{"id":"https://openalex.org/W4403827993","doi":"https://doi.org/10.22331/q-2024-10-28-1511","title":"Hardness results for decoding the surface code with Pauli noise","display_name":"Hardness results for decoding the surface code with Pauli noise","publication_year":2024,"publication_date":"2024-10-28","ids":{"openalex":"https://openalex.org/W4403827993","doi":"https://doi.org/10.22331/q-2024-10-28-1511"},"language":"en","primary_location":{"id":"doi:10.22331/q-2024-10-28-1511","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-10-28-1511","pdf_url":"https://quantum-journal.org/papers/q-2024-10-28-1511/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2024-10-28-1511/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111043135","display_name":"Alex Fischer","orcid":null},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alex Fischer","raw_affiliation_strings":["Department of Physics and Astronomy, Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87106, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87106, USA","institution_ids":["https://openalex.org/I169521973"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085372862","display_name":"Akimasa Miyake","orcid":null},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Akimasa Miyake","raw_affiliation_strings":["Department of Physics and Astronomy, Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87106, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87106, USA","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111043135"],"corresponding_institution_ids":["https://openalex.org/I169521973"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23137023,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":null,"first_page":"1511","last_page":"1511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9955000281333923,"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/decoding-methods","display_name":"Decoding methods","score":0.7464697957038879},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.6033588647842407},{"id":"https://openalex.org/keywords/pauli-exclusion-principle","display_name":"Pauli exclusion principle","score":0.5983708500862122},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4628531038761139},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.45823150873184204},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3495692014694214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2261134386062622},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2066134512424469},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10801368951797485},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.08677911758422852},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.06307229399681091}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7464697957038879},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.6033588647842407},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.5983708500862122},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4628531038761139},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.45823150873184204},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3495692014694214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2261134386062622},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2066134512424469},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10801368951797485},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.08677911758422852},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.06307229399681091},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2024-10-28-1511","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-10-28-1511","pdf_url":"https://quantum-journal.org/papers/q-2024-10-28-1511/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3b30b4b10f954137a616528dd07b11bf","is_oa":true,"landing_page_url":"https://doaj.org/article/3b30b4b10f954137a616528dd07b11bf","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 8, p 1511 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2024-10-28-1511","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-10-28-1511","pdf_url":"https://quantum-journal.org/papers/q-2024-10-28-1511/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403827993.pdf","grobid_xml":"https://content.openalex.org/works/W4403827993.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1671959929","https://openalex.org/W1964821516","https://openalex.org/W1971261557","https://openalex.org/W2006912660","https://openalex.org/W2013520638","https://openalex.org/W2024710200","https://openalex.org/W2026181396","https://openalex.org/W2030867075","https://openalex.org/W2035929826","https://openalex.org/W2036265926","https://openalex.org/W2075431083","https://openalex.org/W2085970623","https://openalex.org/W2088636071","https://openalex.org/W2094848842","https://openalex.org/W2173810284","https://openalex.org/W2239674394","https://openalex.org/W2892395081","https://openalex.org/W2946582523","https://openalex.org/W3008561103","https://openalex.org/W3100736866","https://openalex.org/W3101716590","https://openalex.org/W4281479206","https://openalex.org/W4285029287","https://openalex.org/W4298227433","https://openalex.org/W4313484121","https://openalex.org/W4321610982","https://openalex.org/W4384828237","https://openalex.org/W4387047665","https://openalex.org/W4403310488"],"related_works":["https://openalex.org/W3006983566","https://openalex.org/W2052382920","https://openalex.org/W2024371448","https://openalex.org/W2352949123","https://openalex.org/W1611230162","https://openalex.org/W2747066503","https://openalex.org/W1572121409","https://openalex.org/W2951304272","https://openalex.org/W1968289971","https://openalex.org/W4300588357"],"abstract_inverted_index":{"Real":[0],"quantum":[1,28,95,102],"computers":[2],"will":[3],"be":[4],"subject":[5],"to":[6,51,62,131],"complicated,":[7],"qubit-dependent":[8,138],"noise,":[9],"instead":[10],"of":[11,55,80,82,144,151,158,193],"simple":[12],"noise":[13,17,46,75,140,199],"such":[14],"as":[15],"depolarizing":[16],"with":[18,207,220],"the":[19,44,53,60,63,69,78,108,148,152,174,186,208],"same":[20],"strength":[21],"for":[22,86,107,121,126,161,190,196,212,216],"all":[23],"qubits.":[24],"We":[25,116,154],"can":[26],"do":[27,171],"error":[29],"correction":[30],"more":[31],"effectively":[32],"if":[33],"our":[34],"decoding":[35,58,64,98,105],"algorithms":[36],"take":[37],"into":[38,136],"account":[39],"this":[40,90],"prior":[41],"information":[42],"about":[43],"specific":[45],"present.":[47],"This":[48],"motivates":[49],"us":[50],"consider":[52],"complexity":[54],"surface":[56,109,180],"code":[57,110,181],"where":[59],"input":[61],"problem":[65],"is":[66],"not":[67,172],"only":[68],"syndrome-measurement":[70],"results,":[71],"but":[72],"also":[73,155],"a":[74,133,137],"model":[76,141],"in":[77,185],"form":[79],"probabilities":[81],"single-qubit":[83],"Pauli":[84,139],"errors":[85],"every":[87],"qubit.":[88],"In":[89],"setting,":[91],"we":[92],"show":[93],"that":[94,146,170,177],"maximum":[96,103],"likelihood":[97,104],"(QMLD)":[99],"and":[100,113,123,142,163,195,214,224],"degenerate":[101],"(DQMLD)":[106],"are":[111,166,183,204],"NP-hard":[112],"#P-hard,":[114],"respectively.":[115],"reduce":[117],"directly":[118],"from":[119,124],"SAT":[120],"QMLD,":[122],"#SAT":[125],"DQMLD,":[127],"by":[128],"showing":[129],"how":[130],"transform":[132],"boolean":[134],"formula":[135],"set":[143],"syndromes":[145,194],"encode":[147],"satisfiability":[149],"properties":[150],"formula.":[153],"give":[156],"hardness":[157,168,202,210],"approximation":[159],"results":[160,169,203,211],"QMLD":[162,213],"DQMLD.":[164],"These":[165,201],"worst-case":[167],"contradict":[173],"empirical":[175],"fact":[176],"many":[178],"efficient":[179],"decoders":[182],"correct":[184],"average":[187],"case":[188],"(i.e.,":[189],"most":[191,197],"sets":[192],"reasonable":[198],"models).":[200],"nicely":[205],"analogous":[206],"known":[209],"DQMLD":[215],"arbitrary":[217],"stabilizer":[218],"codes":[219],"independent":[221],"<mml:math":[222,225],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>X</mml:mi></mml:math>":[223],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Z</mml:mi></mml:math>":[226],"noise.":[227]},"counts_by_year":[],"updated_date":"2026-03-08T06:56:09.383167","created_date":"2025-10-10T00:00:00"}
