{"id":"https://openalex.org/W3108855249","doi":"https://doi.org/10.22331/q-2022-05-09-708","title":"Finite-Function-Encoding Quantum States","display_name":"Finite-Function-Encoding Quantum States","publication_year":2022,"publication_date":"2022-05-09","ids":{"openalex":"https://openalex.org/W3108855249","doi":"https://doi.org/10.22331/q-2022-05-09-708","mag":"3108855249"},"language":"en","primary_location":{"id":"doi:10.22331/q-2022-05-09-708","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-05-09-708","pdf_url":"https://quantum-journal.org/papers/q-2022-05-09-708/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-2022-05-09-708/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071922970","display_name":"Paul L. Appel","orcid":"https://orcid.org/0000-0001-8319-1321"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]},{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Paul Appel","raw_affiliation_strings":["Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria","Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I138211613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003567164","display_name":"Alexander J. Heilman","orcid":null},"institutions":[{"id":"https://openalex.org/I154006206","display_name":"Lebanon Valley College","ror":"https://ror.org/05py5qd41","country_code":"US","type":"education","lineage":["https://openalex.org/I154006206"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alexander J. Heilman","raw_affiliation_strings":["Mathematics and Physics, Lebanon Valley College, 101 North College Avenue, Annville, Pennsylvania, 17003, United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Physics, Lebanon Valley College, 101 North College Avenue, Annville, Pennsylvania, 17003, United States of America","institution_ids":["https://openalex.org/I154006206"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065407306","display_name":"Ezekiel W. Wertz","orcid":null},"institutions":[{"id":"https://openalex.org/I154006206","display_name":"Lebanon Valley College","ror":"https://ror.org/05py5qd41","country_code":"US","type":"education","lineage":["https://openalex.org/I154006206"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ezekiel W. Wertz","raw_affiliation_strings":["Mathematics and Physics, Lebanon Valley College, 101 North College Avenue, Annville, Pennsylvania, 17003, United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Physics, Lebanon Valley College, 101 North College Avenue, Annville, Pennsylvania, 17003, United States of America","institution_ids":["https://openalex.org/I154006206"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090498800","display_name":"David W. Lyons","orcid":"https://orcid.org/0000-0002-5589-8343"},"institutions":[{"id":"https://openalex.org/I154006206","display_name":"Lebanon Valley College","ror":"https://ror.org/05py5qd41","country_code":"US","type":"education","lineage":["https://openalex.org/I154006206"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David W. Lyons","raw_affiliation_strings":["Mathematics and Physics, Lebanon Valley College, 101 North College Avenue, Annville, Pennsylvania, 17003, United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Physics, Lebanon Valley College, 101 North College Avenue, Annville, Pennsylvania, 17003, United States of America","institution_ids":["https://openalex.org/I154006206"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027058735","display_name":"Marcus Huber","orcid":"https://orcid.org/0000-0003-1985-4623"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]},{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Marcus Huber","raw_affiliation_strings":["Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria","Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I138211613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002547095","display_name":"Matej Pivoluska","orcid":"https://orcid.org/0000-0001-6876-2085"},"institutions":[{"id":"https://openalex.org/I147747303","display_name":"Institute of Chemistry of the Slovak Academy of Sciences","ror":"https://ror.org/02te3c603","country_code":"SK","type":"facility","lineage":["https://openalex.org/I147747303","https://openalex.org/I207624831"]},{"id":"https://openalex.org/I207624831","display_name":"Slovak Academy of Sciences","ror":"https://ror.org/03h7qq074","country_code":"SK","type":"government","lineage":["https://openalex.org/I207624831"]},{"id":"https://openalex.org/I21449261","display_name":"Masaryk University","ror":"https://ror.org/02j46qs45","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21449261"]},{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]},{"id":"https://openalex.org/I4210159745","display_name":"Institute of Physics of the Slovak Academy of Sciences","ror":"https://ror.org/05mgxqt50","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210159745"]}],"countries":["CZ","SK"],"is_corresponding":false,"raw_author_name":"Matej Pivoluska","raw_affiliation_strings":["Institute of Computer Science, Masaryk University, Botanick\u00e1 68a, 60200 Brno, Czech Republic","Institute of Physics, Slovak Academy of Sciences, D\u00fabravsk\u00e1 cesta 5807/9, 845 11 Karlova Ves, Slovakia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Masaryk University, Botanick\u00e1 68a, 60200 Brno, Czech Republic","institution_ids":["https://openalex.org/I21449261","https://openalex.org/I4210155092"]},{"raw_affiliation_string":"Institute of Physics, Slovak Academy of Sciences, D\u00fabravsk\u00e1 cesta 5807/9, 