{"id":"https://openalex.org/W7214736964","doi":"https://doi.org/10.48550/arxiv.2609.35239","title":"Computational Complexity of Clifford Template Compilation: Are Quantum Computers Useful for Compiling Quantum Circuits?","display_name":"Computational Complexity of Clifford Template Compilation: Are Quantum Computers Useful for Compiling Quantum Circuits?","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214736964","doi":"https://doi.org/10.48550/arxiv.2609.35239"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35239","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35239","pdf_url":"https://arxiv.org/pdf/2609.35239","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/2609.35239","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128537637","display_name":"Keisuke Fujii","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fujii, Keisuke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5128537637"],"corresponding_institution_ids":[],"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-compilation","display_name":"quantum circuit compilation","score":0.781000018119812},{"id":"https://openalex.org/keywords/computational-complexity","display_name":"computational complexity","score":0.9380000233650208},{"id":"https://openalex.org/keywords/np-completeness","display_name":"NP-completeness","score":0.9539999961853027},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":0.6069999933242798},{"id":"https://openalex.org/keywords/logical-operations","display_name":"logical operations","score":0.6980000138282776},{"id":"https://openalex.org/keywords/pauli-operators","display_name":"Pauli operators","score":0.7350000143051147},{"id":"https://openalex.org/keywords/cnot-gate","display_name":"CNOT gate","score":0.6039999723434448},{"id":"https://openalex.org/keywords/classical-simulation-of-quantum-circuits","display_name":"classical simulation of quantum circuits","score":0.5}],"concepts":[{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5888000130653381},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.5533999800682068},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5281999707221985},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4925000071525574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44999998807907104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44769999384880066},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4426000118255615},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.39809998869895935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39750000834465027},{"id":"https://openalex.org/C2776141515","wikidata":"https://www.wikidata.org/wiki/Q1274479","display_name":"Repetition (rhetorical device)","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35269999504089355},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.34689998626708984},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.3262999951839447},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3237000107765198},{"id":"https://openalex.org/C177547823","wikidata":"https://www.wikidata.org/wiki/Q5133083","display_name":"Clifford analysis","level":3,"score":0.3086000084877014},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C180347388","wikidata":"https://www.wikidata.org/wiki/Q336233","display_name":"Pauli matrices","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C108277079","wikidata":"https://www.wikidata.org/wiki/Q7233576","display_name":"Post-quantum cryptography","level":4,"score":0.29109999537467957},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C82714645","wikidata":"https://www.wikidata.org/wiki/Q438331","display_name":"Template","level":2,"score":0.2770000100135803},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.2667999863624573},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.25049999356269836},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35239","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35239","pdf_url":"https://arxiv.org/pdf/2609.35239","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.2609.35239","doi":"https://doi.org/10.48550/arxiv.2609.35239","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35239","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:2609.35239","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35239","pdf_url":"https://arxiv.org/pdf/2609.35239","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":[{"id":"https://openalex.org/G4627739467","display_name":null,"funder_award_id":"JP-MXS0120319794","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"},{"id":"https://openalex.org/G5567475573","display_name":null,"funder_award_id":"JPMJPF2014","funder_id":"https://openalex.org/F4320320912","funder_display_name":"Ministry of Education, Culture, Sports, Science and Technology"},{"id":"https://openalex.org/G6938554167","display_name":null,"funder_award_id":"JPMJCR24I3","funder_id":"https://openalex.org/F4320338075","funder_display_name":"Core Research for Evolutional Science and Technology"},{"id":"https://openalex.org/G7570018266","display_name":null,"funder_award_id":"JPMJMS256E","funder_id":"https://openalex.org/F4320338247","funder_display_name":"Moonshot Research and Development Program"}],"funders":[{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"},{"id":"https://openalex.org/F4320338247","display_name":"Moonshot Research and Development Program","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214736964.pdf","grobid_xml":"https://content.openalex.org/works/W7214736964.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1839785972","https://openalex.org/W2104590612","https://openalex.org/W7128646311"],"related_works":["https://openalex.org/W3158389508","https://openalex.org/W2346289635","https://openalex.org/W7203861086","https://openalex.org/W7164254884","https://openalex.org/W4387797758","https://openalex.org/W7097868522","https://openalex.org/W4405254759","https://openalex.org/W7095263182","https://openalex.org/W7216421547","https://openalex.org/W4406261588"],"abstract_inverted_index":{"A":[0],"Clifford":[1,10,24,62,72,154,191],"template":[2,25,38,192],"is":[3,21,74,177],"a":[4,40,97,102,170,186],"finite":[5],"ordered":[6],"family":[7],"of":[8,43,161],"repeatable":[9],"operations,":[11],"and":[12,96,135,148,159,203],"an":[13],"instantiation":[14],"specifies":[15],"how":[16,29],"many":[17],"times":[18],"each":[19],"operation":[20],"applied.":[22],"The":[23],"compilation":[26],"problem":[27,47,80],"asks":[28],"to":[30,129],"choose":[31],"these":[32],"repetition":[33,116,175],"numbers":[34],"so":[35],"that":[36],"the":[37,107,115,132,173],"realizes":[39],"target":[41],"transformation":[42],"Pauli":[44],"operators.":[45],"This":[46],"arises,":[48],"for":[49,53,139,143,180],"example,":[50],"when":[51],"searching":[52],"logical":[54],"operations":[55,63,147],"in":[56,94],"quantum":[57,99,200],"error":[58],"correction":[59],"using":[60],"only":[61],"permitted":[64],"by":[65],"physical":[66],"or":[67],"fault-tolerance":[68],"constraints.":[69],"Although":[70],"forward":[71],"dynamics":[73],"efficiently":[75],"classically":[76,165,195],"simulable,":[77],"this":[78],"inverse":[79],"has":[81],"sharp":[82],"complexity":[83,188],"transitions.":[84],"For":[85,151],"commuting":[86,145,152],"templates":[87],"with":[88,106],"unrestricted":[89],"integer":[90],"exponents,":[91],"feasibility":[92,137,158],"lies":[93],"$\\mathrm{NP}\\cap\\mathrm{BQP}$":[95],"constructive":[98],"algorithm":[100],"returns":[101],"particular":[103],"solution":[104,163],"together":[105],"full":[108],"exponent-relation":[109],"lattice;":[110],"already":[111],"at":[112],"$k=1$,":[113],"recovering":[114],"number":[117],"contains":[118],"finite-field":[119],"discrete":[120],"logarithm":[121],"over":[122],"$\\mathbb{F}_{2^r}^{\\times}$.":[123],"In":[124],"general,":[125],"restricting":[126],"every":[127],"exponent":[128],"$\\{0,1\\}$":[130],"removes":[131],"Abelian-group":[133],"closure":[134],"makes":[136],"NP-complete":[138,204],"variable":[140],"$k$,":[141],"even":[142,179],"exactly":[144],"CNOT-only":[146,181],"X-type":[149],"Paulis.":[150],"self-inverse":[153],"actions,":[155],"both":[156],"binary":[157],"recovery":[160],"one":[162],"are":[164],"polynomial-time":[166,201],"solvable,":[167],"but":[168],"imposing":[169],"bound":[171],"on":[172],"total":[174],"count":[176],"NP-complete,":[178],"operations.":[182],"These":[183],"results":[184],"reveal":[185],"rich":[187],"landscape":[189],"within":[190],"compilation,":[193],"spanning":[194],"tractable":[196],"cases,":[197],"problems":[198],"admitting":[199],"algorithms,":[202],"variants.":[205]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}