{"id":"https://openalex.org/W4416257553","doi":"https://doi.org/10.48550/arxiv.2509.18204","title":"Generalized Gottesman-Kitaev-Preskill States on a Quantum Torus","display_name":"Generalized Gottesman-Kitaev-Preskill States on a Quantum Torus","publication_year":2025,"publication_date":"2025-09-20","ids":{"openalex":"https://openalex.org/W4416257553","doi":"https://doi.org/10.48550/arxiv.2509.18204"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.18204","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.18204","pdf_url":"https://arxiv.org/pdf/2509.18204","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.18204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019154516","display_name":"Sijo K. Joseph","orcid":"https://orcid.org/0000-0002-2263-6996","observed_orcids":["https://orcid.org/0000-0002-2263-6996"]},"institutions":[{"id":"https://openalex.org/I885392262","display_name":"GITAM University","ror":"https://ror.org/0440p1d37","country_code":"IN","type":"education","lineage":["https://openalex.org/I885392262"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Joseph, Sijo K.","raw_affiliation_strings":["Department of Physics , GITAM Deemed to be University , Bengaluru , Karnataka 562163 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , GITAM Deemed to be University , Bengaluru , Karnataka 562163 , India","institution_ids":["https://openalex.org/I885392262"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026235630","display_name":"Sudhir Kumar Singh","orcid":"https://orcid.org/0000-0001-8465-0649","observed_orcids":["https://orcid.org/0000-0001-8465-0649","https://orcid.org/0000-0001-7099-7297"]},"institutions":[{"id":"https://openalex.org/I885392262","display_name":"GITAM University","ror":"https://ror.org/0440p1d37","country_code":"IN","type":"education","lineage":["https://openalex.org/I885392262"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Singh, Sudhir","raw_affiliation_strings":["Department of Mathematics , GITAM Deemed to be University , Bengaluru , Karnataka 562163 , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , GITAM Deemed to be University , Bengaluru , Karnataka 562163 , India","institution_ids":["https://openalex.org/I885392262"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I885392262"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9345999956130981,"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":0.9345999956130981,"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":0.050599999725818634,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.004100000020116568,"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-torus","display_name":"quantum torus","score":0.8299999833106995},{"id":"https://openalex.org/keywords/squeezed-coherent-states","display_name":"squeezed coherent states","score":0.9940000176429749},{"id":"https://openalex.org/keywords/riemann-theta-function","display_name":"Riemann theta function","score":0.9449999928474426},{"id":"https://openalex.org/keywords/compact-phase-space","display_name":"compact phase space","score":0.6480000019073486},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":0.8069999814033508},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"noncommutative geometry","score":0.9679999947547913},{"id":"https://openalex.org/keywords/generalized-theta-functions","display_name":"generalized theta functions","score":0.8130000233650208}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.6085000038146973},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5740000009536743},{"id":"https://openalex.org/C152026323","wikidata":"https://www.wikidata.org/wiki/Q1032070","display_name":"Coherent states","level":3,"score":0.5254999995231628},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5062000155448914},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.49309998750686646},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.48559999465942383},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.4681999981403351},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4571000039577484},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.4350999891757965},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4291999936103821},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4291999936103821},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4099000096321106},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.38100001215934753},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.35679998993873596},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.31459999084472656},{"id":"https://openalex.org/C84883863","wikidata":"https://www.wikidata.org/wiki/Q7825777","display_name":"Toric code","level":4,"score":0.31150001287460327},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.3027999997138977},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2953999936580658},{"id":"https://openalex.org/C186123792","wikidata":"https://www.wikidata.org/wiki/Q7390277","display_name":"SIC-POVM","level":5,"score":0.2928999960422516},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.28700000047683716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2694000005722046},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.26499998569488525},{"id":"https://openalex.org/C190463098","wikidata":"https://www.wikidata.org/wiki/Q2081419","display_name":"Quantum technology","level":4,"score":0.2623000144958496}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2509.18204","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.18204","pdf_url":"https://arxiv.org/pdf/2509.18204","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2509.18204","doi":"https://doi.org/10.48550/arxiv.2509.18204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.18204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2509.18204","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.18204","pdf_url":"https://arxiv.org/pdf/2509.18204","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416257553.pdf","grobid_xml":"https://content.openalex.org/works/W4416257553.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2582444396","https://openalex.org/W4414402690","https://openalex.org/W7110820700"],"related_works":["https://openalex.org/W6926878946","https://openalex.org/W3085342944","https://openalex.org/W3011304246","https://openalex.org/W3113386034","https://openalex.org/W7155096566","https://openalex.org/W4386557666","https://openalex.org/W7171591926","https://openalex.org/W2943293861","https://openalex.org/W4382395217","https://openalex.org/W2979361000"],"abstract_inverted_index":{"We":[0,25],"introduce":[1],"a":[2,6,56,105,112,130],"novel":[3],"formulation":[4],"of":[5,14,32,92,124],"Generalized":[7,57],"Gottesman-Kitaev-Preskill":[8],"(GKP)":[9],"state":[10,60],"that":[11,27,61,85],"resolves":[12],"all":[13],"its":[15],"foundational":[16],"pathologies,":[17],"such":[18],"as":[19],"infinite":[20],"energy,":[21],"non-normalizability,":[22],"and":[23,65,121],"orthogonality.":[24],"demonstrate":[26],"these":[28,93],"issues":[29],"are":[30,88],"artifacts":[31],"defining":[33],"the":[34,42,89,96,122],"code":[35],"on":[36,95],"an":[37,73],"unbounded":[38],"phase-space.":[39,99],"By":[40],"considering":[41],"compact":[43],"quantum-phase-space":[44],"intrinsic":[45],"to":[46,79],"systems":[47],"like":[48],"coupled":[49],"quantum":[50,97,107,116,136],"harmonic":[51],"oscillators,":[52],"we":[53],"have":[54],"obtained":[55,74],"GKP":[58],"(GGKP)":[59],"is":[62,69],"both":[63],"exact":[64],"physically":[66],"realizable.":[67],"This":[68,100,128],"achieved":[70],"by":[71],"applying":[72],"Quantum":[75],"Zak":[76],"Transform":[77],"(QZT)":[78],"Squeezed":[80],"Coherent":[81],"States,":[82],"which":[83],"reveals":[84,111],"Riemann-Theta":[86],"functions":[87],"natural":[90],"representation":[91],"states":[94],"torus":[98],"framework":[101],"not":[102],"only":[103],"provides":[104],"well-behaved":[106],"state,":[108],"but":[109],"also":[110],"deep":[113],"connection":[114],"between":[115],"error":[117],"correction,":[118],"non-commutative":[119],"geometry,":[120],"theory":[123],"generalized":[125],"Theta":[126],"functions.":[127],"opens":[129],"new":[131],"avenue":[132],"for":[133],"fault-tolerant":[134],"photonic":[135],"computing.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-10T00:00:00"}
