{"id":"https://openalex.org/W7207855677","doi":"https://doi.org/10.48550/arxiv.2609.01901","title":"Need One Bell-pair Only (NOBOL) for Low-Overhead Fault-Tolerant Quantum Computing","display_name":"Need One Bell-pair Only (NOBOL) for Low-Overhead Fault-Tolerant Quantum Computing","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7207855677","doi":"https://doi.org/10.48550/arxiv.2609.01901"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01901","pdf_url":"https://arxiv.org/pdf/2609.01901","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/2609.01901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139150789","display_name":"Sean Grzenda","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Grzenda, Sean","raw_affiliation_strings":["Computer Science and Engineering University at Buffalo Buffalo , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Engineering University at Buffalo Buffalo , USA","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056429026","display_name":"Shahram Babaie","orcid":"https://orcid.org/0000-0001-7830-2496","observed_orcids":["https://orcid.org/0000-0001-7830-2496"]},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Babaie, Shahram","raw_affiliation_strings":["Computer Science and Engineering University at Buffalo Buffalo , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Engineering University at Buffalo Buffalo , USA","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100728176","display_name":"Chunming Qiao","orcid":"https://orcid.org/0000-0002-4679-6572","observed_orcids":["https://orcid.org/0000-0002-4679-6572"]},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qiao, Chunming","raw_affiliation_strings":["Computer Science and Engineering University at Buffalo Buffalo , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Engineering University at Buffalo Buffalo , USA","institution_ids":["https://openalex.org/I63190737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63190737"],"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/T10020","display_name":"Quantum Information and Cryptography","score":0.0005000000237487257,"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/T11804","display_name":"Quantum many-body systems","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fault-tolerant-quantum-computation","display_name":"fault-tolerant quantum computing","score":0.8859999775886536},{"id":"https://openalex.org/keywords/bell-pairs","display_name":"Bell pairs","score":0.7519999742507935},{"id":"https://openalex.org/keywords/css-codes","display_name":"CSS codes","score":0.9300000071525574},{"id":"https://openalex.org/keywords/surface-code","display_name":"surface code","score":0.9779999852180481},{"id":"https://openalex.org/keywords/logical-qubit-encoding","display_name":"logical qubit encoding","score":0.6679999828338623},{"id":"https://openalex.org/keywords/error-propagation","display_name":"error propagation","score":0.6209999918937683},{"id":"https://openalex.org/keywords/distributed-quantum-computing","display_name":"distributed quantum computing","score":0.6809999942779541}],"concepts":[{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.641700029373169},{"id":"https://openalex.org/C182953411","wikidata":"https://www.wikidata.org/wiki/Q917713","display_name":"Controlled NOT gate","level":5,"score":0.6344000101089478},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.5605999827384949},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.49900001287460327},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.48820000886917114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4749999940395355},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4584999978542328},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.4124999940395355},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.41040000319480896},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.383899986743927},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3698999881744385},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.362199991941452},{"id":"https://openalex.org/C194989596","wikidata":"https://www.wikidata.org/wiki/Q211790","display_name":"Logical connective","level":2,"score":0.352400004863739},{"id":"https://openalex.org/C69497775","wikidata":"https://www.wikidata.org/wiki/Q7269025","display_name":"Quantum convolutional code","level":5,"score":0.3483999967575073},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3319000005722046},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.3305000066757202},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3077000081539154},{"id":"https://openalex.org/C21847791","wikidata":"https://www.wikidata.org/wiki/Q191081","display_name":"Logical conjunction","level":2,"score":0.2937999963760376},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.2879999876022339},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C91717678","wikidata":"https://www.wikidata.org/wiki/Q1135332","display_name":"Quantum