{"id":"https://openalex.org/W4390136660","doi":"https://doi.org/10.1007/978-3-031-57267-8_2","title":"On the Hardness of Analyzing Quantum Programs Quantitatively","display_name":"On the Hardness of Analyzing Quantum Programs Quantitatively","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4390136660","doi":"https://doi.org/10.1007/978-3-031-57267-8_2"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-57267-8_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-57267-8_2","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57267-8_2.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57267-8_2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048841494","display_name":"Martin Avanzini","orcid":"https://orcid.org/0000-0002-6445-8833"},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Martin Avanzini","raw_affiliation_strings":["Centre Inria d\u2019Universit\u00e9 C\u00f4te d\u2019Azur, Valbonne, France","Centre Inria d'Universit\u00e9 C\u00f4te d'Azur, Valbonne, France"],"affiliations":[{"raw_affiliation_string":"Centre Inria d\u2019Universit\u00e9 C\u00f4te d\u2019Azur, Valbonne, France","institution_ids":["https://openalex.org/I201841394"]},{"raw_affiliation_string":"Centre Inria d'Universit\u00e9 C\u00f4te d'Azur, Valbonne, France","institution_ids":["https://openalex.org/I201841394"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050172197","display_name":"Georg Moser","orcid":"https://orcid.org/0000-0001-9240-6128"},"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":"Georg Moser","raw_affiliation_strings":["Universit\u00e4t Innsbruck, Innsbruck, Austria"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Innsbruck, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051353259","display_name":"Romain P\u00e9choux","orcid":"https://orcid.org/0000-0003-0601-5425"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Romain P\u00e9choux","raw_affiliation_strings":["CNRS-Inria-Universit\u00e9 de Lorraine, LORIA, Nancy, France"],"affiliations":[{"raw_affiliation_string":"CNRS-Inria-Universit\u00e9 de Lorraine, LORIA, Nancy, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I90183372","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029014455","display_name":"Simon Perdrix","orcid":"https://orcid.org/0000-0002-1808-2409"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Simon Perdrix","raw_affiliation_strings":["CNRS-Inria-Universit\u00e9 de Lorraine, LORIA, Nancy, France"],"affiliations":[{"raw_affiliation_string":"CNRS-Inria-Universit\u00e9 de Lorraine, LORIA, Nancy, France","institution_ids":["https://openalex.org/I4210121838","https://openalex.org/I90183372","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048841494"],"corresponding_institution_ids":["https://openalex.org/I201841394"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.5189,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.79197356,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"31","last_page":"58"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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":1.0,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.992900013923645,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9926999807357788,"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/computer-science","display_name":"Computer science","score":0.6874136328697205},{"id":"https://openalex.org/keywords/sketch","display_name":"Sketch","score":0.6340539455413818},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5341723561286926},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.4940805733203888},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4760441780090332},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.4222901165485382},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39924973249435425},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3280056118965149},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31494367122650146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2305668294429779},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.138674795627594}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6874136328697205},{"id":"https://openalex.org/C2779231336","wikidata":"https://www.wikidata.org/wiki/Q7534724","display_name":"Sketch","level":2,"score":0.6340539455413818},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5341723561286926},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.4940805733203888},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4760441780090332},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.4222901165485382},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39924973249435425},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3280056118965149},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31494367122650146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2305668294429779},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.138674795627594},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-3-031-57267-8_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-57267-8_2","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57267-8_2.