{"id":"https://openalex.org/W3201587870","doi":"https://doi.org/10.22331/q-2022-07-07-757","title":"Bounds on approximating Max <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>XOR with quantum and classical local algorithms","display_name":"Bounds on approximating Max <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>XOR with quantum and classical local algorithms","publication_year":2022,"publication_date":"2022-07-07","ids":{"openalex":"https://openalex.org/W3201587870","doi":"https://doi.org/10.22331/q-2022-07-07-757","mag":"3201587870"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-07-07-757","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-07-07-757","pdf_url":"https://quantum-journal.org/papers/q-2022-07-07-757/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-2022-07-07-757/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031645515","display_name":"Kunal Marwaha","orcid":"https://orcid.org/0000-0001-9084-6971"},"institutions":[{"id":"https://openalex.org/I1280536761","display_name":"Ames Research Center","ror":"https://ror.org/02acart68","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280536761","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I143663144","display_name":"Research Institute for Advanced Computer Science","ror":"https://ror.org/022qmyy53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1329765538","https://openalex.org/I143663144"]},{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kunal Marwaha","raw_affiliation_strings":["Berkeley Center for Quantum Information and Computation, University of California, Berkeley, CA","Department of Computer Science, University of Chicago, Chicago, IL","Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA","USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA"],"raw_orcid":"https://orcid.org/0000-0001-9084-6971","affiliations":[{"raw_affiliation_string":"Berkeley Center for Quantum Information and Computation, University of California, Berkeley, CA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Computer Science, University of Chicago, Chicago, IL","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA","institution_ids":["https://openalex.org/I1280536761"]},{"raw_affiliation_string":"USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA","institution_ids":["https://openalex.org/I143663144"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076190671","display_name":"Stuart Hadfield","orcid":"https://orcid.org/0000-0002-4607-3921"},"institutions":[{"id":"https://openalex.org/I1280536761","display_name":"Ames Research Center","ror":"https://ror.org/02acart68","country_code":"US","type":"facility","lineage":["https://openalex.org/I1280536761","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I143663144","display_name":"Research Institute for Advanced Computer Science","ror":"https://ror.org/022qmyy53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1329765538","https://openalex.org/I143663144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stuart Hadfield","raw_affiliation_strings":["Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA","USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA"],"raw_orcid":"https://orcid.org/0000-0002-4607-3921","affiliations":[{"raw_affiliation_string":"Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, CA","institution_ids":["https://openalex.org/I1280536761"]},{"raw_affiliation_string":"USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, CA","institution_ids":["https://openalex.org/I143663144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":3.4683,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.93249341,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"6","issue":null,"first_page":"757","last_page":"757"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9939000010490417,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7427305579185486},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42189744114875793},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37672948837280273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3649614453315735},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.33640623092651367}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7427305579185486},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42189744114875793},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37672948837280273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3649614453315735},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.33640623092651367}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2022-07-07-757","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-07-07-757","pdf_url":"https://quantum-journal.org/papers/q-2022-07-07-757/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:2109.10833","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.10833","pdf_url":"https://arxiv.org/pdf/2109.10833","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:doaj.org/article:e412a6898a4b47e49dbe3045b61d260e","is_oa":true,"landing_page_url":"https://doaj.org/article/e412a6898a4b47e49dbe3045b61d260e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 6, p 757 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-07-07-757","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-07-07-757","pdf_url":"https://quantum-journal.org/papers/q-2022-07-07-757/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/G1267328461","display_name":null,"funder_award_id":"NNA16BD14C","funder_id":"https://openalex.org/F4320332374","funder_display_name":"Ames Research Center"},{"id":"https://openalex.org/G153237324","display_name":null,"funder_award_id":"NNA16BD14C","funder_id":"https://openalex.org/F4320318328","funder_display_name":"Universities Space Research Association"},{"id":"https://openalex.org/G2277900919","display_name":null,"funder_award_id":"IAA 8839","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G360598742","display_name":null,"funder_award_id":"NNA16BD14C","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G4194478833","display_name":null,"funder_award_id":"DARPA-NASA IAA 