{"id":"https://openalex.org/W7212152177","doi":"https://doi.org/10.48550/arxiv.2609.09457","title":"A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography","display_name":"A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography","publication_year":2026,"publication_date":"2026-09-08","ids":{"openalex":"https://openalex.org/W7212152177","doi":"https://doi.org/10.48550/arxiv.2609.09457"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.09457","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09457","pdf_url":"https://arxiv.org/pdf/2609.09457","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/2609.09457","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015313721","display_name":"Shakir Showkat Sofi","orcid":"https://orcid.org/0000-0003-4491-099X","observed_orcids":["https://orcid.org/0000-0003-4491-099X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sofi, Shakir Showkat","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092273000","display_name":"Charlotte Vermeylen","orcid":"https://orcid.org/0000-0002-3615-6571","observed_orcids":["https://orcid.org/0000-0002-3615-6571"]},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Vermeylen, Charlotte","raw_affiliation_strings":["Leuven.AI -KU Leuven institute for AI , B-3000 , Leuven , Belgium. Department of Electrical Engineering (ESAT) ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Leuven.AI -KU Leuven institute for AI , B-3000 , Leuven , Belgium. Department of Electrical Engineering (ESAT) ,","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123602368","display_name":"Fatemeh Mohammadi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Mohammadi, Fatemeh","raw_affiliation_strings":["KU Leuven Kulak , Kortrijk , Belgium. Departments of Computer Science and Mathematics ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven Kulak , Kortrijk , Belgium. Departments of Computer Science and Mathematics ,","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009006026","display_name":"Lieven De Lathauwer","orcid":"https://orcid.org/0000-0001-5562-5014","observed_orcids":["https://orcid.org/0000-0001-5562-5014"]},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"De Lathauwer, Lieven","raw_affiliation_strings":["KU Leuven , Leuven , Belgium","Leuven.AI -KU Leuven institute for AI , B-3000 , Leuven , Belgium. Department of Electrical Engineering (ESAT) ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven , Leuven , Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Leuven.AI -KU Leuven institute for AI , B-3000 , Leuven , Belgium. Department of Electrical Engineering (ESAT) ,","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T11804","display_name":"Quantum many-body systems","score":0.47510001063346863,"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":0.47510001063346863,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.3700999915599823,"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":0.08009999990463257,"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-state-tomography","display_name":"quantum state tomography","score":0.9950000047683716},{"id":"https://openalex.org/keywords/burer-monteiro-factorization","display_name":"Burer-Monteiro factorization","score":0.9879999756813049},{"id":"https://openalex.org/keywords/density-matrix","display_name":"density matrix","score":0.5450000166893005},{"id":"https://openalex.org/keywords/mixed-states","display_name":"mixed states","score":0.5870000123977661},{"id":"https://openalex.org/keywords/density-matrix-renormalization-group","display_name":"density matrix renormalization group","score":0.9480000138282776},{"id":"https://openalex.org/keywords/compressed-measurements","display_name":"compressed measurements","score":0.8420000076293945},{"id":"https://openalex.org/keywords/tensor-network-contraction","display_name":"tensor network contraction","score":0.6589999794960022},{"id":"https://openalex.org/keywords/memory-and-computational-cost-reduction","display_name":"memory and computational cost reduction","score":0.656000018119812}],"concepts":[{"id":"https://openalex.org/C166834278","wikidata":"https://www.wikidata.org/wiki/Q4218494","display_name":"Quantum tomography","level":4,"score":0.7519999742507935},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5788999795913696},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.5557000041007996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5458999872207642},{"id":"https://openalex.org/C29547527","wikidata":"https://www.wikidata.org/wiki/Q5259335","display_name":"Density matrix renormalization group","level":3,"score":0.5303999781608582},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5231999754905701},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5206000208854675},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.48829999566078186},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.4878999888896942},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.45809999108314514},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.4465000033378601},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.44119998812675476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4196000099182129},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41519999504089355},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.41110000014305115},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.40700000524520874},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.38089999556541443},{"id":"https://openalex.org/C163716698","wikidata":"https://www.wikidata.org/wiki/Q841267","display_name":"Tomography","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C90408235","wikidata":"https://www.wikidata.org/wiki/Q938141","display_name":"Quantum