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:2312.13657","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.13657","pdf_url":"https://arxiv.org/pdf/2312.13657","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04349874v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-04349874","pdf_url":"https://inria.hal.science/hal-04349874v1/file/synthesis-hal.pdf","source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://link.springer.com/chapter/10.1007/978-3-031-57267-8_2","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.2312.13657","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.13657","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-57267-8_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-57267-8_2","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-57267-8_2.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2191957979","display_name":null,"funder_award_id":"ANR-22-PETQ-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2233425273","display_name":null,"funder_award_id":"ANR-19-CE48-0014","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2447788411","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G2970831653","display_name":null,"funder_award_id":"ANR-22-PNCQ-0002","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G488932057","display_name":"Automated Amortised Resource Analysis of Data Structures","funder_award_id":"P 36623","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6612625481","display_name":null,"funder_award_id":"France 2030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8184292771","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8266173377","display_name":null,"funder_award_id":"19-CE48-0014","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4390136660.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W9166514","https://openalex.org/W136633354","https://openalex.org/W438580906","https://openalex.org/W1480039477","https://openalex.org/W1492999010","https://openalex.org/W1496947201","https://openalex.org/W1509579779","https://openalex.org/W1511668635","https://openalex.org/W1553894716","https://openalex.org/W1595069411","https://openalex.org/W1734364899","https://openalex.org/W1999626800","https://openalex.org/W2000108089","https://openalex.org/W2001097638","https://openalex.org/W2011665527","https://openalex.org/W2014354084","https://openalex.org/W2037009101","https://openalex.org/W2052146120","https://openalex.org/W2058440484","https://openalex.org/W2079294297","https://openalex.org/W2103953153","https://openalex.org/W2119851779","https://openalex.org/W2137147061","https://openalex.org/W2137722266","https://openalex.org/W2157601714","https://openalex.org/W2222812367","https://openalex.org/W2946053196","https://openalex.org/W2949292350","https://openalex.org/W2951490272","https://openalex.org/W2982085742","https://openalex.org/W2982169647","https://openalex.org/W3107232269","https://openalex.org/W3110898182","https://openalex.org/W3193902563","https://openalex.org/W4206481739","https://openalex.org/W4224863640","https://openalex.org/W4234924236","https://openalex.org/W4285783048","https://openalex.org/W4288018418","https://openalex.org/W4289855867","https://openalex.org/W4289874378","https://openalex.org/W4301808069","https://openalex.org/W4315631112","https://openalex.org/W4379536095","https://openalex.org/W4379538081"],"related_works":["https://openalex.org/W2378994405","https://openalex.org/W2385974820","https://openalex.org/W2000071592","https://openalex.org/W2373478030","https://openalex.org/W2378679551","https://openalex.org/W1660676450","https://openalex.org/W3149739944","https://openalex.org/W1586473494","https://openalex.org/W2392363776","https://openalex.org/W2382181079"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,56,143],"study":[5],"quantitative":[6,79,99],"properties":[7],"of":[8,12,30,32,42,53,63,88,119,129,139],"quantum":[9,35,54,65,140],"programs.":[10,141],"Properties":[11],"interest":[13],"include":[14],"(positive)":[15],"almost-sure":[16],"termination,":[17],"expected":[18,21,28],"runtime":[19],"or":[20],"cost,":[22],"that":[23,73,97],"is,":[24],"for":[25],"example,":[26],"the":[27,40,46,50,98,108,117,130,135,146],"number":[29],"applications":[31],"a":[33,61,64,68,82,92,120],"given":[34],"gate,":[36],"etc.":[37],"After":[38],"studying":[39],"completeness":[41],"these":[43,58,78],"problems":[44,59],"in":[45,103,113,116],"arithmetical":[47],"hierarchy":[48],"over":[49,91],"Clifford+T":[51],"fragment":[52],"mechanics,":[55],"express":[57],"using":[60],"variation":[62],"pre-expectation":[66],"transformer,":[67],"weakest":[69],"pre-condition":[70],"based":[71],"technique":[72],"allows":[74],"to":[75,86,107],"symbolically":[76],"compute":[77],"properties.":[80],"Under":[81],"smooth":[83],"restriction\u2014a":[84],"restriction":[85],"polynomials":[87],"bounded":[89],"degree":[90],"real":[93],"closed":[94],"field\u2014we":[95],"show":[96],"problem,":[100],"which":[101],"consists":[102],"finding":[104],"an":[105,152],"upper-bound":[106],"pre-expectation,":[109],"can":[110,148],"be":[111,149],"decided":[112],"time":[114],"double-exponential":[115],"size":[118],"program,":[121],"thus":[122],"providing,":[123],"despite":[124],"its":[125],"great":[126],"complexity,":[127],"one":[128],"first":[131],"decidable":[132],"results":[133],"on":[134],"analysis":[136],"and":[137],"verification":[138],"Finally,":[142],"sketch":[144],"how":[145],"latter":[147],"transformed":[150],"into":[151],"efficient":[153],"synthesis":[154],"method.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2023-12-23T00:00:00"}