845 11 Karlova Ves, Slovakia","institution_ids":["https://openalex.org/I147747303","https://openalex.org/I4210159745","https://openalex.org/I207624831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042262914","display_name":"Giuseppe Vitagliano","orcid":"https://orcid.org/0000-0002-5563-3222"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]},{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Giuseppe Vitagliano","raw_affiliation_strings":["Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria","Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Atominstitut, Technische Universit\u00e4t Wien, Stadionallee 2, 1020 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Quantum Optics and Quantum Information \u2013 IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I138211613"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"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":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00294805,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":null,"first_page":"708","last_page":"708"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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":1.0,"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":0.9995999932289124,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5116848945617676},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.49276140332221985},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4533421993255615},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.4321558475494385},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41262608766555786},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4100697636604309},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4016481637954712}],"concepts":[{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5116848945617676},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.49276140332221985},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4533421993255615},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4321558475494385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41262608766555786},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4100697636604309},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4016481637954712},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2022-05-09-708","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-05-09-708","pdf_url":"https://quantum-journal.org/papers/q-2022-05-09-708/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:2012.00490","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.00490","pdf_url":"https://arxiv.org/pdf/2012.00490","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:09c2ea7fc9374fee9c57ecd0dbb1ea46","is_oa":false,"landing_page_url":"https://doaj.org/article/09c2ea7fc9374fee9c57ecd0dbb1ea46","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 708 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2022-05-09-708","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2022-05-09-708","pdf_url":"https://quantum-journal.org/papers/q-2022-05-09-708/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/G1789609306","display_name":null,"funder_award_id":"2/0136/19","funder_id":"https://openalex.org/F4320312330","funder_display_name":"Slovensk\u00e1 Akad\u00e9mia Vied"},{"id":"https://openalex.org/G2657502196","display_name":null,"funder_award_id":"Lise-Meitner project M 2462-N27","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2658636482","display_name":null,"funder_award_id":"Y879-N27","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5731140042","display_name":null,"funder_award_id":"MUNI/G/1596/2019","funder_id":"https://openalex.org/F4320323641","funder_display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV"},{"id":"https://openalex.org/G5950002704","display_name":null,"funder_award_id":"M 2462-N27","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6151329236","display_name":null,"funder_award_id":"START project Y879-N27","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6607310958","display_name":"CQIS: RUI: Quantum State Symmetry and Applications","funder_award_id":"2011074","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8398904990","display_name":null,"funder_award_id":"2/0136/19","funder_id":"https://openalex.org/F4320323641","funder_display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV"},{"id":"https://openalex.org/G8652008378","display_name":"CQIS: RUI: Entanglement and Applications via Local and Permutational Symmetry","funder_award_id":"1713868","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G948171648","display_name":"Macroscopic Quantum Coherence: detection and quantification","funder_award_id":"M 2462","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320312330","display_name":"Slovensk\u00e1 Akad\u00e9mia