{"id":"https://openalex.org/W7140132331","doi":"https://doi.org/10.48550/arxiv.2603.19901","title":"SDP bounds on quantum codes: rational certificates","display_name":"SDP bounds on quantum codes: rational certificates","publication_year":2026,"publication_date":"2026-03-20","ids":{"openalex":"https://openalex.org/W7140132331","doi":"https://doi.org/10.48550/arxiv.2603.19901"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.19901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19901","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.2603.19901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130391825","display_name":"Gerard Angl\u00e8s Munn\u00e9","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Munn\u00e9, Gerard Angl\u00e8s","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5052589954","display_name":"Felix Huber","orcid":"https://orcid.org/0000-0002-3856-4018"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huber, Felix","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":0.8113999962806702,"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":0.8113999962806702,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.0892999991774559,"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":0.013000000268220901,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.6320000290870667},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.605400025844574},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.47589999437332153},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4641999900341034},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.45320001244544983},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.3824000060558319},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.3628999888896942},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.3513000011444092}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.605400025844574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5597000122070312},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.47589999437332153},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4641999900341034},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40149998664855957},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.33340001106262207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32989999651908875},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3190000057220459},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.3116999864578247},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.29980000853538513},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.28760001063346863},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.27410000562667847},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.19901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19901","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.2603.19901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.19901","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.425214558839798}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0,22],"fundamental":[1],"problem":[2],"in":[3],"quantum":[4,14,34,65,109],"coding":[5,110],"theory":[6],"is":[7],"to":[8,75],"determine":[9],"the":[10,32,42,49,86,101],"maximum":[11,87],"size":[12,88],"of":[13,16,44,64,89,105],"codes":[15,91],"given":[17],"block":[18],"length":[19],"and":[20,103],"distance.":[21],"recent":[23],"work":[24,99],"introduced":[25],"bounds":[26,84],"based":[27],"on":[28,85],"semidefinite":[29,106],"programming,":[30],"strengthening":[31],"well-known":[33],"linear":[35],"programming":[36,107],"bounds.":[37,111],"However,":[38],"floating-point":[39],"inaccuracies":[40],"prevent":[41],"extraction":[43],"rigorous":[45],"non-existence":[46],"proofs":[47],"from":[48],"numerical":[50],"methods.":[51],"Here,":[52],"we":[53,78],"address":[54],"this":[55],"by":[56],"providing":[57],"rational":[58],"infeasibility":[59],"certificates":[60],"for":[61,108],"a":[62,68],"range":[63],"codes.":[66],"Using":[67],"clustered":[69],"low-rank":[70],"solver":[71],"with":[72,92],"heuristic":[73],"rounding":[74],"algebraic":[76],"expressions,":[77],"can":[79],"improve":[80],"upon":[81],"$18$":[82],"upper":[83],"$n$-qubit":[90],"$6":[93],"\\leq":[94,96],"n":[95],"19$.":[97],"Our":[98],"highlights":[100],"practicality":[102],"scalability":[104]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-24T00:00:00"}
