{"id":"https://openalex.org/W7140132509","doi":"https://doi.org/10.22331/q-2026-03-23-2036","title":"The non-stabilizerness of fermionic Gaussian states","display_name":"The non-stabilizerness of fermionic Gaussian states","publication_year":2026,"publication_date":"2026-03-23","ids":{"openalex":"https://openalex.org/W7140132509","doi":"https://doi.org/10.22331/q-2026-03-23-2036"},"language":"en","primary_location":{"id":"doi:10.22331/q-2026-03-23-2036","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-03-23-2036","pdf_url":"https://quantum-journal.org/papers/q-2026-03-23-2036/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2026-03-23-2036/pdf/","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029954873","display_name":"Mario Collura","orcid":"https://orcid.org/0000-0003-2615-8140"},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]},{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]},{"id":"https://openalex.org/I4210151851","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Trieste","ror":"https://ror.org/05j3snm48","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210151851"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Mario Collura","raw_affiliation_strings":["INFN Sezione di Trieste, 34136 Trieste, Italy","International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy"],"affiliations":[{"raw_affiliation_string":"INFN Sezione di Trieste, 34136 Trieste, Italy","institution_ids":["https://openalex.org/I142444530","https://openalex.org/I4210151851"]},{"raw_affiliation_string":"International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016712389","display_name":"Jacopo De Nardis","orcid":"https://orcid.org/0000-0001-7877-0329"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jacopo De Nardis","raw_affiliation_strings":["Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation, CNRS UMR 8089, CY Cergy Paris Universit\u00e9, 95302 Cergy-Pontoise Cedex, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation, CNRS UMR 8089, CY Cergy Paris Universit\u00e9, 95302 Cergy-Pontoise Cedex, France","institution_ids":["https://openalex.org/I4210142324","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130356626","display_name":"Vincenzo Alba","orcid":null},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]},{"id":"https://openalex.org/I4210160382","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Pisa","ror":"https://ror.org/05symbg58","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210160382"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Vincenzo Alba","raw_affiliation_strings":["Dipartimento di Fisica dell\u2019Universit\u00e0 di Pisa, 56127 Pisa, Italy","INFN Sezione di Pisa, 56127 Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica dell\u2019Universit\u00e0 di Pisa, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"INFN Sezione di Pisa, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I4210160382"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130364473","display_name":"Guglielmo Lami","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210142324","display_name":"CY Cergy Paris Universit\u00e9","ror":"https://ror.org/043htjv09","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142324"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guglielmo Lami","raw_affiliation_strings":["Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation, CNRS UMR 8089, CY Cergy Paris Universit\u00e9, 95302 Cergy-Pontoise Cedex, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique et Mod\u00e9lisation, CNRS UMR 8089, CY Cergy Paris Universit\u00e9, 95302 Cergy-Pontoise Cedex, France","institution_ids":["https://openalex.org/I4210142324","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5029954873"],"corresponding_institution_ids":["https://openalex.org/I138549579","https://openalex.org/I142444530","https://openalex.org/I4210151851"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.94482871,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":null,"first_page":"2036","last_page":"2036"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9872999787330627,"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":0.9872999787330627,"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":0.00279999990016222,"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":0.0026000000070780516,"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/gaussian","display_name":"Gaussian","score":0.7117999792098999},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.6514000296592712},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6014999747276306},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.46399998664855957},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.45320001244544983},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42100000381469727},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.3711000084877014},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.3569999933242798}],"concepts":[{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7117999792098999},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6514000296592712},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6014999747276306},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5867000222206116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5253999829292297},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.46399998664855957},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42100000381469727},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.3711000084877014},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.3569999933242798},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.33809998631477356},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.32120001316070557},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.30239999294281006},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.30079999566078186},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2985000014305115},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.28940001130104065},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28780001401901245},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.2791000008583069},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2773999869823456},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.26579999923706055},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.22331/q-2026-03-23-2036","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