8839","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G5207989263","display_name":null,"funder_award_id":"Annex 114","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G6094436989","display_name":null,"funder_award_id":"NNA16BD14C","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"},{"id":"https://openalex.org/G6739092064","display_name":null,"funder_award_id":"IAA 8839, Annex 114","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G727702052","display_name":null,"funder_award_id":"1746045","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8380571957","display_name":null,"funder_award_id":"DGE-1746045","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320318328","display_name":"Universities Space Research Association","ror":"https://ror.org/043pgqy52"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332374","display_name":"Ames Research Center","ror":"https://ror.org/02acart68"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3201587870.pdf","grobid_xml":"https://content.openalex.org/works/W3201587870.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1549436331","https://openalex.org/W1650240946","https://openalex.org/W1739872454","https://openalex.org/W1999032440","https://openalex.org/W2073094582","https://openalex.org/W2077168589","https://openalex.org/W2083715726","https://openalex.org/W2087226760","https://openalex.org/W2101936356","https://openalex.org/W2116466689","https://openalex.org/W2171641771","https://openalex.org/W2225611404","https://openalex.org/W2493458272","https://openalex.org/W2554913830","https://openalex.org/W2738325034","https://openalex.org/W2802230929","https://openalex.org/W2933498165","https://openalex.org/W2945459433","https://openalex.org/W2952425173","https://openalex.org/W2956731923","https://openalex.org/W2962767882","https://openalex.org/W2962950054","https://openalex.org/W2963229940","https://openalex.org/W2963540536","https://openalex.org/W2964041306","https://openalex.org/W2964154443","https://openalex.org/W2971940014","https://openalex.org/W2980835754","https://openalex.org/W2982304552","https://openalex.org/W2997163556","https://openalex.org/W3016618834","https://openalex.org/W3089060063","https://openalex.org/W3101686982","https://openalex.org/W3103259309","https://openalex.org/W3103672205","https://openalex.org/W3104170093","https://openalex.org/W3105135121","https://openalex.org/W3112568121","https://openalex.org/W3119398506","https://openalex.org/W3120117903","https://openalex.org/W3156499817","https://openalex.org/W3171066440","https://openalex.org/W3205061038","https://openalex.org/W4205860582","https://openalex.org/W4240189201"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W3046775127","https://openalex.org/W3107602296","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W4364306694","https://openalex.org/W4312192474","https://openalex.org/W4283697347"],"abstract_inverted_index":{"We":[0,127,184,212],"consider":[1],"the":[2,38,68,73,87,97,101,109,117,135,152,178,196],"power":[3],"of":[4,15,40,72,86,139,161,180,204],"local":[5,88],"algorithms":[6,26],"for":[7,104,116,191,219],"approximately":[8],"solving":[9],"Max":[10,29,32,145],"<mml:math":[11,33,42,61,105,146,157,164,173,199,210,221],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>XOR,":[12],"a":[13,46,84,130,162,187,202,215],"generalization":[14,85],"two":[16],"constraint":[17,36],"satisfaction":[18],"problems":[19],"previously":[20],"studied":[21],"with":[22,51,83,172],"classical":[23],"and":[24,28,45,60,81],"quantum":[25,98,122,193],"(MaxCut":[27],"E3LIN2).":[30],"In":[31],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>XOR":[34,147],"each":[35],"is":[37],"XOR":[39],"exactly":[41],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>":[43,174],"variables":[44],"parity":[47],"bit.":[48],"On":[49],"instances":[50,148],"either":[52],"random":[53,143],"signs":[54],"(parities)":[55],"or":[56],"no":[57],"overlapping":[58],"clauses":[59,63],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>D</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>":[62],"per":[64],"variable,":[65],"we":[66,112],"calculate":[67],"expected":[69],"satisfying":[70,137],"fraction":[71,138],"depth-1":[74],"QAOA":[75,118],"from":[76,91],"Farhi":[77],"et":[78,93,206],"al":[79,94,207],"[arXiv:1411.4028]":[80],"compare":[82],"threshold":[89,102],"algorithm":[90,99,103],"Hirvonen":[92],"[arXiv:1402.2543].":[95],"Notably,":[96],"outperforms":[100],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math><mml:math":[106],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo>&amp;#x003E;</mml:mo></mml:math><mml:math":[107],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>4</mml:mn></mml:math>.On":[108],"other":[110],"hand,":[111],"highlight":[113],"potential":[114],"difficulties":[115],"to":[119],"achieve":[120],"computational":[121],"advantage":[123],"on":[124,134],"this":[125],"problem.":[126],"first":[128],"compute":[129],"tight":[131],"upper":[132,169],"bound":[133,170],"maximum":[136],"nearly":[140],"all":[141,220],"large":[142],"regular":[144],"by":[149],"numerically":[150],"calculating":[151],"ground":[153],"state":[154],"energy":[155],"density":[156],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>P</mml:mi><mml:mo":[158],"stretchy=\"false\">(</mml:mo><mml:mi>k</mml:mi><mml:mo":[159],"stretchy=\"false\">)</mml:mo></mml:math>":[160],"mean-field":[163],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>-spin":[165],"glass":[166],"[arXiv:1606.02365].":[167],"The":[168],"grows":[171],"much":[175],"faster":[176],"than":[177],"performance":[179],"both":[181],"one-local":[182],"algorithms.":[183],"also":[185],"identify":[186],"new":[188],"obstruction":[189,217],"result":[190,203],"low-depth":[192],"circuits":[194],"(including":[195],"QAOA)":[197],"when":[198,209],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>3</mml:mn></mml:math>,":[200],"generalizing":[201],"Bravyi":[205],"[arXiv:1910.08980]":[208],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math>.":[211],"conjecture":[213],"that":[214],"similar":[216],"exists":[218],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>.":[222]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2021-09-27T00:00:00"}