{"id":"https://openalex.org/W7160304344","doi":"https://doi.org/10.48550/arxiv.2605.02211","title":"Many Hamiltonians Are Sparsifiable","display_name":"Many Hamiltonians Are Sparsifiable","publication_year":2026,"publication_date":"2026-05-04","ids":{"openalex":"https://openalex.org/W7160304344","doi":"https://doi.org/10.48550/arxiv.2605.02211"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.02211","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02211","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.02211","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135300680","display_name":"Arpon Basu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Basu, Arpon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028220417","display_name":"Joshua Brakensiek","orcid":"https://orcid.org/0000-0003-4149-7298"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Brakensiek, Joshua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135283888","display_name":"Aaron Putterman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Putterman, Aaron","raw_affiliation_strings":[],"raw_orcid":null,"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":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":0.7491000294685364,"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":0.7491000294685364,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.09319999814033508,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.027000000700354576,"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/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.7904000282287598},{"id":"https://openalex.org/keywords/pauli-exclusion-principle","display_name":"Pauli exclusion principle","score":0.657800018787384},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5654000043869019},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5263000130653381},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.49889999628067017},{"id":"https://openalex.org/keywords/pauli-matrices","display_name":"Pauli matrices","score":0.43220001459121704},{"id":"https://openalex.org/keywords/quantum-system","display_name":"Quantum system","score":0.4047999978065491},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.391400009393692}],"concepts":[{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.7904000282287598},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.657800018787384},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5654000043869019},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5263000130653381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5206999778747559},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.49889999628067017},{"id":"https://openalex.org/C180347388","wikidata":"https://www.wikidata.org/wiki/Q336233","display_name":"Pauli matrices","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.4047999978065491},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.391400009393692},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.374099999666214},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3734999895095825},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3375999927520752},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.329800009727478},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3262999951839447},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.3003000020980835},{"id":"https://openalex.org/C171972299","wikidata":"https://www.wikidata.org/wiki/Q6500908","display_name":"Self-adjoint operator","level":3,"score":0.29190000891685486},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2856999933719635},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.266400009393692},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2648000121116638},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.25519999861717224},{"id":"https://openalex.org/C192353077","wikidata":"https://www.wikidata.org/wiki/Q4682635","display_name":"Adiabatic quantum computation","level":4,"score":0.2535000145435333},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.02211","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02211","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.02211","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.02211","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,111],"study":[1],"the":[2,20,81,91,96,103,106,181],"problem":[3],"of":[4,22,93,105,122,149,167,183],"Hamiltonian":[5,16],"sparsification:":[6],"given":[7],"a":[8,36,120,186,215],"parameter":[9],"$\\varepsilon":[10],"\\in":[11,59,67],"(0,1)$":[12],"and":[13,156,221],"an":[14,135,145,163],"$n$-qubit":[15],"$H$":[17],"which":[18],"is":[19,33,84,108,134,144,162,185],"sum":[21],"$r$-local":[23,136,146,165],"positive":[24],"semi-definite":[25],"(PSD)":[26],"terms":[27,94,123],"$H_1,":[28],"\\dots":[29],"H_m$,":[30],"our":[31,177,227],"goal":[32],"to":[34,119,190,207,237],"compute":[35],"sparse":[37],"set":[38,82],"$L":[39],"\\subseteq":[40],"[m]$,":[41],"along":[42],"with":[43],"weights":[44],"$w:":[45],"L":[46],"\\rightarrow":[47],"\\mathbb{R}_{\\geq":[48],"0}$":[49],"such":[50],"that":[51,102,113,180,231],"for":[52,152,194,205,211],"every":[53],"state":[54],"$|\u03c8\\rangle\\in":[55],"\\mathbb{C}^{2^n}$,":[56],"$$":[57],"\\sum_{i":[58,71],"L}":[60],"w(i)":[61],"\\langle":[62,74],"\u03c8|":[63,75],"H_i":[64,76],"|":[65,77],"\u03c8\\rangle":[66,78],"(1":[68],"\\pm":[69],"\u03b5)":[70],"=":[72],"1}^m":[73],"$$.":[79],"When":[80],"$L$":[83],"significantly":[85],"smaller":[86,125],"than":[87,126,239],"$m$,":[88],"this":[89],"reduces":[90],"number":[92,121],"in":[95],"underlying":[97],"system,":[98],"while":[99],"still":[100],"ensuring":[101],"behavior":[104],"system":[107],"essentially":[109],"unchanged.":[110],"show":[112,179],"many":[114],"Hamiltonians":[115,130,140,158,184],"indeed":[116],"are":[117,234],"sparsifiable":[118],"much":[124],"$n^r$,":[127],"including:":[128],"(a)":[129],"where":[131,141,159],"each":[132,142,160],"term":[133,143,161],"Pauli":[137],"string,":[138],"(b)":[139],"random":[147],"operator":[148,166],"rank":[150,168],"$R$,":[151],"$R":[153],"\\geq":[154],"2^{r-1}+1$,":[155],"(c)":[157],"arbitrary":[164],"$\\geq":[169],"2^r":[170],"-1$":[171],"(a.k.a.":[172],"Quantum":[173],"SAT).":[174],"Taken":[175],"together,":[176],"results":[178,202,228],"sparsifiability":[182],"robust":[187],"phenomenon,":[188],"contrary":[189],"prevailing":[191],"belief":[192],"(see":[193],"instance,":[195,206],"Aharonov-Zhou":[196],"ITCS":[197],"2019,":[198],"QIP":[199],"2019).":[200],"Our":[201],"find":[203],"applications,":[204],"better":[208],"(semi-)streaming":[209],"algorithms":[210],"quantum":[212,232],"Max-Cut,":[213],"answering":[214],"question":[216],"left":[217],"open":[218],"by":[219],"Kallaugher":[220],"Parekh":[222],"(FOCS":[223],"2022).":[224],"In":[225],"fact,":[226],"even":[229],"codify":[230],"systems":[233],"often":[235],"easier":[236],"sparsify":[238],"their":[240],"classical":[241],"counterparts.":[242]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-06T00:00:00"}
