{"id":"https://openalex.org/W2066284946","doi":"https://doi.org/10.1145/1060590.1060661","title":"Polynomial time quantum algorithm for the computation of the unit group of a number field","display_name":"Polynomial time quantum algorithm for the computation of the unit group of a number field","publication_year":2005,"publication_date":"2005-05-22","ids":{"openalex":"https://openalex.org/W2066284946","doi":"https://doi.org/10.1145/1060590.1060661","mag":"2066284946"},"language":"en","primary_location":{"id":"doi:10.1145/1060590.1060661","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060590.1060661","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-seventh annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086433209","display_name":"Arthur R. Schmidt","orcid":"https://orcid.org/0000-0002-7579-0030"},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Arthur Schmidt","raw_affiliation_strings":["Technische Universit\u00e4t Darmstadt, Fachbereich Informatik, Hochschulstr., Darmstadt"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Darmstadt, Fachbereich Informatik, Hochschulstr., Darmstadt","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039634370","display_name":"Ulrich Vollmer","orcid":null},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technical University of Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrich Vollmer","raw_affiliation_strings":["Technische Universit\u00e4t Darmstadt, Fachbereich Informatik, Hochschulstr., Darmstadt"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Darmstadt, Fachbereich Informatik, Hochschulstr., Darmstadt","institution_ids":["https://openalex.org/I31512782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086433209"],"corresponding_institution_ids":["https://openalex.org/I31512782"],"apc_list":null,"apc_paid":null,"fwci":5.0279,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.95070783,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"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":0.9991999864578247,"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":0.9991999864578247,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9976999759674072,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/computation","display_name":"Computation","score":0.5911152958869934},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5637549161911011},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5496677756309509},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5302229523658752},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5278962254524231},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.509339451789856},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4967227578163147},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48818832635879517},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4879552721977234},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42807579040527344},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4215855598449707},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36888137459754944},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3481253385543823},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.28315651416778564},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15285497903823853},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11151105165481567},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09891536831855774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06837743520736694}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5911152958869934},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5637549161911011},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5496677756309509},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5302229523658752},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5278962254524231},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.509339451789856},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4967227578163147},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48818832635879517},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4879552721977234},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42807579040527344},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4215855598449707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36888137459754944},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3481253385543823},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.28315651416778564},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15285497903823853},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11151105165481567},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09891536831855774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06837743520736694},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1060590.1060661","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1060590.1060661","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-seventh annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.420.6344","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.420.6344","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cdc.informatik.tu-darmstadt.de/reports/reports/Schmidt_Vollmer_STOC05.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.59.552","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.informatik.tu-darmstadt.de/ftp/pub/TI/TR/TI-04-01.qalg_unit_group.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W197145066","https://openalex.org/W1487721777","https://openalex.org/W1587133324","https://openalex.org/W1966914095","https://openalex.org/W1986347052","https://openalex.org/W2001093624","https://openalex.org/W2009132957","https://openalex.org/W2011167826","https://openalex.org/W2066153786","https://openalex.org/W2137005141","https://openalex.org/W2143677375","https://openalex.org/W2151592708","https://openalex.org/W2156190205","https://openalex.org/W3023478445","https://openalex.org/W3099197349","https://openalex.org/W3111297213","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2155794351","https://openalex.org/W4353086852","https://openalex.org/W2067607153","https://openalex.org/W1995074057","https://openalex.org/W1028212721","https://openalex.org/W4376876762","https://openalex.org/W1981560782","https://openalex.org/W3183333684","https://openalex.org/W2951721482","https://openalex.org/W1969815193"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,14,22],"quantum":[3],"algorithm":[4,26],"for":[5,41,64],"the":[6,9,31,50,53,65],"computation":[7],"of":[8,13,34,37,52],"irrational":[10],"period":[11],"lattice":[12],"function":[15],"on":[16],"Z":[17],"which":[18],"is":[19,27,47],"periodic":[20],"in":[21,49],"relaxed":[23],"sense.":[24],"This":[25],"applied":[28],"to":[29,69],"compute":[30],"unit":[32],"group":[33],"finite":[35],"extensions":[36],"Q.":[38],"Execution":[39],"time":[40],"fixed":[42],"field":[43],"degree":[44],"over":[45],"Q":[46],"polynomial":[48],"discriminant":[51],"field.":[54],"Our":[55],"algorithms":[56],"generalize":[57],"and":[58],"improve":[59],"upon":[60],"Hallgren&amp;apos;s":[61],"work":[62],"[Hal02]":[63],"one-dimensional":[66],"case":[67],"corresponding":[68],"real-quadratic":[70],"fields.":[71]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