teleportation","level":5,"score":0.2745000123977661},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.2606000006198883},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25769999623298645},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01901","pdf_url":"https://arxiv.org/pdf/2609.01901","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.2609.01901","doi":"https://doi.org/10.48550/arxiv.2609.01901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01901","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:2609.01901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01901","pdf_url":"https://arxiv.org/pdf/2609.01901","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/W7207855677.pdf","grobid_xml":"https://content.openalex.org/works/W7207855677.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W387088958","https://openalex.org/W1985315536","https://openalex.org/W2029658458","https://openalex.org/W2030867075","https://openalex.org/W2086947442","https://openalex.org/W2758259983","https://openalex.org/W2897264299","https://openalex.org/W3014684719","https://openalex.org/W3023478445","https://openalex.org/W3082220326","https://openalex.org/W4321443503","https://openalex.org/W4366826586","https://openalex.org/W4391885348","https://openalex.org/W4394581296","https://openalex.org/W4394662590","https://openalex.org/W4399495635","https://openalex.org/W4402585749","https://openalex.org/W4404569756","https://openalex.org/W4405331036","https://openalex.org/W4415276509","https://openalex.org/W7077879799","https://openalex.org/W7108207678","https://openalex.org/W7134268901","https://openalex.org/W7151598133"],"related_works":["https://openalex.org/W7161066837","https://openalex.org/W3081235969","https://openalex.org/W4416176252","https://openalex.org/W2965712458","https://openalex.org/W1959392488","https://openalex.org/W2885813516","https://openalex.org/W2078014384","https://openalex.org/W4385872060","https://openalex.org/W4416339399","https://openalex.org/W4404257466"],"abstract_inverted_index":{"Fault-tolerant":[0],"quantum":[1,46,54,89,250],"computation":[2],"fundamentally":[3],"relies":[4],"on":[5,60,118,149,166,270],"encoding":[6],"a":[7,11,24,34,57,69,96,109,128,134,145,210,246,272],"logical":[8,29,63,80,110,125,146,168,176,223],"qubit":[9,260],"into":[10],"structured":[12],"block":[13],"of":[14,39,43,72,99,174,195,207,218,221,249],"physical":[15],"qubits,":[16],"typically":[17],"in":[18,37,52,75,87,102,124,154,216,255],"the":[19,41,79,121,167,175,184,193,196,219,222],"tens":[20],"to":[21,77,83,104,143,230,245,259],"hundreds.":[22],"As":[23],"trade-off":[25],"for":[26,264],"improved":[27],"fault-tolerance,":[28],"gate":[30,58,164],"operations":[31,74,165],"will":[32,65,93],"incur":[33],"linear":[35,70,97],"overhead":[36,122],"terms":[38,217],"both":[40],"amount":[42],"time":[44],"and":[45,262],"resources":[47],"than":[48,192],"before.":[49],"For":[50,178],"example,":[51],"monolithic":[53,273],"computing,":[55,90],"performing":[56,163],"operation":[59,148],"two":[61,150],"distant":[62,151],"qubits":[64,81,101,152],"first":[66,94],"require":[67,95],"using":[68],"number":[71,98],"SWAP":[73],"order":[76,103],"move":[78],"next":[82],"each":[84],"other;":[85],"while":[86],"distributed":[88,276],"doing":[91],"so":[92],"ancilla":[100],"form":[105],"entanglement":[106],"connections":[107],"(or":[108],"Bell":[111,141],"pair).":[112],"In":[113,199],"this":[114,200],"paper,":[115,201],"we":[116,202,226],"focus":[117],"significantly":[119,190],"reducing":[120],"involved":[123],"CNOT":[126,147],"operations,":[127],"fundamental":[129],"primitive.":[130],"We":[131],"propose":[132,227],"NOBOL,":[133,208],"novel":[135],"approach":[136],"that":[137],"requires":[138,162],"only":[139,161],"one":[140],"pair":[142],"perform":[144],"encoded":[153],"arbitrary":[155],"CSS":[156,180],"codes.":[157],"More":[158],"importantly,":[159],"NOBOL":[160,240],"X":[169],"or":[170,275],"Z":[171],"operator":[172],"subsets":[173,188],"qubits.":[177],"many":[179],"codes,":[181],"such":[182],"as":[183],"surface":[185],"code,":[186],"these":[187],"are":[189],"smaller":[191],"size":[194,220],"code":[197],"itself.":[198],"describe":[203],"various":[204,265],"circuit":[205,212],"realizations":[206],"including":[209,267],"depth-optimal":[211],"with":[213],"logarithmic":[214],"depth":[215],"operators.":[224],"Finally,":[225],"effective":[228,263],"methods":[229],"contain":[231],"error":[232],"propagation":[233],"without":[234],"incurring":[235],"much":[236],"additional":[237],"overhead.":[238],"Since":[239],"can":[241],"be":[242],"effectively":[243],"applied":[244],"wide":[247],"range":[248],"error-correcting":[251],"(QEC)":[252],"codes":[253],"and,":[254],"addition,":[256],"is":[257],"agnostic":[258],"modalities":[261],"architectures,":[266],"those":[268],"based":[269],"either":[271],"QPU":[274],"QPUs.":[277]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}