{"id":"https://openalex.org/W7163132656","doi":"https://doi.org/10.48550/arxiv.2606.02418","title":"Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search","display_name":"Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search","publication_year":2026,"publication_date":"2026-06-01","ids":{"openalex":"https://openalex.org/W7163132656","doi":"https://doi.org/10.48550/arxiv.2606.02418"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.02418","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.02418","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.2606.02418","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085459979","display_name":"Juan Cruz-Benito","orcid":"https://orcid.org/0000-0003-2045-8329"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cruz-Benito, Juan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064909614","display_name":"Andrew W. Cross","orcid":"https://orcid.org/0000-0001-9786-8196"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cross, Andrew W.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137705356","display_name":"David Kremer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kremer, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055771565","display_name":"Ismael Faro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Faro, Ismael","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":0.947700023651123,"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":0.947700023651123,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.015799999237060547,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.00419999985024333,"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/python","display_name":"Python (programming language)","score":0.41269999742507935},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3578999936580658},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.35109999775886536},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.3476000130176544},{"id":"https://openalex.org/keywords/search-algorithm","display_name":"Search algorithm","score":0.33869999647140503},{"id":"https://openalex.org/keywords/source-code","display_name":"Source code","score":0.335999995470047},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.319599986076355},{"id":"https://openalex.org/keywords/workflow","display_name":"Workflow","score":0.3156000077724457},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.31150001287460327}],"concepts":[{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.541100025177002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5264000296592712},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4341999888420105},{"id":"https://openalex.org/C519991488","wikidata":"https://www.wikidata.org/wiki/Q28865","display_name":"Python (programming language)","level":2,"score":0.41269999742507935},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3578999936580658},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3476000130176544},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3303000032901764},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C177212765","wikidata":"https://www.wikidata.org/wiki/Q627335","display_name":"Workflow","level":2,"score":0.3156000077724457},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.31150001287460327},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.3037000000476837},{"id":"https://openalex.org/C105902424","wikidata":"https://www.wikidata.org/wiki/Q1197129","display_name":"Evolutionary computation","level":2,"score":0.3001999855041504},{"id":"https://openalex.org/C2777655017","wikidata":"https://www.wikidata.org/wiki/Q1501161","display_name":"Toolbox","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C28034677","wikidata":"https://www.wikidata.org/wiki/Q17092530","display_name":"Interleaving","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.28600001335144043},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C46900642","wikidata":"https://www.wikidata.org/wiki/Q2647","display_name":"Huffman coding","level":3,"score":0.28040000796318054},{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.2718000113964081},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.2621999979019165},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.02418","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.02418","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.2606.02418","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.02418","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":{"Quantum":[0],"LDPC":[1],"code":[2,41,139],"discovery":[3,201],"requires":[4],"searching":[5],"large":[6],"algebraic":[7],"design":[8],"spaces":[9],"while":[10],"reliably":[11],"certifying":[12],"the":[13,46,107,161],"parameters":[14],"and":[15,38,60,66,87,97,118,130,140],"equivalence":[16,99],"classes":[17],"of":[18,64,164],"any":[19],"candidates":[20,172],"found.":[21],"We":[22],"introduce":[23],"an":[24,136],"LLM-guided":[25,189],"evolutionary":[26,51],"workflow":[27,108],"in":[28,68],"which":[29],"language":[30],"models":[31],"mutate":[32],"Python":[33],"programs":[34],"that":[35,188],"generate":[36],"bivariate-bicycle":[37,40,116],"perturbed":[39,121,158],"ans\u00e4tze.":[42],"Across":[43],"five":[44],"campaigns,":[45],"system":[47],"performed":[48],"approximately":[49],"1{,}650":[50],"iterations,":[52],"screened":[53],"about":[54],"$2":[55],"\\times":[56],"10^5$":[57],"candidate":[58,112],"codes,":[59],"required":[61],"${\\sim}140$":[62],"hours":[63],"computation":[65],"${\\sim}$US\\$400":[67],"LLM":[69],"inference":[70],"cost.":[71],"Candidate":[72],"codes":[73,117,129,142,159],"are":[74],"evaluated":[75],"through":[76],"a":[77,195],"staged":[78],"validation":[79],"pipeline":[80],"combining":[81],"$\\mathrm{GF}(2)$":[82],"rank":[83],"computation,":[84],"distance":[85,150],"estimation":[86],"certification,":[88],"mixed-integer":[89],"linear":[90],"programming,":[91],"BLISS":[92],"Tanner-graph":[93],"deduplication,":[94],"decomposability":[95],"analysis,":[96],"local-Clifford":[98],"checks.":[100],"At":[101],"block":[102],"length":[103],"$n":[104],"\\leq":[105],"360$,":[106],"identifies":[109],"465":[110],"distinct":[111],"codes:":[113],"97":[114],"CSS":[115,124],"368":[119],"non-CSS":[120,155],"variants.":[122],"The":[123,154],"search":[125,156],"recovers":[126],"known":[127],"high-performing":[128],"finds":[131],"new":[132],"finite-length":[133],"representatives,":[134],"including":[135],"indecomposable":[137],"[[288,16,12]]":[138],"higher-weight":[141],"with":[143,169,204],"up":[144],"to":[145,181],"$k":[146],"=":[147,152],"50$":[148],"at":[149,166],"$d":[151],"8$.":[153],"produces":[157],"matching":[160],"gross-code":[162],"figure":[163],"merit":[165],"[[144,12,12]],":[167],"along":[168],"additional":[170],"high-distance":[171],"reported":[173],"as":[174,194],"certified":[175],"values":[176],"or":[177],"upper":[178],"bounds":[179],"according":[180],"MILP":[182],"status.":[183],"Overall,":[184],"these":[185],"results":[186],"show":[187],"program":[190],"evolution":[191],"can":[192],"serve":[193],"practical":[196],"tool":[197],"for":[198],"structured":[199],"quantum-code":[200],"when":[202],"paired":[203],"independent":[205],"evaluation.":[206]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-03T00:00:00"}
