{"id":"https://openalex.org/W7128780628","doi":"https://doi.org/10.1007/s11227-026-08255-5","title":"Low-qubit quantum circuits for efficient integer squaring","display_name":"Low-qubit quantum circuits for efficient integer squaring","publication_year":2026,"publication_date":"2026-02-13","ids":{"openalex":"https://openalex.org/W7128780628","doi":"https://doi.org/10.1007/s11227-026-08255-5"},"language":"en","primary_location":{"id":"doi:10.1007/s11227-026-08255-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11227-026-08255-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11227-026-08255-5.pdf","source":{"id":"https://openalex.org/S32326811","display_name":"The Journal of Supercomputing","issn_l":"0920-8542","issn":["0920-8542","1573-0484"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Supercomputing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11227-026-08255-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093037103","display_name":"Laura Mar\u00eda Donaire","orcid":"https://orcid.org/0009-0004-6610-2795"},"institutions":[{"id":"https://openalex.org/I52354020","display_name":"University of Almer\u00eda","ror":"https://ror.org/003d3xx08","country_code":"ES","type":"education","lineage":["https://openalex.org/I52354020"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Laura M. Donaire","raw_affiliation_strings":["Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain","institution_ids":["https://openalex.org/I52354020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028589501","display_name":"Gloria Ortega","orcid":"https://orcid.org/0000-0002-6563-2717"},"institutions":[{"id":"https://openalex.org/I52354020","display_name":"University of Almer\u00eda","ror":"https://ror.org/003d3xx08","country_code":"ES","type":"education","lineage":["https://openalex.org/I52354020"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gloria Ortega","raw_affiliation_strings":["Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain","institution_ids":["https://openalex.org/I52354020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007447524","display_name":"Ester M. Garz\u00f3n","orcid":"https://orcid.org/0000-0002-0568-5470"},"institutions":[{"id":"https://openalex.org/I52354020","display_name":"University of Almer\u00eda","ror":"https://ror.org/003d3xx08","country_code":"ES","type":"education","lineage":["https://openalex.org/I52354020"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ester M. Garz\u00f3n","raw_affiliation_strings":["Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain","institution_ids":["https://openalex.org/I52354020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077440677","display_name":"Ernestas Filatovas","orcid":"https://orcid.org/0000-0002-9329-6431"},"institutions":[{"id":"https://openalex.org/I173212132","display_name":"Vilnius University","ror":"https://ror.org/03nadee84","country_code":"LT","type":"education","lineage":["https://openalex.org/I173212132"]}],"countries":["LT"],"is_corresponding":false,"raw_author_name":"Ernestas Filatovas","raw_affiliation_strings":["Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Data Science and Digital Technologies, Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania","institution_ids":["https://openalex.org/I173212132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5122932101","display_name":"Francisco Orts","orcid":null},"institutions":[{"id":"https://openalex.org/I52354020","display_name":"University of Almer\u00eda","ror":"https://ror.org/003d3xx08","country_code":"ES","type":"education","lineage":["https://openalex.org/I52354020"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Francisco Orts","raw_affiliation_strings":["Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Supercomputing-Algorithms Group, University of Almer\u00eda, Almer\u00eda, Spain","institution_ids":["https://openalex.org/I52354020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5122932101"],"corresponding_institution_ids":["https://openalex.org/I52354020"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.169327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"82","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9771999716758728,"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":0.9771999716758728,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.007199999876320362,"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"}},{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.003100000089034438,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.722599983215332},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.673799991607666},{"id":"https://openalex.org/keywords/operand","display_name":"Operand","score":0.6273999810218811},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.6079000234603882},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5813999772071838},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5299000144004822},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5167999863624573},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.49959999322891235}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7361000180244446},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.722599983215332},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.673799991607666},{"id":"https://openalex.org/C55526617","wikidata":"https://www.wikidata.org/wiki/Q719375","display_name":"Operand","level":2,"score":0.6273999810218811},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.6079000234603882},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5813999772071838},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5299000144004822},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5167999863624573},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.49959999322891235},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4392000138759613},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.41370001435279846},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4016999900341034},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3476000130176544},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.3440000116825104},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.30649998784065247},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.28349998593330383},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C55615164","wikidata":"https://www.wikidata.org/wiki/Q830791","display_name":"Quantum