{"id":"https://openalex.org/W7216517015","doi":"https://doi.org/10.48550/arxiv.2610.02166","title":"Beyond light cones: State preparation complexity in quantum spin glasses","display_name":"Beyond light cones: State preparation complexity in quantum spin glasses","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216517015","doi":"https://doi.org/10.48550/arxiv.2610.02166"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02166","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02166","pdf_url":"https://arxiv.org/pdf/2610.02166","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/2610.02166","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103016627","display_name":"Omar Ghattas","orcid":"https://orcid.org/0000-0001-7742-2509","observed_orcids":["https://orcid.org/0000-0001-7742-2509"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Al-Ghattas, Omar","raw_affiliation_strings":["Department of Mathematics , Massachusetts Institute of Technology , Cambridge , MA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Massachusetts Institute of Technology , Cambridge , MA , USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031648070","display_name":"David Gamarnik","orcid":"https://orcid.org/0000-0001-8898-8778","observed_orcids":["https://orcid.org/0000-0001-8898-8778"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gamarnik, David","raw_affiliation_strings":["Sloan School of Management , Operations Research Center , and Institute for Data, Systems, and Society , Massachusetts Institute of Technology , Cambridge , MA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sloan School of Management , Operations Research Center , and Institute for Data, Systems, and Society , Massachusetts Institute of Technology , Cambridge , MA , USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079855181","display_name":"Bobak T. Kiani","orcid":"https://orcid.org/0000-0003-1477-0308","observed_orcids":["https://orcid.org/0000-0003-1477-0308"]},"institutions":[{"id":"https://openalex.org/I135474949","display_name":"Bowdoin College","ror":"https://ror.org/03gh96r95","country_code":"US","type":"education","lineage":["https://openalex.org/I135474949"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kiani, Bobak T","raw_affiliation_strings":["Department of Computer Science , Bowdoin College , Brunswick , ME , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Bowdoin College , Brunswick , ME , USA","institution_ids":["https://openalex.org/I135474949"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.8022000193595886,"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":0.8022000193595886,"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":0.18639999628067017,"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":0.004100000020116568,"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-spin-glass","display_name":"quantum spin glass","score":0.8740000128746033},{"id":"https://openalex.org/keywords/p-spin-model","display_name":"p-spin model","score":0.890999972820282},{"id":"https://openalex.org/keywords/circuit-lower-bounds","display_name":"circuit lower bounds","score":0.7350000143051147},{"id":"https://openalex.org/keywords/metric-entropy","display_name":"metric entropy","score":0.9160000085830688},{"id":"https://openalex.org/keywords/entanglement-depth","display_name":"entanglement depth","score":0.9160000085830688},{"id":"https://openalex.org/keywords/gaussian-processes","display_name":"Gaussian processes","score":0.578000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5318999886512756},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.48969998955726624},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.46399998664855957},{"id":"https://openalex.org/C180347388","wikidata":"https://www.wikidata.org/wiki/Q336233","display_name":"Pauli matrices","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44359999895095825},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4178999960422516},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4115999937057495},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.41019999980926514},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.3767000138759613},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3756999969482422},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3727000057697296},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.3707999885082245},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3684000074863434},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3662000000476837},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3359000086784363},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.33320000767707825},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33309999108314514},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3296000063419342},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32409998774528503},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3138999938964844},{"id":"https://openalex.org/C70662872","wikidata":"https://www.wikidata.org/wiki/Q766202","display_name":"Vacuum