[118],"than":[119],"most":[121],"established":[122],"approaches.":[123],"As":[124],"different":[125,129],"underlying":[126],"geometries":[127],"suit":[128],"methods,":[130],"also":[132],"introduce":[133],"hyper-optimization":[135],"approach,":[136],"where":[137],"both":[138],"method":[140],"applied":[141],"its":[143],"algorithmic":[144],"parameters":[145],"are":[146],"tuned":[147],"during":[148],"finding.":[151],"The":[152],"increase":[153],"schemes":[158],"found":[159],"has":[160],"significant":[161],"practical":[162],"implications":[163],"particularly":[172],"benchmarking":[175],"Concretely,":[180],"estimate":[182],"speed-up":[184],"over":[186],"10,000<mml:math":[187],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo>\u00d7</mml:mo></mml:math>compared":[188],"original":[191],"expectation":[192],"Sycamore":[199],"`supremacy'":[200]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":42},{"year":2024,"cited_by_count":45},{"year":2023,"cited_by_count":36},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":17}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2020-02-14T00:00:00"}