{"id":"https://openalex.org/W7160655849","doi":"https://doi.org/10.48550/arxiv.2605.05942","title":"Architecture Shape Governs QNN Trainability: Jacobian Null Space Growth and Parameter Efficiency","display_name":"Architecture Shape Governs QNN Trainability: Jacobian Null Space Growth and Parameter Efficiency","publication_year":2026,"publication_date":"2026-05-07","ids":{"openalex":"https://openalex.org/W7160655849","doi":"https://doi.org/10.48550/arxiv.2605.05942"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.05942","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05942","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.2605.05942","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135671298","display_name":"Michael Poppel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Poppel, Michael","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135700247","display_name":"David Bucher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bucher, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083875469","display_name":"Maximilian Zorn","orcid":"https://orcid.org/0009-0006-2750-7495"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zorn, Maximilian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135651578","display_name":"Markus Baumann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Baumann, Markus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5099173793","display_name":"Sebastian W\u00f6lckert","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W\u00f6lckert, Sebastian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135670636","display_name":"Claudia Linnhoff-Popien","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Linnhoff-Popien, Claudia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135647599","display_name":"Philipp Altmann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Altmann, Philipp","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134827906","display_name":"Jonas Stein","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stein, Jonas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":8,"corresponding_author_ids":[],"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":0.4535999894142151,"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":0.4535999894142151,"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/T11804","display_name":"Quantum many-body systems","score":0.17030000686645508,"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":0.14110000431537628,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.8544999957084656},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.60589998960495},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.49300000071525574},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.47870001196861267},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4399999976158142},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.43950000405311584},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.3806999921798706},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.3781999945640564},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.37560001015663147}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8544999957084656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6909000277519226},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.60589998960495},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.49300000071525574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49219998717308044},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.47870001196861267},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4406999945640564},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4399999976158142},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38029998540878296},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3781999945640564},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.26109999418258667},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.25999999046325684},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.05942","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05942","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.05942","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.05942","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Variational":[0],"quantum":[1],"circuits":[2],"with":[3,15,51,87,179,202],"angle":[4],"encoding":[5,17,22],"implement":[6],"truncated":[7],"Fourier":[8],"series,":[9],"and":[10,35,174],"architectures":[11,121],"arranging":[12],"$N$":[13],"qubits":[14],"$L$":[16],"layers":[18,166],"each":[19],"--":[20,27,95],"sharing":[21],"budget":[23],"$E":[24],"=":[25],"NL$":[26],"generate":[28],"identical":[29,32],"frequency":[30,33],"spectra,":[31],"redundancy,":[34],"require":[36],"the":[37,64,70,112,150,169,198],"same":[38],"minimum":[39],"parameter":[40,84,139,156],"count":[41,85,157],"for":[42,133],"coefficient":[43,65],"control.":[44],"Despite":[45],"this":[46,123],"equivalence,":[47],"trainability":[48],"varies":[49],"substantially":[50],"architecture":[52],"shape":[53],"$(N,L)$":[54],"at":[55,117],"fixed":[56,118],"$E$.":[57],"We":[58],"identify":[59],"structural":[60],"rank":[61],"deficiency":[62],"of":[63,83,106],"matching":[66],"Jacobian":[67,170],"$J$":[68],"as":[69,114],"mechanism":[71,201],"responsible.":[72],"For":[73,144],"serial":[74],"single-qubit":[75],"architectures,":[76,190],"we":[77,98,146],"prove":[78],"$\\mathrm{rank}(J)":[79],"\\leq":[80,135],"2L+1$":[81],"regardless":[82],"$P$,":[86],"$\\dim(\\ker":[88],"J)":[89],"\\geq":[90,177],"P-(2L+1)$":[91],"growing":[92,104],"without":[93],"bound":[94],"a":[96,103],"phenomenon":[97],"term":[99],"\\emph{structural":[100],"gradient":[101],"starvation}:":[102],"fraction":[105],"parameters":[107,182],"become":[108],"structurally":[109],"decoupled":[110],"from":[111],"loss":[113],"$P$":[115],"increases":[116],"$L$.":[119],"Parallel":[120],"avoid":[122],"via":[124],"independent":[125],"phase":[126],"trajectories,":[127],"ensuring":[128],"$\u03c3_{\\min}(J^{(\\mathrm{par})})":[129],"&gt;":[130],"0$":[131],"generically":[132],"$P":[134],"2E+1$,":[136],"so":[137],"no":[138,203],"lies":[140],"in":[141],"$\\ker":[142],"J$.":[143],"practitioners,":[145],"further":[147],"show":[148],"that":[149],"two":[151],"natural":[152],"routes":[153],"to":[154],"increasing":[155],"have":[158],"fundamentally":[159],"different":[160],"effects:":[161],"adding":[162,184],"feature":[163],"map":[164],"(FM)":[165],"monotonically":[167],"strengthens":[168],"QFIM":[171],"eigenvalue":[172],"spectrum":[173],"achieves":[175],"$R^2":[176],"0.95$":[178],"$1.6$--$2.2\\times$":[180],"fewer":[181],"than":[183],"trainable":[185,192],"blocks":[186,193],"across":[187],"all":[188],"tested":[189],"while":[191],"improve":[194],"training":[195],"only":[196],"through":[197],"classical":[199],"interpolation":[200],"quantum-specific":[204],"benefit.":[205]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-09T00:00:00"}