Vied","ror":"https://ror.org/03h7qq074"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320323641","display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","ror":"https://ror.org/044gwpv05"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3108855249.pdf","grobid_xml":"https://content.openalex.org/works/W3108855249.grobid-xml"},"referenced_works_count":74,"referenced_works":["https://openalex.org/W32507011","https://openalex.org/W1412175172","https://openalex.org/W1508926025","https://openalex.org/W1617270134","https://openalex.org/W1695111371","https://openalex.org/W1973237732","https://openalex.org/W1977370289","https://openalex.org/W1978938446","https://openalex.org/W1986320748","https://openalex.org/W1986556555","https://openalex.org/W2002842428","https://openalex.org/W2005144372","https://openalex.org/W2005868823","https://openalex.org/W2009600348","https://openalex.org/W2011277039","https://openalex.org/W2012845654","https://openalex.org/W2013891597","https://openalex.org/W2015302454","https://openalex.org/W2018296419","https://openalex.org/W2019203881","https://openalex.org/W2028763650","https://openalex.org/W2033070138","https://openalex.org/W2035993353","https://openalex.org/W2039842791","https://openalex.org/W2041910380","https://openalex.org/W2047969991","https://openalex.org/W2050334794","https://openalex.org/W2057575439","https://openalex.org/W2059010572","https://openalex.org/W2067100062","https://openalex.org/W2084652510","https://openalex.org/W2103368228","https://openalex.org/W2123862442","https://openalex.org/W2134220584","https://openalex.org/W2137134425","https://openalex.org/W2238893341","https://openalex.org/W2254931868","https://openalex.org/W2342048570","https://openalex.org/W2517466239","https://openalex.org/W2580150930","https://openalex.org/W2592149281","https://openalex.org/W2598775831","https://openalex.org/W2604433771","https://openalex.org/W2747039703","https://openalex.org/W2749085385","https://openalex.org/W2754786087","https://openalex.org/W2806163378","https://openalex.org/W2889958137","https://openalex.org/W2898803803","https://openalex.org/W2912856848","https://openalex.org/W2951491729","https://openalex.org/W2963697722","https://openalex.org/W2974809711","https://openalex.org/W2980685390","https://openalex.org/W2991100542","https://openalex.org/W3012274304","https://openalex.org/W3018627994","https://openalex.org/W3046716817","https://openalex.org/W3096582819","https://openalex.org/W3096699309","https://openalex.org/W3098801862","https://openalex.org/W3099091343","https://openalex.org/W3099310808","https://openalex.org/W3099527992","https://openalex.org/W3099879538","https://openalex.org/W3100315042","https://openalex.org/W3100704244","https://openalex.org/W3101073761","https://openalex.org/W3103642445","https://openalex.org/W3107989842","https://openalex.org/W3114058289","https://openalex.org/W3133844222","https://openalex.org/W4312106990","https://openalex.org/W4394643745"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2399505800","https://openalex.org/W2018253224","https://openalex.org/W333749553","https://openalex.org/W1966623661","https://openalex.org/W2942288111","https://openalex.org/W2039516134","https://openalex.org/W1509594480","https://openalex.org/W2788737482","https://openalex.org/W1594844022"],"abstract_inverted_index":{"We":[0,30,174],"introduce":[1,83],"finite-function-encoding":[2,87],"(FFE)":[3],"states":[4,118,124,143,163,201],"which":[5,57,91],"encode":[6],"arbitrary":[7],"<mml:math":[8,21],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>d</mml:mi></mml:math>-valued":[9],"logic":[10],"functions,":[11],"i.e.,":[12],"multivariate":[13],"functions":[14],"over":[15,229],"the":[16,71,74,79,100,112,139,151,159,167,195,211,214,224,230],"ring":[17],"of":[18,26,61,73,86,95,131,141,153,161,216,226],"integers":[19],"modulo":[20],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>d</mml:mi></mml:math>,":[22],"and":[23,38,119,164,178,184,187,202,223],"investigate":[24,138],"some":[25,34],"their":[27,220],"structural":[28],"properties.":[29],"also":[31,82,210],"point":[32],"out":[33,194],"differences":[35],"between":[36,197,213],"polynomial":[37],"non-polynomial":[39],"function":[40],"encoding":[41,70],"states:":[42],"The":[43],"former":[44],"can":[45],"be":[46],"associated":[47,115],"to":[48,67,93,116],"graphical":[49],"objects,":[50],"that":[51],"we":[52,81,110,137,156],"dub":[53],"tensor-edge":[54],"hypergraphs":[55,62],"(TEH),":[56],"are":[58],"a":[59,64,84,132],"generalization":[60],"with":[63],"tensor":[65],"attached":[66],"each":[68],"hyperedge":[69],"coefficients":[72],"different":[75],"monomials.":[76],"To":[77],"complete":[78],"framework,":[80],"notion":[85],"Pauli":[88],"(FP)":[89],"operators,":[90],"correspond":[92],"elements":[94],"what":[96],"is":[97],"known":[98],"as":[99],"generalized":[101],"symmetric":[102],"group":[103,114],"in":[104,126],"mathematics.":[105],"First,":[106],"using":[107],"this":[108,154],"machinery,":[109],"study":[111,188],"stabilizer":[113],"FFE":[117,142,200,217],"observe":[120],"how":[121],"qudit":[122],"hypergraph":[123],"introduced":[125],"Ref.":[127],"\\cite{2017PhRvA..95e2340S}":[128],"admit":[129],"stabilizers":[130],"particularly":[133],"simpler":[134],"form.":[135],"Afterwards,":[136],"classification":[140,168],"under":[144,169],"local":[145,170],"unitaries":[146],"(LU),":[147],"and,":[148],"after":[149],"showing":[150],"complexity":[152],"problem,":[155],"focus":[157],"on":[158,166],"case":[160],"bipartite":[162],"especially":[165,219],"FP":[171],"operations":[172],"(LFP).":[173],"find":[175],"all":[176],"LU":[177,221],"LFP":[179],"classes":[180],"for":[181],"two":[182,185],"qutrits":[183],"ququarts":[186],"several":[189],"other":[190],"special":[191],"classes,":[192],"pointing":[193],"relation":[196,212],"maximally":[198],"entangled":[199],"complex":[203],"Butson-type":[204],"Hadamard":[205],"matrices.":[206],"Our":[207],"investigation":[208],"showcases":[209],"properties":[215],"states,":[218],"classification,":[222],"theory":[225],"finite":[227],"rings":[228],"integers.":[231]},"counts_by_year":[],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}