-03-23-2036","pdf_url":"https://quantum-journal.org/papers/q-2026-03-23-2036/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"}],"best_oa_location":{"id":"doi:10.22331/q-2026-03-23-2036","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-03-23-2036","pdf_url":"https://quantum-journal.org/papers/q-2026-03-23-2036/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":[{"score":0.5917057394981384,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7140132509.pdf","grobid_xml":"https://content.openalex.org/works/W7140132509.grobid-xml"},"referenced_works_count":105,"referenced_works":["https://openalex.org/W1658890454","https://openalex.org/W1860626550","https://openalex.org/W1958800402","https://openalex.org/W1966619759","https://openalex.org/W1969246646","https://openalex.org/W1970087737","https://openalex.org/W1970684941","https://openalex.org/W1970948459","https://openalex.org/W1988148014","https://openalex.org/W2006672084","https://openalex.org/W2007833526","https://openalex.org/W2020332193","https://openalex.org/W2024261335","https://openalex.org/W2043647075","https://openalex.org/W2054795560","https://openalex.org/W2069149225","https://openalex.org/W2069285834","https://openalex.org/W2079294297","https://openalex.org/W2108724037","https://openalex.org/W2130550844","https://openalex.org/W2138779671","https://openalex.org/W2141708961","https://openalex.org/W2145062370","https://openalex.org/W2147265170","https://openalex.org/W2169656062","https://openalex.org/W2182649182","https://openalex.org/W2264002775","https://openalex.org/W2281603866","https://openalex.org/W2306451729","https://openalex.org/W2334023673","https://openalex.org/W2471006772","https://openalex.org/W2486166576","https://openalex.org/W2512685237","https://openalex.org/W2524307097","https://openalex.org/W2599425326","https://openalex.org/W2604989170","https://openalex.org/W2620407091","https://openalex.org/W2766333524","https://openalex.org/W2783011248","https://openalex.org/W2788041265","https://openalex.org/W2794633558","https://openalex.org/W2808319042","https://openalex.org/W2889126882","https://openalex.org/W2906150513","https://openalex.org/W2944913150","https://openalex.org/W2972666339","https://openalex.org/W3007567394","https://openalex.org/W3031543227","https://openalex.org/W3036260179","https://openalex.org/W3037850448","https://openalex.org/W3117932051","https://openalex.org/W3118380360","https://openalex.org/W3127523586","https://openalex.org/W3134444578","https://openalex.org/W3200768889","https://openalex.org/W3211718983","https://openalex.org/W3212046771","https://openalex.org/W4212821541","https://openalex.org/W4280579466","https://openalex.org/W4281932964","https://openalex.org/W4291992583","https://openalex.org/W4293114468","https://openalex.org/W4301787874","https://openalex.org/W4306752492","https://openalex.org/W4381573114","https://openalex.org/W4386224680","https://openalex.org/W4387307624","https://openalex.org/W4387399711","https://openalex.org/W4387461427","https://openalex.org/W4387956203","https://openalex.org/W4387963876","https://openalex.org/W4388047769","https://openalex.org/W4391420775","https://openalex.org/W4391871417","https://openalex.org/W4392885456","https://openalex.org/W4394906605","https://openalex.org/W4396821160","https://openalex.org/W4396953681","https://openalex.org/W4396977138","https://openalex.org/W4398167124","https://openalex.org/W4399510749","https://openalex.org/W4400185528","https://openalex.org/W4400732871","https://openalex.org/W4401541833","https://openalex.org/W4403539713","https://openalex.org/W4403887493","https://openalex.org/W4404360745","https://openalex.org/W4404993159","https://openalex.org/W4405035545","https://openalex.org/W4406903215","https://openalex.org/W4407173133","https://openalex.org/W4407173519","https://openalex.org/W4407309828","https://openalex.org/W4407321635","https://openalex.org/W4408165506","https://openalex.org/W4408326378","https://openalex.org/W4408475821","https://openalex.org/W4408655708","https://openalex.org/W4410021524","https://openalex.org/W4410601115","https://openalex.org/W4411023104","https://openalex.org/W4411959757","https://openalex.org/W4415294930","https://openalex.org/W4415964300","https://openalex.org/W4416735330"],"related_works":[],"abstract_inverted_index":{"We":[0,73,102],"introduce":[1],"an":[2,28,58,99],"efficient":[3],"method":[4],"to":[5,63,136],"quantify":[6],"nonstabilizerness":[7],"in":[8,89,110,122,147,159,168],"fermionic":[9],"Gaussian":[10,49,116],"states,":[11,68],"overcoming":[12],"the":[13,35,86,90,105,129,133,150,154],"long-standing":[14],"challenge":[15],"posed":[16],"by":[17],"their":[18],"extensive":[19,59],"entanglement.":[20],"Using":[21],"a":[22,81,111,123,137,144],"perfect":[23],"sampling":[24,134],"scheme":[25],"based":[26],"on":[27,47],"underlying":[29],"determinantal":[30],"point":[31],"process,":[32],"we":[33,56,97,142],"compute":[34],"Stabilizer":[36],"Renyi":[37],"Entropies":[38],"(SREs)":[39],"for":[40,80,95],"systems":[41],"with":[42,51,69,77,115,128],"hundreds":[43],"of":[44,65,83,108,156,163],"qubits.":[45],"Benchmarking":[46],"random":[48,67,112],"states":[50],"and":[52],"without":[53],"particle":[54],"conservation,":[55],"reveal":[57],"leading":[60],"behavior":[61],"equal":[62],"that":[64,119,125],"Haar":[66],"logarithmic":[70],"subleading":[71],"corrections.":[72],"support":[74],"these":[75],"findings":[76],"analytical":[78],"calculations":[79],"set":[82],"related":[84],"quantities,":[85],"participation":[87],"entropies":[88],"computational":[91],"(or":[92],"Fock)":[93],"basis,":[94],"which":[96],"derive":[98],"exact":[100],"formula.":[101],"also":[103],"investigate":[104],"time":[106,124],"evolution":[107],"non-stabilizerness":[109,148],"unitary":[113],"circuit":[114],"gates,":[117],"observing":[118],"it":[120],"converges":[121],"scales":[126],"logarithmically":[127],"system":[130],"size.":[131],"Applying":[132],"algorithm":[135],"two-dimensional":[138],"free-fermionic":[139],"topological":[140],"model,":[141],"uncover":[143],"sharp":[145],"transition":[146],"at":[149],"phase":[151],"boundaries,":[152],"highlighting":[153],"power":[155],"our":[157],"approach":[158],"exploring":[160],"different":[161],"phases":[162],"quantum":[164],"many-body":[165],"systems,":[166],"even":[167],"higher":[169],"dimensions.":[170]},"counts_by_year":[],"updated_date":"2026-03-24T06:04:31.470712","created_date":"2026-03-24T00:00:00"}