{"id":"https://openalex.org/W2804037619","doi":null,"title":"Invariant Theory for Matrix Product States","display_name":"Invariant Theory for Matrix Product States","publication_year":2012,"publication_date":"2012-09-04","ids":{"openalex":"https://openalex.org/W2804037619","mag":"2804037619"},"language":"en","primary_location":{"id":"mag:2804037619","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1209.0631v1","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1209.0631v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079523895","display_name":"Jacob Biamonte","orcid":"https://orcid.org/0000-0002-0590-3327","observed_orcids":["https://orcid.org/0000-0002-0590-3327"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jacob Biamonte","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-0590-3327","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045706381","display_name":"Ville Bergholm","orcid":"https://orcid.org/0000-0003-1078-9693","observed_orcids":["https://orcid.org/0000-0003-1078-9693"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ville Bergholm","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1078-9693","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5088584992","display_name":"Marco O. Lanzagorta","orcid":"https://orcid.org/0000-0002-7064-6136","observed_orcids":["https://orcid.org/0000-0002-7064-6136"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marco Lanzagorta","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7064-6136","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"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/T11804","display_name":"Quantum many-body systems","score":0.9926999807357788,"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"}},"topics":[{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.9926999807357788,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.003000000026077032,"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":0.0010999999940395355,"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/invariant-theory","display_name":"invariant theory","score":0.9929999709129333},{"id":"https://openalex.org/keywords/matrix-product-states","display_name":"matrix product states","score":0.9670000076293945},{"id":"https://openalex.org/keywords/local-unitary-invariants","display_name":"local unitary invariants","score":0.9760000109672546},{"id":"https://openalex.org/keywords/tensor-networks","display_name":"tensor networks","score":0.7519999742507935},{"id":"https://openalex.org/keywords/polynomial-invariants","display_name":"polynomial invariants","score":0.6430000066757202},{"id":"https://openalex.org/keywords/renyi-entropy","display_name":"R\u00e9nyi entropy","score":0.7289999723434448},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"tensor contraction","score":0.7799999713897705},{"id":"https://openalex.org/keywords/quantum-states","display_name":"quantum states","score":0.675000011920929}],"concepts":[{"id":"https://openalex.org/C158158286","wikidata":"https://www.wikidata.org/wiki/Q9009080","display_name":"Invariants of tensors","level":3,"score":0.7955605387687683},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6923450827598572},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6855653524398804},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6234695315361023},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6230131983757019},{"id":"https://openalex.org/C2778351468","wikidata":"https://www.wikidata.org/wiki/Q17149634","display_name":"Matrix product state","level":4,"score":0.554800271987915},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.49226418137550354},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4831463694572449},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.47800198197364807},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.46718743443489075},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.4667057991027832},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4552239179611206},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4450850188732147},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41970252990722656},{"id":"https://openalex.org/C134530390","wikidata":"https://www.wikidata.org/wiki/Q2920801","display_name":"Invariant polynomial","level":4,"score":0.415372371673584},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.34615421295166016},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2718425393104553},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12388509511947632},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09877452254295349},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09560936689376831},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08493161201477051},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08076387643814087},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0746920108795166},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2804037619","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1209.0631v1","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2804037619","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1209.0631v1","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2051255561","https://openalex.org/W4313303612","https://openalex.org/W2090161225","https://openalex.org/W7165795746","https://openalex.org/W2937943636","https://openalex.org/W1983701428","https://openalex.org/W3109918640","https://openalex.org/W4404312157","https://openalex.org/W3147477662","https://openalex.org/W1966543567"],"abstract_inverted_index":{"Invariant":[0],"theory":[1,74],"is":[2],"concerned":[3],"with":[4,56],"functions":[5],"that":[6,45,113,124,171],"do":[7],"not":[8],"change":[9],"under":[10],"the":[11,42,77,119,125,136,176],"action":[12],"of":[13,32,54,93,101,109,154,178],"a":[14,51,99,106],"given":[15],"group.":[16],"Here":[17],"we":[18,90],"communicate":[19],"an":[20,39,143],"approach":[21,37,63,127],"based":[22],"on":[23],"tensor":[24,72,102,160],"networks":[25],"to":[26,41,59,67,117,128,150],"represent":[27],"polynomial":[28,43,84,152],"local":[29,110],"unitary":[30,111],"invariants":[31,92,112,130,137,153],"quantum":[33,155],"states.":[34,96,156],"This":[35,62],"graphical":[36,126],"provides":[38],"alternative":[40],"equations":[44],"describe":[46],"invariants,":[47],"which":[48],"often":[49],"contain":[50,168],"large":[52],"number":[53],"terms":[55],"coefficients":[57],"raised":[58],"high":[60],"powers.":[61],"also":[64],"enables":[65],"one":[66],"use":[68],"known":[69],"methods":[70],"from":[71],"network":[73,161],"(such":[75],"as":[76,140,142,164],"matrix":[78,94,165],"product":[79,95,166],"state":[80],"factorization)":[81],"when":[82],"studying":[83],"invariants.":[85,179],"As":[86],"our":[87],"main":[88],"example,":[89],"consider":[91],"We":[97,122],"generate":[98],"family":[100],"contractions":[103],"resulting":[104],"in":[105,175],"complete":[107],"set":[108],"can":[114,131,172],"be":[115,173],"used":[116],"express":[118],"Renyi":[120],"entropies.":[121],"find":[123],"representing":[129],"provide":[132],"structural":[133],"insight":[134],"into":[135],"being":[138],"contracted,":[139],"well":[141],"alternative,":[144],"and":[145],"sometimes":[146],"much":[147],"simpler,":[148],"means":[149],"study":[151,177],"In":[157],"addition,":[158],"many":[159],"methods,":[162],"such":[163],"states,":[167],"excellent":[169],"tools":[170],"applied":[174]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2018-06-01T00:00:00"}