{"id":"https://openalex.org/W4392588892","doi":"https://doi.org/10.46298/lmcs-20(1:20)2024","title":"Rewriting and Completeness of Sum-Over-Paths in Dyadic Fragments of Quantum Computing","display_name":"Rewriting and Completeness of Sum-Over-Paths in Dyadic Fragments of Quantum Computing","publication_year":2024,"publication_date":"2024-03-07","ids":{"openalex":"https://openalex.org/W4392588892","doi":"https://doi.org/10.46298/lmcs-20(1:20)2024"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-20(1:20)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(1:20)2024","pdf_url":"https://lmcs.episciences.org/13200/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/13200/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060401218","display_name":"Renaud Vilmart","orcid":"https://orcid.org/0000-0002-8828-4671"},"institutions":[{"id":"https://openalex.org/I4387154672","display_name":"Laboratoire M\u00e9thodes Formelles","ror":"https://ror.org/00gdtta79","country_code":null,"type":"facility","lineage":["https://openalex.org/I11559806","https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4387154672"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Renaud Vilmart","raw_affiliation_strings":["QuaCS - Quantum Computation Structures (ENS Paris Saclay, 4, avenue des Sciences, 91190\r\nGif-sur-Yvette, France - France)","LMF - Laboratoire M\u00e9thodes Formelles (4, avenue des Sciences, 91190, Gif-sur-Yvette - France)"],"affiliations":[{"raw_affiliation_string":"QuaCS - Quantum Computation Structures (ENS Paris Saclay, 4, avenue des Sciences, 91190\r\nGif-sur-Yvette, France - France)","institution_ids":[]},{"raw_affiliation_string":"LMF - Laboratoire M\u00e9thodes Formelles (4, avenue des Sciences, 91190, Gif-sur-Yvette - France)","institution_ids":["https://openalex.org/I4387154672"]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060401218"],"corresponding_institution_ids":["https://openalex.org/I4387154672"],"apc_list":null,"apc_paid":null,"fwci":0.3407,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61138299,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"Volume 20, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9958000183105469,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9958000183105469,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9950000047683716,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9908999800682068,"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/toffoli-gate","display_name":"Toffoli gate","score":0.8786802887916565},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.6233490705490112},{"id":"https://openalex.org/keywords/rewriting","display_name":"Rewriting","score":0.5400920510292053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45422059297561646},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4297032654285431},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.39993521571159363},{"id":"https://openalex.org/keywords/quantum-gate","display_name":"Quantum gate","score":0.37955355644226074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37388521432876587},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35877835750579834},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22878336906433105},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1300586462020874},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09889712929725647}],"concepts":[{"id":"https://openalex.org/C142465778","wikidata":"https://www.wikidata.org/wiki/Q2502619","display_name":"Toffoli gate","level":5,"score":0.8786802887916565},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.6233490705490112},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.5400920510292053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45422059297561646},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4297032654285431},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.39993521571159363},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.37955355644226074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37388521432876587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35877835750579834},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22878336906433105},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1300586462020874},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09889712929725647},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.46298/lmcs-20(1:20)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(1:20)2024","pdf_url":"https://lmcs.episciences.org/13200/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04496100v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04496100","pdf_url":"https://hal.science/hal-04496100v1/file/2307.14223.pdf","source":{"id":"https://openalex.org/S4406922466","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, 2024, 