state","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28619998693466187},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.2815999984741211},{"id":"https://openalex.org/C150775274","wikidata":"https://www.wikidata.org/wiki/Q1490646","display_name":"Spin glass","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.2513999938964844},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.25099998712539673},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02166","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02166","pdf_url":"https://arxiv.org/pdf/2610.02166","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.2610.02166","doi":"https://doi.org/10.48550/arxiv.2610.02166","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02166","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.02166","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02166","pdf_url":"https://arxiv.org/pdf/2610.02166","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":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320314070","display_name":"Broad Institute","ror":"https://ror.org/05a0ya142"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216517015.pdf","grobid_xml":"https://content.openalex.org/works/W7216517015.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W9166514","https://openalex.org/W2107029088","https://openalex.org/W2949757588","https://openalex.org/W3099923448","https://openalex.org/W4282013219","https://openalex.org/W4283713089","https://openalex.org/W4385020958","https://openalex.org/W4387322939","https://openalex.org/W4414125010","https://openalex.org/W4416385736","https://openalex.org/W4417166394","https://openalex.org/W7169535740","https://openalex.org/W7213606510"],"related_works":["https://openalex.org/W7169535740","https://openalex.org/W4404350118","https://openalex.org/W4310808773","https://openalex.org/W7119104562","https://openalex.org/W4417210074","https://openalex.org/W4415252800","https://openalex.org/W4411516585","https://openalex.org/W6939125162","https://openalex.org/W4417539426","https://openalex.org/W4320712916"],"abstract_inverted_index":{"We":[0,31,72,166,192],"introduce":[1],"a":[2,17,50,96,119,133,239,249],"technique":[3],"for":[4,75,174,209,259],"studying":[5],"state":[6,37,203],"preparation":[7,38],"complexity":[8,46,85,106],"in":[9,270],"the":[10,33,43,48,54,58,90,99,104,111,115,144,157,260,265,271],"quantum":[11,19,251],"$p$-spin":[12],"model":[13],"on":[14,25,98,197],"$n$":[15],"qubits,":[16],"disordered":[18],"spin":[20],"system":[21],"with":[22,82,227,256],"random":[23],"interactions":[24],"every":[26,215],"set":[27,59],"of":[28,35,47,57,60,122,146,163,218,248,268],"$p$":[29],"qubits.":[30],"reduce":[32],"task":[34],"proving":[36],"lower":[39,172,195],"bounds":[40,139,196,258],"to":[41],"bounding":[42],"local":[44,83,266],"profile":[45,84,105],"class,":[49],"quantity":[51],"derived":[52],"from":[53,89],"metric":[55],"entropy":[56],"vectors":[61],"recording":[62],"each":[63],"state's":[64],"expectation":[65],"values":[66],"against":[67],"all":[68],"weight-$p$":[69],"Pauli":[70],"strings.":[71],"show":[73],"that,":[74],"sufficiently":[76],"large":[77],"fixed":[78,216],"$p$,":[79],"any":[80],"class":[81,116,121],"$O(n^2)$":[86],"remains":[87],"separated":[88],"ground-state":[91],"energy":[92,101,207,232],"by":[93,264],"$\u03a9(\\sqrt":[94],"n)$,":[95],"gap":[97],"leading":[100,126],"scale.":[102],"When":[103],"is":[107],"$o(n^2)$,":[108],"we":[109,229],"prove":[110],"stronger":[112],"conclusion":[113],"that":[114],"cannot":[117],"outperform":[118],"benchmark":[120],"simpler":[123],"states":[124,129,177,237,269],"at":[125,214],"order.":[127],"Product":[128],"always":[130],"provide":[131],"such":[132],"benchmark.":[134,242],"Our":[135],"framework":[136],"strengthens":[137],"known":[138],"and":[140,178,184,187,200,206,211],"covers":[141],"classes":[142],"beyond":[143],"reach":[145],"previous":[147],"methods.":[148],"These":[149],"include":[150],"examples":[151],"where":[152],"circuit":[153],"lightcones":[154],"extend":[155],"across":[156],"entire":[158],"system,":[159],"preventing":[160],"an":[161,168,246],"application":[162],"standard":[164],"arguments.":[165],"obtain":[167,230],"$\u03a9(n^2/\\log":[169],"n)$":[170],"gate":[171],"bound":[173],"preparing":[175],"near-ground":[176],"depth--width":[179],"tradeoffs,":[180],"allowing":[181],"arbitrary":[182],"one-":[183],"two-qubit":[185],"gates":[186],"arbitrarily":[188],"many":[189],"discardable":[190],"ancillas.":[191],"also":[193],"derive":[194],"entanglement":[198],"depth":[199],"matrix":[201],"product":[202,235],"bond":[204],"dimension,":[205],"obstructions":[208],"forward":[210],"reverse":[212],"magic":[213,220],"level":[217],"Parham's":[219],"hierarchy":[221],"(arXiv:2504.19966).":[222],"For":[223],"Clifford":[224],"circuits":[225],"doped":[226],"$T$-gates,":[228],"sharper":[231],"comparisons":[233],"using":[234],"stabilizer":[236],"as":[238],"more":[240],"restrictive":[241],"The":[243],"proof":[244],"combines":[245],"adaptation":[247],"nonsymmetric":[250],"de":[252],"Finetti":[253],"theorem":[254],"(arXiv:1810.12197)":[255],"metric-entropy":[257],"Gaussian":[261],"process":[262],"indexed":[263],"profiles":[267],"class.":[272]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-03T00:00:00"}