annealing","level":4,"score":0.3596000075340271},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.33899998664855957},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33739998936653137},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3059999942779541},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30250000953674316},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.298799991607666},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.26969999074935913},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.26179999113082886},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.25690001249313354},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.09457","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09457","pdf_url":"https://arxiv.org/pdf/2609.09457","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.2609.09457","doi":"https://doi.org/10.48550/arxiv.2609.09457","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.09457","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.09457","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09457","pdf_url":"https://arxiv.org/pdf/2609.09457","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":[{"id":"https://openalex.org/G4869584417","display_name":null,"funder_award_id":"iBOF/23/064","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G6905264830","display_name":"Between linear and nonlinear: new tensor perspectives","funder_award_id":"C14/22/096","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G7424168635","display_name":null,"funder_award_id":"C14/22/096","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G7512198267","display_name":"Tensor Tools for Taming the Curse","funder_award_id":"iBOF/23/064","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"}],"funders":[{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212152177.pdf","grobid_xml":"https://content.openalex.org/works/W7212152177.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2973172184","https://openalex.org/W4417028091","https://openalex.org/W7130437280","https://openalex.org/W7162562893"],"related_works":["https://openalex.org/W4417053855","https://openalex.org/W7170171905","https://openalex.org/W7130437280","https://openalex.org/W4403159646","https://openalex.org/W7160487316","https://openalex.org/W4285483469","https://openalex.org/W4416365725","https://openalex.org/W2140336578","https://openalex.org/W4385848996","https://openalex.org/W1529624360"],"abstract_inverted_index":{"Quantum":[0],"state":[1,10,69,201],"tomography":[2,70,220],"is":[3,83,173],"a":[4,12,20,52,62,73,89,96,176],"fundamental":[5],"technique":[6],"for":[7,66,143,168],"estimating":[8,144],"the":[9,25,38,44,48,56,80,86,100,114,124,156],"of":[11,27,47,58,88,99,116,126,179],"quantum":[13,28,53,68,145,181],"system":[14,39],"from":[15,119,147,203],"measured":[16],"data":[17],"and":[18,107,135,163,189,213],"plays":[19],"crucial":[21],"role":[22],"in":[23,123,210],"evaluating":[24],"performance":[26],"devices.":[29],"However,":[30],"standard":[31],"estimation":[32],"methods":[33,152],"become":[34],"computationally":[35],"prohibitive":[36],"as":[37,85],"size":[40],"increases":[41],"due":[42],"to":[43,121,175],"exponential":[45,120],"growth":[46],"density":[49,81,137],"matrix,":[50],"describing":[51],"state,":[54],"with":[55,91,207,217],"number":[57,115,125],"qubits.":[59,127],"We":[60],"propose":[61],"low-rank":[63,180,219],"tensor-network":[64,166,195],"framework":[65,172],"mixed-state":[67],"based":[71],"on":[72,129,155],"block":[74],"tensor":[75],"train":[76],"(Block-TT)":[77],"factorization.":[78,102],"Specifically,":[79],"matrix":[82,138],"represented":[84],"contraction":[87],"Block-TT":[90],"its":[92],"Hermitian":[93],"transpose,":[94],"yielding":[95],"TT":[97],"analogue":[98],"Burer-Monteiro":[101],"This":[103],"parameterization":[104],"guarantees":[105],"Hermiticity":[106],"positive":[108],"semidefiniteness":[109],"by":[110],"construction":[111],"while":[112],"compressing":[113],"optimization":[117],"variables":[118],"linear":[122],"Building":[128],"this":[130],"representation,":[131],"we":[132],"develop":[133],"single-site":[134],"two-site":[136],"renormalization":[139],"group":[140],"(DMRG)":[141],"algorithms":[142],"states":[146,191],"compressed":[148,157],"measurements.":[149],"The":[150,171],"resulting":[151],"operate":[153],"directly":[154],"parameterization,":[158],"support":[159],"adaptive":[160],"rank":[161],"refinement,":[162],"exploit":[164],"efficient":[165],"contractions":[167],"expectation-value":[169],"evaluation.":[170],"applicable":[174],"broad":[177],"class":[178],"states,":[182,185,188],"including":[183],"pure":[184,187],"nearly":[186],"ground":[190],"that":[192],"admit":[193],"accurate":[194,200],"approximations.":[196],"Numerical":[197],"experiments":[198],"demonstrate":[199],"reconstruction":[202],"limited":[204],"measurements":[205],"together":[206],"substantial":[208],"reductions":[209],"memory":[211],"requirements":[212],"computational":[214],"cost":[215],"compared":[216],"conventional":[218],"methods.":[221]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-11T00:00:00"}