{"id":"https://openalex.org/W3206309997","doi":"https://doi.org/10.22331/q-2022-04-20-692","title":"New techniques for bounding stabilizer rank","display_name":"New techniques for bounding stabilizer rank","publication_year":2022,"publication_date":"2022-04-20","ids":{"openalex":"https://openalex.org/W3206309997","doi":"https://doi.org/10.22331/q-2022-04-20-692","mag":"3206309997"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-04-20-692","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-20-692","pdf_url":"https://quantum-journal.org/papers/q-2022-04-20-692/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-2022-04-20-692/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110715494","display_name":"Benjamin Lovitz","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Benjamin Lovitz","raw_affiliation_strings":["Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON, Canada"],"raw_orcid":"https://orcid.org/0000-0002-2445-2701","affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032649728","display_name":"Vincent Steffan","orcid":"https://orcid.org/0000-0003-4913-6833"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Vincent Steffan","raw_affiliation_strings":["QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark"],"raw_orcid":"https://orcid.org/0000-0003-4913-6833","affiliations":[{"raw_affiliation_string":"QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":2,"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":0.8324,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76629929,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"6","issue":null,"first_page":"692","last_page":"692"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9932000041007996,"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":0.9922999739646912,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7876195907592773},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7606532573699951},{"id":"https://openalex.org/keywords/stabilizer","display_name":"Stabilizer (aeronautics)","score":0.6954919695854187},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5867742300033569},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.5555581450462341},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5331156849861145},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4178483188152313},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4153844118118286},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32999807596206665},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3181747496128082},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3042616844177246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13610365986824036},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1071384847164154},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06147846579551697}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7876195907592773},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7606532573699951},{"id":"https://openalex.org/C2777502316","wikidata":"https://www.wikidata.org/wiki/Q2712515","display_name":"Stabilizer (aeronautics)","level":2,"score":0.6954919695854187},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5867742300033569},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.5555581450462341},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5331156849861145},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4178483188152313},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4153844118118286},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32999807596206665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3181747496128082},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3042616844177246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13610365986824036},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1071384847164154},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06147846579551697},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.22331/q-2022-04-20-692","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-20-692","pdf_url":"https://quantum-journal.org/papers/q-2022-04-20-692/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:2110.07781","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.07781","pdf_url":"https://arxiv.org/pdf/2110.07781","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:344bb488047142ceb132aa553c6b0891","is_oa":false,"landing_page_url":"https://doaj.org/article/344bb488047142ceb132aa553c6b0891","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 6, p 692 (2022)","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/2a2f9201-79f4-402a-8109-0ab76bb51305","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/2a2f9201-79f4-402a-8109-0ab76bb51305","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"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":"Lovitz , B & Steffan , V 2022 , ' New techniques for bounding stabilizer rank ' , Quantum , vol. 6 , 692 , pp. 1-22 . https://doi.org/10.22331/q-2022-04-20-692","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-04-20-692","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-04-20-692","pdf_url":"https://quantum-journal.org/papers/q-2022-04-20-692/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/G7352392636","display_name":null,"funder_award_id":"10059","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"}],"funders":[{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320314607","display_name":"Government of Ontario","ror":"https://ror.org/015pzp858"},{"id":"https://openalex.org/F4320322676","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3206309997.pdf","grobid_xml":"https://content.openalex.org/works/W3206309997.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1594735250","https://openalex.org/W1631356911","https://openalex.org/W1789015869","https://openalex.org/W1839785972","https://openalex.org/W1908413158","https://openalex.org/W1923824182","https://openalex.org/W1974309340","https://openalex.org/W2002261561","https://openalex.org/W2009169733","https://openalex.org/W2009994177","https://openalex.org/W2070678975","https://openalex.org/W2079294297","https://openalex.org/W2090781531","https://openalex.org/W2102892751","https://openalex.org/W2142610181","https://openalex.org/W2162699574","https://openalex.org/W2299781645","https://openalex.org/W2751862591","https://openalex.org/W2885845431","https://openalex.org/W2949864545","https://openalex.org/W2990961515","https://openalex.org/W3016573600","https://openalex.org/W3091959632","https://openalex.org/W3101236123","https://openalex.org/W3103699324","https://openalex.org/W3105782957","https://openalex.org/W3106326670","https://openalex.org/W3137828432","https://openalex.org/W3145796852","https://openalex.org/W3170369836","https://openalex.org/W3176763179","https://openalex.org/W4212984255","https://openalex.org/W4244593923"],"related_works":["https://openalex.org/W2392919231","https://openalex.org/W2373888082","https://openalex.org/W2384382117","https://openalex.org/W2043828253","https://openalex.org/W4252630758","https://openalex.org/W2368845495","https://openalex.org/W2352943411","https://openalex.org/W2369119520","https://openalex.org/W2566068142","https://openalex.org/W2358365047"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3,18,68,86],"present":[4],"number-theoretic":[5,21],"and":[6,42,58,88],"algebraic-geometric":[7,95],"techniques":[8],"for":[9],"bounding":[10],"the":[11,50,70,82,90],"stabilizer":[12,35,40,56,60,79,92],"rank":[13,36,57,80,93],"of":[14,23,30,49,74],"quantum":[15,75],"states.":[16],"First,":[17],"refine":[19],"a":[20,64],"theorem":[22],"Moulton":[24],"to":[25,43,63],"exhibit":[26],"an":[27],"explicit":[28],"sequence":[29],"product":[31],"states":[32,76],"with":[33,77],"exponential":[34],"but":[37],"constant":[38],"approximate":[39,59],"rank,":[41,61],"provide":[44],"alternate":[45],"(and":[46],"simplified)":[47],"proofs":[48],"best-known":[51],"asymptotic":[52],"lower":[53],"bounds":[54],"on":[55],"up":[62],"log":[65],"factor.":[66],"Second,":[67],"find":[69],"first":[71],"non-trivial":[72],"examples":[73],"multiplicative":[78],"under":[81],"tensor":[83],"product.":[84],"Third,":[85],"introduce":[87],"study":[89],"generic":[91],"using":[94],"techniques.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
