{"id":"https://openalex.org/W7224857421","doi":"https://doi.org/10.48550/arxiv.2610.39670","title":"Error-Corrected Quantum Optimization via Rydberg Atom Array Embeddings","display_name":"Error-Corrected Quantum Optimization via Rydberg Atom Array Embeddings","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224857421","doi":"https://doi.org/10.48550/arxiv.2610.39670"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39670","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39670","pdf_url":"https://arxiv.org/pdf/2610.39670","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.39670","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073564225","display_name":"Andrew Byun","orcid":"https://orcid.org/0000-0001-8306-1818","observed_orcids":["https://orcid.org/0000-0001-8306-1818"]},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Byun, Andrew","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , A-6020 Innsbruck , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , A-6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015609887","display_name":"Berend Klaver","orcid":"https://orcid.org/0009-0004-0169-9340","observed_orcids":["https://orcid.org/0009-0004-0169-9340"]},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]},{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]},{"id":"https://openalex.org/I4210137770","display_name":"Alpine Quantum Technologies (Austria)","ror":"https://ror.org/03xxp1119","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210137770"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Klaver, Berend","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , A-6020 Innsbruck , Austria","Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , A-6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I4210137770"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102027803","display_name":"Arinjoy De","orcid":"https://orcid.org/0000-0001-9184-8434","observed_orcids":["https://orcid.org/0000-0001-9184-8434"]},"institutions":[{"id":"https://openalex.org/I4210111145","display_name":"QuEra Computing (United States)","ror":"https://ror.org/01njdjw78","country_code":"US","type":"company","lineage":["https://openalex.org/I4210111145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"De, Arinjoy","raw_affiliation_strings":["QuEra Computing Inc. , Boston , MA 02139 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QuEra Computing Inc. , Boston , MA 02139 , USA","institution_ids":["https://openalex.org/I4210111145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012826911","display_name":"Pedro Ildefonso","orcid":"https://orcid.org/0000-0003-1362-8596","observed_orcids":["https://orcid.org/0000-0003-1362-8596"]},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]},{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]},{"id":"https://openalex.org/I4210137770","display_name":"Alpine Quantum Technologies (Austria)","ror":"https://ror.org/03xxp1119","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210137770"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Ildefonso, Pedro","raw_affiliation_strings":["Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , A-6020 Innsbruck , Austria","Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik , Universit\u00e4t Innsbruck , A-6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I4210137770"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114412439","display_name":"Davit Khachatryan","orcid":"https://orcid.org/0000-0003-0412-8768","observed_orcids":["https://orcid.org/0000-0003-0412-8768"]},"institutions":[{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]},{"id":"https://openalex.org/I4210137770","display_name":"Alpine Quantum Technologies (Austria)","ror":"https://ror.org/03xxp1119","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210137770"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Khachatryan, Davit","raw_affiliation_strings":["Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I4210137770"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063700634","display_name":"Alexei Bylinskii","orcid":"https://orcid.org/0000-0001-8276-8256","observed_orcids":["https://orcid.org/0000-0001-8276-8256"]},"institutions":[{"id":"https://openalex.org/I4210111145","display_name":"QuEra Computing (United States)","ror":"https://ror.org/01njdjw78","country_code":"US","type":"company","lineage":["https://openalex.org/I4210111145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bylinskii, Alexei","raw_affiliation_strings":["QuEra Computing Inc. , Boston , MA 02139 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QuEra Computing Inc. , Boston , MA 02139 , USA","institution_ids":["https://openalex.org/I4210111145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071054283","display_name":"Michael Schuler","orcid":"https://orcid.org/0000-0003-3557-8913","observed_orcids":["https://orcid.org/0000-0003-3557-8913"]},"institutions":[{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]},{"id":"https://openalex.org/I4210137770","display_name":"Alpine Quantum Technologies (Austria)","ror":"https://ror.org/03xxp1119","country_code":"AT","type":"company","lineage":["https://openalex.org/I4210137770"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Schuler, Michael","raw_affiliation_strings":["Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Parity Quantum Computing GmbH , A-6020 Innsbruck , Austria","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I4210137770"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034419704","display_name":"Wolfgang Lechner","orcid":"https://orcid.org/0000-0003-3662-1020","observed_orcids":["https://orcid.org/0000-0003-3662-1020"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lechner, Wolfgang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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":0.9990000128746033,"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":0.9990000128746033,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.00039999998989515007,"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":0.00019999999494757503,"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/rydberg-atom-arrays","display_name":"Rydberg atom arrays","score":0.9449999928474426},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":0.8399999737739563},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"combinatorial optimization","score":0.8349999785423279},{"id":"https://openalex.org/keywords/embeddings","display_name":"embeddings","score":0.38499999046325684},{"id":"https://openalex.org/keywords/rydberg-blockade","display_name":"Rydberg blockade","score":0.7289999723434448},{"id":"https://openalex.org/keywords/classical-error-correcting-codes","display_name":"classical error-correcting codes","score":0.8399999737739563},{"id":"https://openalex.org/keywords/bit-flip-errors","display_name":"bit-flip