{"id":"https://openalex.org/W7214044973","doi":"https://doi.org/10.48550/arxiv.2609.22669","title":"Metric Self-Dual Completion and Optimal Additive Hardness for Quantum and Graph-State Distance","display_name":"Metric Self-Dual Completion and Optimal Additive Hardness for Quantum and Graph-State Distance","publication_year":2026,"publication_date":"2026-09-19","ids":{"openalex":"https://openalex.org/W7214044973","doi":"https://doi.org/10.48550/arxiv.2609.22669"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.22669","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22669","pdf_url":"https://arxiv.org/pdf/2609.22669","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/2609.22669","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020375635","display_name":"Rafail Ostrovsky","orcid":"https://orcid.org/0000-0002-1501-1330","observed_orcids":["https://orcid.org/0000-0002-1501-1330"]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ostrovsky, Rafail","raw_affiliation_strings":["UCLA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020375635"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.8398000001907349,"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":0.8398000001907349,"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/T11130","display_name":"Coding theory and cryptography","score":0.15119999647140503,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.001500000013038516,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/np-hardness-of-approximation","display_name":"NP-hardness of approximation","score":0.796999990940094},{"id":"https://openalex.org/keywords/css-codes","display_name":"CSS codes","score":0.9319999814033508},{"id":"https://openalex.org/keywords/stabilizer-codes","display_name":"stabilizer codes","score":0.5450000166893005},{"id":"https://openalex.org/keywords/balanced-bipartite-graphs","display_name":"balanced bipartite graphs","score":0.75},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6320000290870667},{"id":"https://openalex.org/keywords/self-dual-codes","display_name":"self-dual codes","score":0.6389999985694885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.823199987411499},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.635699987411499},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.531499981880188},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5221999883651733},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5174999833106995},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4846999943256378},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.47130000591278076},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.42289999127388},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.40959998965263367},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4056999981403351},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.3815999925136566},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.34369999170303345},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.34279999136924744},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.3199000060558319},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.3183000087738037},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3163999915122986},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.22669","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22669","pdf_url":"https://arxiv.org/pdf/2609.22669","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.2609.22669","doi":"https://doi.org/10.48550/arxiv.2609.22669","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.22669","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:2609.22669","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22669","pdf_url":"https://arxiv.org/pdf/2609.22669","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214044973.pdf","grobid_xml":"https://content.openalex.org/works/W7214044973.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1567129586","https://openalex.org/W2042474962","https://openalex.org/W2045476715","https://openalex.org/W2078536889","https://openalex.org/W2114207424","https://openalex.org/W2153267198","https://openalex.org/W2169665116","https://openalex.org/W4380905717","https://openalex.org/W4415330780","https://openalex.org/W7108689730","https://openalex.org/W7128646609"],"related_works":["https://openalex.org/W4415330780","https://openalex.org/W4380905717","https://openalex.org/W7214722336","https://openalex.org/W3106513669","https://openalex.org/W3105797017","https://openalex.org/W2067100062","https://openalex.org/W7097829117","https://openalex.org/W4220854529","https://openalex.org/W2952741118","https://openalex.org/W4298212857"],"abstract_inverted_index":{"We":[0,103,209],"prove":[1],"that":[2,85,160,252],"the":[3,26,36,45,100,106,199,212],"quantum":[4,101],"code":[5,183,191],"distance":[6,112,147],"is":[7,25,80,161,175,205],"NP-hard":[8],"to":[9,41,123,180],"approximate":[10],"within":[11],"an":[12],"additive":[13,39],"error":[14],"of":[15,28,50,109,116,185,193,216,255,257],"$c":[16,21],"N$,":[17],"for":[18,57,151,170],"some":[19],"constant":[20,69,72,82],">0$,":[22],"where":[23],"$N$":[24,114],"number":[27],"qubits.":[29],"Our":[30,54,144,167],"reductions":[31],"are":[32,134,140,262],"deterministic.":[33],"This":[34],"improves":[35],"previous":[37],"square-root":[38],"gap":[40,108],"$\u03a9(N)$":[42],"and":[43,52,63,66,71,119,207,241],"resolves":[44],"explicitly":[46,127],"stated":[47,128],"linear-gap":[48],"question":[49],"Kapshikar":[51],"Kundu.":[53],"result":[55,149],"holds":[56,88,150],"CSS":[58],"codes":[59],"with":[60,67,155,220],"identical":[61],"$X$-":[62],"$Z$-check":[64],"spaces,":[65],"a":[68,81,156,189,221],"rate":[70],"relative":[73],"distance.":[74,102],"For":[75],"every":[76,91],"fixed":[77],"$\u03bb>1$,":[78],"there":[79],"$c>0$":[83],"such":[84],"hardness":[86,107,132,148,172],"still":[87],"even":[89],"when":[90],"nonidentity":[92],"stabilizer":[93],"has":[94],"weight":[95,258],"greater":[96],"than":[97],"$\u03bb$":[98],"times":[99],"also":[104,250],"improve":[105],"graph":[110,145],"state":[111,146],"on":[113],"vertices":[115],"Grigorescu,":[117],"Jha,":[118],"Samperton":[120],"from":[121],"cube-root":[122],"$\u03a9(N)$,":[124],"resolving":[125],"their":[126],"open":[129],"question.":[130],"Both":[131],"results":[133],"asymptotically":[135],"optimal":[136],"since":[137],"both":[138,171],"distances":[139,235,244],"at":[141,259],"most":[142,260],"$N$.":[143],"balanced":[152],"bipartite":[153],"graphs":[154],"binary":[157],"adjacency":[158],"matrix":[159],"its":[162],"own":[163],"inverse":[164],"(mod":[165],"2).":[166],"main":[168],"technique":[169],"bounds":[173],"above":[174],"classical:":[176],"we":[177],"show":[178],"how":[179],"convert":[181],"any":[182],"$C$":[184],"length":[186,194],"$m$":[187],"into":[188],"self-dual":[190,214],"$A(C)$":[192,256],"$N=\u0398(m)$":[195],"while":[196],"exactly":[197,263],"doubling":[198],"original":[200],"coset":[201],"metric.":[202],"The":[203,230,248],"conversion":[204],"deterministic":[206],"efficient.":[208],"call":[210],"it":[211],"metric":[213],"completion":[215],"$C$.":[217],"It":[218],"comes":[219],"linear":[222],"embedding":[223,231,249],"$\u03c4:":[224],"\\mathbb":[225,228],"F_2^m":[226],"\\hookrightarrow":[227],"F_2^N$.":[229],"doubles":[232],"all":[233,242,253],"Hamming":[234],"between":[236,245],"vectors":[237],"in":[238],"$\\mathbb":[239],"F_2^m$":[240],"pairwise":[243],"corresponding":[246],"cosets.":[247],"guarantees":[251],"codewords":[254],"$2m$":[261],"$\u03c4(C)$.":[264]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}