{"id":"https://openalex.org/W7130372478","doi":"https://doi.org/10.48550/arxiv.2602.15180","title":"Efficient quantum circuits for high-dimensional representations of SU(n) and Ramanujan quantum expanders","display_name":"Efficient quantum circuits for high-dimensional representations of SU(n) and Ramanujan quantum expanders","publication_year":2026,"publication_date":"2026-02-16","ids":{"openalex":"https://openalex.org/W7130372478","doi":"https://doi.org/10.48550/arxiv.2602.15180"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2602.15180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15180","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2602.15180","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063591874","display_name":"Vishnu Iyer","orcid":"https://orcid.org/0000-0001-8072-1390"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Iyer, Vishnu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101683208","display_name":"Siddhartha Jain","orcid":"https://orcid.org/0000-0003-2142-5801"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jain, Siddhartha","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126357849","display_name":"Stephen Jordan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jordan, Stephen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126359877","display_name":"Rolando Somma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Somma, Rolando","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063591874"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":0.906499981880188,"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":0.906499981880188,"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":0.038600001484155655,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.005900000222027302,"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/quantum-algorithm","display_name":"Quantum algorithm","score":0.5672000050544739},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.5584999918937683},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.5558000206947327},{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"Quantum Fourier transform","score":0.5210000276565552},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.49559998512268066},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.46799999475479126},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.4413999915122986},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43869999051094055},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.4350999891757965},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4072999954223633}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6179999709129333},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5672000050544739},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.5584999918937683},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.5558000206947327},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.5210000276565552},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.49559998512268066},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.46799999475479126},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.4413999915122986},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43869999051094055},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.4350999891757965},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4072999954223633},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3785000145435333},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3634999990463257},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.3603000044822693},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.35830000042915344},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.35749998688697815},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.3562000095844269},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.35530000925064087},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34950000047683716},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.3483000099658966},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3382999897003174},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32839998602867126},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.326200008392334},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.30720001459121704},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C191608238","wikidata":"https://www.wikidata.org/wiki/Q5249552","display_name":"Decoherence-free subspaces","level":5,"score":0.2946999967098236},{"id":"https://openalex.org/C179957908","wikidata":"https://www.wikidata.org/wiki/Q907206","display_name":"POVM","level":5,"score":0.2921000123023987},{"id":"https://openalex.org/C186123792","wikidata":"https://www.wikidata.org/wiki/Q7390277","display_name":"SIC-POVM","level":5,"score":0.2849000096321106},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C122332657","wikidata":"https://www.wikidata.org/wiki/Q677864","display_name":"Quantum harmonic oscillator","level":3,"score":0.2773999869823456},{"id":"https://openalex.org/C190463098","wikidata":"https://www.wikidata.org/wiki/Q2081419","display_name":"Quantum technology","level":4,"score":0.2761000096797943},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.2703999876976013},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.25769999623298645},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2602.15180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15180","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2602.15180","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15180","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"efficient":[2,68],"quantum":[3,29,61,69,86,98,107,124],"circuits":[4,33,99],"that":[5],"implement":[6,93],"high-dimensional":[7],"unitary":[8],"irreducible":[9],"representations":[10],"(irreps)":[11],"of":[12,28,53,59,84,122],"$SU(n)$,":[13],"where":[14],"$n":[15],"\\ge":[16],"2$":[17],"is":[18,34],"constant.":[19],"For":[20],"dimension":[21],"$N$":[22],"and":[23,38],"error":[24],"$\u03b5$,":[25],"the":[26,44,56,77,82,85,120],"number":[27],"gates":[30],"in":[31,36,55],"our":[32],"polynomial":[35],"$\\log(N)$":[37],"$\\log(1/\u03b5)$.":[39],"Our":[40,97],"construction":[41],"relies":[42],"on":[43],"Jordan-Schwinger":[45],"representation,":[46],"which":[47,72],"allows":[48,73,90],"us":[49,74,91],"to":[50,75,81,92,103,118],"realize":[51],"irreps":[52,95],"$SU(n)$":[54],"Hilbert":[57],"space":[58],"$n$":[60],"harmonic":[62,87],"oscillators.":[63],"Together":[64],"with":[65],"a":[66,109],"recent":[67],"Hermite":[70],"transform,":[71],"map":[76],"computational":[78],"basis":[79],"states":[80],"eigenstates":[83],"oscillator,":[88],"this":[89],"these":[94],"efficiently.":[96],"can":[100,114],"be":[101,116],"used":[102,117],"construct":[104],"explicit":[105],"Ramanujan":[106],"expanders,":[108],"longstanding":[110],"open":[111],"problem.":[112],"They":[113],"also":[115],"fast-forward":[119],"evolution":[121],"certain":[123],"systems.":[125]},"counts_by_year":[],"updated_date":"2026-02-19T06:31:58.851227","created_date":"2026-02-19T00:00:00"}