20 (1), ⟨10.46298/LMCS-20(1:20)2024⟩","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:ed737bebdaf8418cb6399a7f2788c4d4","is_oa":true,"landing_page_url":"https://doaj.org/article/ed737bebdaf8418cb6399a7f2788c4d4","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":"Logical Methods in Computer Science, Vol Volume 20, Issue 1 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/lmcs-20(1:20)2024","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-20(1:20)2024","pdf_url":"https://lmcs.episciences.org/13200/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"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/G4630668814","display_name":null,"funder_award_id":"ANR-22-CE47-0012","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"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4392588892.pdf"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1486765721","https://openalex.org/W1494310072","https://openalex.org/W1632729363","https://openalex.org/W1761683182","https://openalex.org/W1925988739","https://openalex.org/W1985875391","https://openalex.org/W2052146120","https://openalex.org/W2075497274","https://openalex.org/W2796162739","https://openalex.org/W2802560682","https://openalex.org/W2803889673","https://openalex.org/W2922906818","https://openalex.org/W2939312767","https://openalex.org/W2952878714","https://openalex.org/W2964268018","https://openalex.org/W2966537942","https://openalex.org/W3013980468","https://openalex.org/W3014617384","https://openalex.org/W3100779651","https://openalex.org/W3104500086","https://openalex.org/W3104863176","https://openalex.org/W3105507374","https://openalex.org/W3105603580","https://openalex.org/W3135453135","https://openalex.org/W3136504866","https://openalex.org/W3141495992","https://openalex.org/W3199718550","https://openalex.org/W4210839962","https://openalex.org/W4229038692","https://openalex.org/W4235233694","https://openalex.org/W4310432979","https://openalex.org/W4310576339","https://openalex.org/W4311001684","https://openalex.org/W4315701127","https://openalex.org/W4376652944","https://openalex.org/W4386093908","https://openalex.org/W4388667423","https://openalex.org/W6853330531"],"related_works":["https://openalex.org/W1250648069","https://openalex.org/W1651824144","https://openalex.org/W3096921252","https://openalex.org/W2114969008","https://openalex.org/W2296345941","https://openalex.org/W3101384241","https://openalex.org/W2092091346","https://openalex.org/W4319663681","https://openalex.org/W2247222799","https://openalex.org/W2549903308"],"abstract_inverted_index":{"The":[0],"\"Sum-Over-Paths\"":[1],"formalism":[2],"is":[3,16,20,44,61,67,183],"a":[4,17,31,187],"way":[5],"to":[6,111,120,131,136,165,173],"symbolically":[7],"manipulate":[8],"linear":[9],"maps":[10],"that":[11,19,42,58,105],"describe":[12],"quantum":[13,54,144,193,200],"systems,":[14],"and":[15,40,83,87,116,154,176],"tool":[18],"used":[21,146],"in":[22,114,147,149,186],"formal":[23],"verification":[24],"of":[25,34,53,72,100,124,143,163,178],"such":[26],"systems.":[27],"We":[28,56,75,97,128],"give":[29],"here":[30],"new":[32,126],"set":[33],"rewrite":[35,103,134],"rules":[36],"for":[37,46,139,190],"the":[38,48,59,70,73,79,91,95,101,133,140,150,166],"formalism,":[39],"show":[41,57,89,118,129,171],"it":[43],"complete":[45],"\"Toffoli-Hadamard\",":[47],"simplest":[49],"approximately":[50],"universal":[51],"fragment":[52],"mechanics.":[55],"rewriting":[60],"terminating,":[62],"but":[63,195],"not":[64,184],"confluent":[65],"(which":[66],"expected":[68],"from":[69],"universality":[71],"fragment).":[74],"do":[76],"so":[77],"using":[78],"connection":[80],"between":[81],"Sum-over-Paths":[82],"graphical":[84],"language":[85],"ZH-calculus,":[86],"also":[88],"how":[90,119,130,172],"axiomatisation":[92],"translates":[93],"into":[94],"latter.":[96],"provide":[98],"generalisations":[99],"presented":[102],"rules,":[104],"can":[106],"prove":[107],"useful":[108],"when":[109,197],"trying":[110],"reduce":[112],"terms":[113],"practice,":[115],"we":[117,170],"graphically":[121],"make":[122],"sense":[123],"these":[125],"rules.":[127],"enrich":[132],"system":[135,188],"reach":[137],"completeness":[138],"dyadic":[141,161],"fragments":[142],"computation,":[145,194],"particular":[148],"Quantum":[151],"Fourier":[152],"Transform,":[153],"obtained":[155],"by":[156],"adding":[157],"phase":[158],"gates":[159],"with":[160],"multiples":[162],"$\\pi$":[164],"Toffoli-Hadamard":[167],"gate-set.":[168],"Finally,":[169],"perform":[174],"sums":[175],"concatenation":[177],"arbitrary":[179],"terms,":[180],"something":[181],"which":[182],"native":[185],"designed":[189],"analysing":[191],"gate-based":[192],"necessary":[196],"considering":[198],"Hamiltonian-based":[199],"computation.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2024-03-09T00:00:00"}