errors","score":0.875},{"id":"https://openalex.org/keywords/maximum-independent-set-problem","display_name":"maximum independent set","score":0.7379999756813049},{"id":"https://openalex.org/keywords/error-threshold","display_name":"error threshold","score":0.7070000171661377},{"id":"https://openalex.org/keywords/nonlinear-codes","display_name":"nonlinear codes","score":0.49799999594688416}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6370999813079834},{"id":"https://openalex.org/C116225407","wikidata":"https://www.wikidata.org/wiki/Q2178236","display_name":"Rydberg atom","level":5,"score":0.6108999848365784},{"id":"https://openalex.org/C70747811","wikidata":"https://www.wikidata.org/wiki/Q661248","display_name":"Rydberg formula","level":4,"score":0.5286999940872192},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5127000212669373},{"id":"https://openalex.org/C171706072","wikidata":"https://www.wikidata.org/wiki/Q128218","display_name":"Superatom","level":3,"score":0.5062000155448914},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4797999858856201},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44110000133514404},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.43560001254081726},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.43369999527931213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.424699991941452},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.35179999470710754},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C58312451","wikidata":"https://www.wikidata.org/wiki/Q4817200","display_name":"Atom (system on chip)","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.337799996137619},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.3328000009059906},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32359999418258667},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.32100000977516174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31610000133514404},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29019999504089355},{"id":"https://openalex.org/C119770614","wikidata":"https://www.wikidata.org/wiki/Q5516347","display_name":"Gadget","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C40969351","wikidata":"https://www.wikidata.org/wiki/Q3516228","display_name":"Word error rate","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.2621999979019165}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39670","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39670","pdf_url":"https://arxiv.org/pdf/2610.39670","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.2610.39670","doi":"https://doi.org/10.48550/arxiv.2610.39670","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39670","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:2610.39670","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39670","pdf_url":"https://arxiv.org/pdf/2610.39670","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":[{"id":"https://openalex.org/G2452079257","display_name":null,"funder_award_id":"DN-01-GA101072964","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3252262385","display_name":null,"funder_award_id":"HORIZON-MSCA-2021-DN-01-GA101072964","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7716710130","display_name":null,"funder_award_id":"F7108-N38","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320323031","display_name":"\u00d6sterreichische Forschungsf\u00f6rderungsgesellschaft","ror":"https://ror.org/028jc0449"},{"id":"https://openalex.org/F4320338388","display_name":"Eurostars","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224857421.pdf","grobid_xml":"https://content.openalex.org/works/W7224857421.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4410395258","https://openalex.org/W4415939163","https://openalex.org/W4399806502","https://openalex.org/W4417183035","https://openalex.org/W7125518570","https://openalex.org/W4320724826","https://openalex.org/W3172556917","https://openalex.org/W4299393113","https://openalex.org/W4415108443","https://openalex.org/W7167507410"],"abstract_inverted_index":{"Rydberg":[0,70,84,183],"atom":[1,184],"quantum":[2,203],"optimizers":[3],"naturally":[4,72],"encode":[5],"the":[6,31,67,116,127,147,151,214],"maximum":[7],"independent":[8],"set":[9],"problem":[10],"on":[11,21,146],"geometric":[12],"graphs.":[13],"However,":[14],"to":[15,29,82,105,169],"solve":[16],"general":[17],"combinatorial":[18],"optimization":[19,156,196,204],"problems":[20],"more":[22],"complex":[23],"topologies,":[24],"an":[25,57,135,159,195],"embedding":[26,71,186],"is":[27,187],"required":[28],"overcome":[30],"limited-range":[32],"native":[33],"interactions.":[34],"Such":[35],"embeddings":[36],"use":[37],"gadgets,":[38],"specific":[39],"arrangements":[40],"of":[41,138,163,167,194],"atoms,":[42,171],"which":[43,121,206],"inevitably":[44],"introduce":[45,115],"ancillary":[46],"atoms.":[47],"Here,":[48],"we":[49,64,114],"show":[50],"that":[51,66,80],"this":[52,132],"apparent":[53],"overhead":[54],"instead":[55],"provides":[56],"intrinsic":[58],"resource":[59],"for":[60,165,202],"error":[61,95,136,210],"correction.":[62],"Specifically,":[63],"demonstrate":[65],"Parity":[68],"Architecture-based":[69],"forms":[73],"a":[74,78,106,191,199],"classical":[75],"error-correcting":[76],"code,":[77],"principle":[79],"extends":[81],"other":[83],"blockade-based":[85],"embeddings.":[86],"Within":[87],"superatom":[88],"substructures,":[89],"exact":[90,155],"Rydberg-excitation-number":[91],"constraints":[92,125],"provide":[93],"local":[94,124],"syndromes":[96],"at":[97],"no":[98],"additional":[99],"hardware":[100,175,192],"cost":[101],"and":[102,126,176,209],"give":[103],"rise":[104],"strictly":[107],"nonlinear":[108],"code.":[109],"To":[110],"correct":[111],"bit-flip":[112],"errors,":[113],"precisely":[117],"tailored":[118],"Cluster":[119,152],"decoder,":[120],"exploits":[122],"these":[123],"underlying":[128],"gadget":[129],"structure.":[130,217],"Numerically,":[131],"approach":[133],"achieves":[134],"threshold":[137],"$p_{\\text{th}}\\gtrsim26":[139],"\\%$":[140],"across":[141],"different":[142],"layout":[143],"geometries.":[144],"Experimentally,":[145],"QuEra":[148],"Aquila":[149],"QPU,":[150],"decoder":[153],"recovers":[154],"solutions":[157],"with":[158],"average":[160],"success":[161],"rate":[162],"$\\gtrsim8\\%$":[164],"systems":[166],"up":[168],"107":[170],"even":[172],"when":[173],"bare":[174],"standard":[177],"greedy":[178],"post-processing":[179],"find":[180],"none.":[181],"A":[182],"array":[185],"therefore":[188],"not":[189],"merely":[190],"mapping":[193],"problem,":[197],"but":[198],"co-designed":[200],"architecture":[201],"in":[205],"embedding,":[207],"computation,":[208],"correction":[211],"emerge":[212],"from":[213],"same":[215],"physical":[216]},"counts_by_year":[],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2026-10-31T00:00:00"}