{"id":"https://openalex.org/W7166661262","doi":"https://doi.org/10.1145/3774895.3815552","title":"When Noisy Quantum Order Finding Remains Recoverable for Shor's Algorithm","display_name":"When Noisy Quantum Order Finding Remains Recoverable for Shor's Algorithm","publication_year":2026,"publication_date":"2026-06-30","ids":{"openalex":"https://openalex.org/W7166661262","doi":"https://doi.org/10.1145/3774895.3815552"},"language":null,"primary_location":{"id":"doi:10.1145/3774895.3815552","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3774895.3815552","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 40th ACM International Conference on Supercomputing - Workshops","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1145/3774895.3815552","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136438727","display_name":"Qingxin Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Qingxin Yang","raw_affiliation_strings":["Department of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0009-0005-3119-7402","affiliations":[{"raw_affiliation_string":"Department of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085178088","display_name":"Stefano Markidis","orcid":"https://orcid.org/0000-0003-0639-0639"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Stefano Markidis","raw_affiliation_strings":["Department of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0003-0639-0639","affiliations":[{"raw_affiliation_string":"Department of Computational Science and Technology, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I86987016"],"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":"125","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.7524999976158142,"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":0.7524999976158142,"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":0.030899999663233757,"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.014499999582767487,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6054999828338623},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.5716000199317932},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5092999935150146},{"id":"https://openalex.org/keywords/order-statistic","display_name":"Order statistic","score":0.5034999847412109},{"id":"https://openalex.org/keywords/subroutine","display_name":"Subroutine","score":0.4348999857902527},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4334000051021576},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4291999936103821},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4122999906539917},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.40139999985694885},{"id":"https://openalex.org/keywords/binary-search-tree","display_name":"Binary search tree","score":0.3865000009536743},{"id":"https://openalex.org/keywords/binary-decision-diagram","display_name":"Binary decision diagram","score":0.38580000400543213}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7185999751091003},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6054999828338623},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.5716000199317932},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5597000122070312},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5092999935150146},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.5034999847412109},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.4348999857902527},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4334000051021576},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4122999906539917},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.3865000009536743},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.38580000400543213},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37369999289512634},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.3698999881744385},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3695000112056732},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3684000074863434},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.33970001339912415},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.33239999413490295},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.32899999618530273},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.3287000060081482},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.311599999666214},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C110546421","wikidata":"https://www.wikidata.org/wiki/Q1315869","display_name":"Arity","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.2632000148296356}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3774895.3815552","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3774895.3815552","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 40th ACM International Conference on Supercomputing - Workshops","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/3774895.3815552","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3774895.3815552","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 40th ACM International Conference on Supercomputing - Workshops","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1532834996","https://openalex.org/W1635919617","https://openalex.org/W1967037487","https://openalex.org/W1974169933","https://openalex.org/W1983312464","https://openalex.org/W2030867075","https://openalex.org/W2084500851","https://openalex.org/W2158698691","https://openalex.org/W2282673650","https://openalex.org/W2471819066","https://openalex.org/W2533940598","https://openalex.org/W2562526363","https://openalex.org/W2611652092","https://openalex.org/W2781738013","https://openalex.org/W2904801124","https://openalex.org/W2911964244","https://openalex.org/W2946582523","https://openalex.org/W2949453985","https://openalex.org/W2995849402","https://openalex.org/W3023478445","https://openalex.org/W3037303154","https://openalex.org/W3037571510","https://openalex.org/W3094656610","https://openalex.org/W3165758468","https://openalex.org/W3167726926","https://openalex.org/W3211386740","https://openalex.org/W3214850722","https://openalex.org/W4389672456","https://openalex.org/W4393259382","https://openalex.org/W4396986598","https://openalex.org/W4403786735","https://openalex.org/W4404566610","https://openalex.org/W4404612429"],"related_works":[],"abstract_inverted_index":{"Order":[0],"finding":[1],"is":[2,174,192,202],"the":[3,46,85,89,143,150,183,187,203,210,218,237],"core":[4],"subroutine":[5],"of":[6,207],"Shor\u2019s":[7],"algorithm.":[8],"On":[9],"NISQ":[10],"hardware,":[11],"its":[12],"phase":[13],"estimation":[14],"output":[15],"distributions":[16,52,229,244],"are":[17,146],"often":[18],"distorted":[19,228],"by":[20],"noise,":[21],"making":[22],"correct":[23],"order":[24,32,87],"recovery":[25],"difficult.":[26],"We":[27,49,92,113,128,170],"study":[28],"recoverability":[29,77,173],"in":[30,182,221],"noisy":[31],"finding:":[33],"given":[34],"a":[35,79,158],"measured":[36,184],"precision-register":[37],"distribution,":[38,67],"when":[39,232],"does":[40],"standard":[41],"classical":[42,247],"post-processing":[43,71,238,248],"still":[44],"return":[45],"true":[47,90],"order?":[48],"analyze":[50],"680":[51],"collected":[53],"from":[54],"IBM":[55],"quantum":[56],"systems":[57],"across":[58,194],"multiple":[59],"problem":[60],"instances":[61],"and":[62,75,109,124,167,186,209],"circuit":[63],"settings.":[64],"For":[65],"each":[66,95],"we":[68,155],"apply":[69],"continued-fraction":[70],"with":[72,177],"modular":[73],"verification":[74],"define":[76],"as":[78],"binary":[80],"outcome":[81],"according":[82],"to":[83,134],"whether":[84],"recovered":[86],"equals":[88],"one.":[91],"then":[93],"characterize":[94],"distribution":[96,185],"using":[97,117],"four":[98],"features:":[99],"autocorrelation":[100],"peak":[101],"strength,":[102],"normalized":[103],"entropy,":[104],"dominant":[105,198],"verified":[106,110,189,199,234,252],"mass":[107,191,200],"fraction,":[108],"margin":[111],"fraction.":[112],"evaluate":[114],"these":[115],"quantities":[116,137],"marginal":[118],"feature":[119],"comparisons,":[120],"single-feature":[121,205],"AUROC":[122],"analysis,":[123],"multivariate":[125],"tree-based":[126,211],"classifiers.":[127],"further":[129],"use":[130],"random-forest":[131],"permutation":[132],"importance":[133],"assess":[135],"which":[136],"contribute":[138],"distinct":[139],"predictive":[140],"information":[141],"once":[142],"other":[144],"features":[145],"known.":[147],"To":[148],"make":[149],"resulting":[151],"classification":[152],"behavior":[153],"interpretable,":[154],"also":[156,216],"train":[157],"decision":[159],"tree":[160],"that":[161,172,214],"exposes":[162],"threshold":[163,224],"rules":[164],"for":[165],"recoverable":[166,231],"non-recoverable":[168],"distributions.":[169],"find":[171],"strongly":[175],"associated":[176],"both":[178],"residual":[179],"comb-like":[180],"structure":[181],"way":[188],"probability":[190],"organized":[193],"candidate":[195],"denominators.":[196],"The":[197],"fraction":[201],"strongest":[204],"indicator":[206],"recoverability,":[208],"analysis":[212],"shows":[213],"it":[215],"provides":[217],"primary":[219],"split":[220],"an":[222,250],"interpretable":[223],"description.":[225],"Some":[226],"highly":[227],"remain":[230],"one":[233],"denominator":[235],"dominates":[236],"mass,":[239],"while":[240],"some":[241],"visibly":[242],"structured":[243],"fail":[245],"because":[246],"favors":[249],"incorrect":[251],"denominator.":[253]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2026-07-01T00:00:00"}
