{"id":"https://openalex.org/W7222931314","doi":"https://doi.org/10.48550/arxiv.2610.22689","title":"Circuit Synthesis for Variational Quantum Algorithms: The Depth of Algebra and Geometry","display_name":"Circuit Synthesis for Variational Quantum Algorithms: The Depth of Algebra and Geometry","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222931314","doi":"https://doi.org/10.48550/arxiv.2610.22689"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.22689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22689","pdf_url":"https://arxiv.org/pdf/2610.22689","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/2610.22689","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082123059","display_name":"Boris Tsvelikhovskiy","orcid":"https://orcid.org/0000-0003-0798-7218","observed_orcids":["https://orcid.org/0000-0003-0798-7218"]},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tsvelikhovskiy, Boris","raw_affiliation_strings":["Department of Mathematics , University of California , Riverside , CA 92521 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of California , Riverside , CA 92521 , USA","institution_ids":["https://openalex.org/I103635307"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082123059"],"corresponding_institution_ids":["https://openalex.org/I103635307"],"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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":1.0,"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":9.999999747378752e-05,"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":0.0,"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/variational-quantum-algorithms","display_name":"variational quantum algorithms","score":0.9309999942779541},{"id":"https://openalex.org/keywords/quantum-approximate-optimization-algorithm","display_name":"quantum approximate optimization algorithm","score":0.7979999780654907},{"id":"https://openalex.org/keywords/network-synthesis","display_name":"network synthesis","score":0.6899999976158142},{"id":"https://openalex.org/keywords/dynamical-lie-algebra","display_name":"dynamical Lie algebra","score":0.9850000143051147},{"id":"https://openalex.org/keywords/reachable-states","display_name":"reachable states","score":0.6190000176429749},{"id":"https://openalex.org/keywords/maximum-independent-set-problem","display_name":"maximum independent set","score":0.8339999914169312},{"id":"https://openalex.org/keywords/ground-state-preparation","display_name":"ground state preparation","score":0.6909999847412109},{"id":"https://openalex.org/keywords/negative-curvature","display_name":"negative curvature","score":0.5099999904632568}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7063000202178955},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.6435999870300293},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6029000282287598},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6008999943733215},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5372999906539917},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41819998621940613},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.37959998846054077},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.3538999855518341},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C2776122010","wikidata":"https://www.wikidata.org/wiki/Q10359539","display_name":"Unitary representation","level":3,"score":0.3061999976634979},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.2955999970436096},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.28439998626708984},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27410000562667847},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.26600000262260437},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.25929999351501465}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.22689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22689","pdf_url":"https://arxiv.org/pdf/2610.22689","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.2610.22689","doi":"https://doi.org/10.48550/arxiv.2610.22689","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.22689","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:2610.22689","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22689","pdf_url":"https://arxiv.org/pdf/2610.22689","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222931314.pdf","grobid_xml":"https://content.openalex.org/works/W7222931314.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1568345435","https://openalex.org/W4397028512","https://openalex.org/W4414597271","https://openalex.org/W7130585773","https://openalex.org/W7213498676"],"related_works":["https://openalex.org/W4298181933","https://openalex.org/W4389160984","https://openalex.org/W4416735321","https://openalex.org/W7167608730","https://openalex.org/W4220927716","https://openalex.org/W4361279418","https://openalex.org/W3159585601","https://openalex.org/W7215090126","https://openalex.org/W4385761041","https://openalex.org/W4406759522"],"abstract_inverted_index":{"The":[0],"analysis":[1],"of":[2,41,66,74,98,129,234,243],"Hamiltonian":[3],"Variational":[4],"Ans\u00e4tze":[5],"centers":[6],"on":[7,158],"three":[8],"fundamental":[9],"questions:":[10],"which":[11],"states":[12],"are":[13,195],"exactly":[14],"reachable":[15,147],"from":[16],"a":[17,33,39,45,88,95,99,239,246],"given":[18],"initial":[19,68,85,236],"state,":[20],"what":[21],"native":[22,130,192],"control":[23,100,131,193],"depth":[24,111,201],"suffices":[25],"for":[26,115,134],"local":[27,135,152],"and":[28,31,63,121,138,179,202,230],"global":[29,156],"synthesis,":[30],"whether":[32],"bounded":[34,247],"circuit":[35,250,262],"extension":[36,251],"can":[37],"expose":[38],"direction":[40],"decreasing":[42],"cost":[43],"at":[44,259],"suboptimal":[46,261],"output.":[47,263],"We":[48,81,125],"address":[49],"these":[50,151],"challenges":[51],"by":[52,198],"leveraging":[53],"the":[54,61,64,67,72,75,127,209,215,228,231,235],"dynamical":[55,77,168,210],"Lie":[56,78,169,211],"algebras":[57],"(DLAs)":[58],"associated":[59],"with":[60,103,162],"circuits":[62],"geometry":[65],"state's":[69],"orbit":[70,91,148,233],"under":[71],"action":[73],"corresponding":[76],"group":[79,212],"$G$.":[80],"show":[82,189],"that":[83,190],"an":[84,219],"state":[86,113,139,237,241],"has":[87],"closed":[89],"projective":[90,232],"whenever":[92],"it":[93],"is":[94,213,227],"nondegenerate":[96],"eigenstate":[97],"Hamiltonian.":[101],"Combined":[102],"asymptotic":[104],"QAOA":[105,185],"convergence,":[106],"this":[107],"guarantees":[108],"exact,":[109],"finite":[110],"ground":[112,240],"preparation":[114,140],"architectures":[116],"employing":[117],"diagonal":[118],"problem":[119],"Hamiltonians":[120],"irreducible":[122],"stoquastic":[123],"mixers.":[124],"bound":[126],"number":[128],"exponentials":[132],"required":[133],"unitary":[136,164,167],"synthesis":[137],"using":[141],"DLA":[142],"commutator":[143,199],"filtration":[144,200],"growth":[145],"alongside":[146],"dimensions.":[149],"Complementing":[150],"results,":[153],"we":[154,188],"construct":[155],"frameworks":[157],"invariant":[159],"sectors":[160],"equipped":[161],"full":[163],"or":[165,256],"special":[166],"algebras.":[170],"These":[171],"constructions":[172],"yield":[173],"explicit":[174],"applications":[175],"to":[176],"Pauli-generated":[177],"systems":[178],"constrained":[180],"maximum":[181],"independent":[182],"set":[183],"multi-angle":[184],"circuits;":[186],"specifically,":[187],"their":[191],"costs":[194],"directly":[196],"determined":[197],"independent-set":[203],"toggle-group":[204],"geometry,":[205],"respectively.":[206],"Finally,":[207],"if":[208],"compact,":[214],"observable":[216],"$H_P$":[217],"generates":[218],"admissible":[220],"evolution":[221],"($iH_P":[222],"\\in":[223],"\\mathfrak{g}$,":[224],"where":[225],"$\\mathfrak{g}$":[226],"DLA),":[229],"contains":[238],"ray":[242],"$H_P$,":[244],"then":[245],"depth,":[248],"identity-initialized":[249],"exhibits":[252],"either":[253],"first-order":[254],"descent":[255],"negative":[257],"curvature":[258],"every":[260]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-20T00:00:00"}