superposition","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.2639000117778778},{"id":"https://openalex.org/C19271316","wikidata":"https://www.wikidata.org/wiki/Q7092353","display_name":"One-way quantum computer","level":5,"score":0.25769999623298645},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.25440001487731934},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11227-026-08255-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11227-026-08255-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11227-026-08255-5.pdf","source":{"id":"https://openalex.org/S32326811","display_name":"The Journal of Supercomputing","issn_l":"0920-8542","issn":["0920-8542","1573-0484"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Supercomputing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11227-026-08255-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11227-026-08255-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11227-026-08255-5.pdf","source":{"id":"https://openalex.org/S32326811","display_name":"The Journal of Supercomputing","issn_l":"0920-8542","issn":["0920-8542","1573-0484"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Supercomputing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1554683258","display_name":null,"funder_award_id":"PID2021-123278OB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G1934620208","display_name":null,"funder_award_id":"S-ITP-25-5","funder_id":"https://openalex.org/F4320322689","funder_display_name":"Lietuvos Mokslo Taryba"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G425668148","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5180808003","display_name":null,"funder_award_id":"PID2021-123278OB-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G586857820","display_name":null,"funder_award_id":"501100011033/FEDER","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6218905885","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320338080","funder_display_name":"European Social Fund"},{"id":"https://openalex.org/G7084143925","display_name":null,"funder_award_id":"AEI/10","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8743986366","display_name":null,"funder_award_id":"POST_2024_00998","funder_id":"https://openalex.org/F4320326754","funder_display_name":"Junta de Andaluc\u00eda"}],"funders":[{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320322689","display_name":"Lietuvos Mokslo Taryba","ror":"https://ror.org/02gs16m83"},{"id":"https://openalex.org/F4320326754","display_name":"Junta de Andaluc\u00eda","ror":"https://ror.org/01jem9c82"},{"id":"https://openalex.org/F4320331435","display_name":"Universidad de Almer\u00eda","ror":"https://ror.org/003d3xx08"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7128780628.pdf","grobid_xml":"https://content.openalex.org/works/W7128780628.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1631356911","https://openalex.org/W2002372750","https://openalex.org/W2035112473","https://openalex.org/W2055906143","https://openalex.org/W2105259569","https://openalex.org/W2168676717","https://openalex.org/W2749687807","https://openalex.org/W2759506558","https://openalex.org/W2781738013","https://openalex.org/W2901323007","https://openalex.org/W2954939433","https://openalex.org/W3082627581","https://openalex.org/W3137833880","https://openalex.org/W4285070256","https://openalex.org/W4293171638","https://openalex.org/W4367176338","https://openalex.org/W4387037040","https://openalex.org/W4387131633","https://openalex.org/W4392738958","https://openalex.org/W4392910579","https://openalex.org/W4394890832","https://openalex.org/W4400877210","https://openalex.org/W4402824346","https://openalex.org/W4406122603","https://openalex.org/W4406320945","https://openalex.org/W4406799037","https://openalex.org/W4411516545"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Quantum":[1],"squaring":[2,45],"circuits":[3],"play":[4],"a":[5,17,39,48,104,126],"critical":[6],"role":[7],"in":[8,69,132],"many":[9],"quantum":[10,41,123,134],"algorithms;":[11],"however,":[12],"most":[13],"existing":[14],"designs":[15,65],"incur":[16],"significant":[18],"qubit":[19,50],"overhead":[20],"due":[21],"to":[22],"the":[23,76,82,97,114],"loss":[24],"of":[25,31,52,71,84,90,99,107,118],"input":[26,77],"states":[27],"and":[28,87,116],"excessive":[29],"use":[30],"ancillary":[32],"qubits.":[33,72,92],"In":[34],"this":[35],"work,":[36],"we":[37],"introduce":[38],"qubit-efficient":[40],"circuit":[42],"for":[43,57,121,129],"integer":[44],"that":[46,66],"achieves":[47],"linear":[49],"cost":[51],"only":[53],"3":[54],"N":[55,59],"qubits":[56],"an":[58],"-bit":[60],"input,":[61],"significantly":[62],"outperforming":[63],"state-of-the-art":[64],"scale":[67],"quadratically":[68],"terms":[70],"Our":[73],"approach":[74],"reintegrates":[75],"operand":[78],"after":[79],"computation,":[80],"enabling":[81],"uncomputation":[83],"intermediate":[85],"results":[86],"efficient":[88],"recycling":[89],"ancilla":[91],"This":[93],"reversible":[94],"strategy":[95],"prevents":[96],"retention":[98],"redundant":[100],"information,":[101],"which":[102],"is":[103],"common":[105],"limitation":[106],"prior":[108],"works.":[109],"The":[110],"comparative":[111],"analysis":[112],"confirms":[113],"scalability":[115],"practicality":[117],"our":[119],"design":[120],"qubit-constrained":[122],"hardware,":[124],"offering":[125],"promising":[127],"solution":[128],"arithmetic":[130],"operations":[131],"resource-limited":[133],"environments.":[135]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2026-02-14T00:00:00"}