{"id":"https://openalex.org/W4415594455","doi":"https://doi.org/10.1109/tc.2025.3625044","title":"Solving the Subset Sum Problem via Quantum Walk Search","display_name":"Solving the Subset Sum Problem via Quantum Walk Search","publication_year":2025,"publication_date":"2025-10-27","ids":{"openalex":"https://openalex.org/W4415594455","doi":"https://doi.org/10.1109/tc.2025.3625044"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2025.3625044","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tc.2025.3625044","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/tc.2025.3625044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114554055","display_name":"Giacomo Lancellotti","orcid":"https://orcid.org/0009-0005-0405-6073"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giacomo Lancellotti","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy"],"raw_orcid":"https://orcid.org/0009-0005-0405-6073","affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003443971","display_name":"Simone Perriello","orcid":"https://orcid.org/0000-0001-9656-7252"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simone Perriello","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy"],"raw_orcid":"https://orcid.org/0000-0001-9656-7252","affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061596244","display_name":"Alessandro Barenghi","orcid":"https://orcid.org/0000-0003-0840-6358"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandro Barenghi","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy"],"raw_orcid":"https://orcid.org/0000-0003-0840-6358","affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059940813","display_name":"Gerardo Pelosi","orcid":"https://orcid.org/0000-0002-3812-5429"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gerardo Pelosi","raw_affiliation_strings":["Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3812-5429","affiliations":[{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering, Politecnico di Milano, Italy","institution_ids":["https://openalex.org/I93860229"]},{"raw_affiliation_string":"Department of Electronics, Information and Bioengineering of Politecnico di Milano, MI, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":1.396,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86703395,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"75","issue":"1","first_page":"164","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9592000246047974,"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":0.9592000246047974,"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/quantum-walk","display_name":"Quantum walk","score":0.6668000221252441},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6226000189781189},{"id":"https://openalex.org/keywords/quadratic-unconstrained-binary-optimization","display_name":"Quadratic unconstrained binary optimization","score":0.6191999912261963},{"id":"https://openalex.org/keywords/bidirectional-search","display_name":"Bidirectional search","score":0.604200005531311},{"id":"https://openalex.org/keywords/search-algorithm","display_name":"Search algorithm","score":0.5791000127792358},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.5394999980926514},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.5351999998092651},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.5266000032424927},{"id":"https://openalex.org/keywords/search-problem","display_name":"Search problem","score":0.5026999711990356},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4343999922275543}],"concepts":[{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.6668000221252441},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6226000189781189},{"id":"https://openalex.org/C177179195","wikidata":"https://www.wikidata.org/wiki/Q7268372","display_name":"Quadratic unconstrained binary optimization","level":4,"score":0.6191999912261963},{"id":"https://openalex.org/C831591","wikidata":"https://www.wikidata.org/wiki/Q59750","display_name":"Bidirectional search","level":5,"score":0.604200005531311},{"id":"https://openalex.org/C125583679","wikidata":"https://www.wikidata.org/wiki/Q755673","display_name":"Search algorithm","level":2,"score":0.5791000127792358},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.5394999980926514},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5351999998092651},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.5266000032424927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.51910001039505},{"id":"https://openalex.org/C201789804","wikidata":"https://www.wikidata.org/wiki/Q2362762","display_name":"Search problem","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4343999922275543},{"id":"https://openalex.org/C46011968","wikidata":"https://www.wikidata.org/wiki/Q830527","display_name":"Best-first search","level":4,"score":0.43369999527931213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4235000014305115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4187999963760376},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3959999978542328},{"id":"https://openalex.org/C139979381","wikidata":"https://www.wikidata.org/wiki/Q17056021","display_name":"Incremental heuristic search","level":4,"score":0.39559999108314514},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.38929998874664307},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.385699987411499},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.3756999969482422},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C204259536","wikidata":"https://www.wikidata.org/wiki/Q787903","display_name":"Linear search","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3140999972820282},{"id":"https://openalex.org/C109275537","wikidata":"https://www.wikidata.org/wiki/Q1154420","display_name":"Subset sum problem","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C19889080","wikidata":"https://www.wikidata.org/wiki/Q2835852","display_name":"Beam search","level":3,"score":0.2870999872684479},{"id":"https://openalex.org/C121610932","wikidata":"https://www.wikidata.org/wiki/Q243754","display_name":"Binary search algorithm","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C165526019","wikidata":"https://www.wikidata.org/wiki/Q942557","display_name":"Maximum cut","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.25540000200271606},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.25459998846054077},{"id":"https://openalex.org/C115874739","wikidata":"https://www.wikidata.org/wiki/Q825377","display_name":"Critical path method","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tc.2025.3625044","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tc.2025.3625044","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/1300687","is_oa":true,"landing_page_url":"https://hdl.handle.net/11311/1300687","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1109/tc.2025.3625044","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tc.2025.3625044","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Quantum":[0],"walk-based":[1],"search":[2,13,18,23,56,144,177],"algorithms":[3,178],"have":[4],"demonstrated":[5],"an":[6],"asymptotic":[7],"quadratic":[8],"speedup":[9],"compared":[10],"to":[11,33],"classical":[12],"methods.":[14],"Formulating":[15],"a":[16,21,25,49,53,70,84,110,147,167],"generic":[17],"problem":[19,73,114],"as":[20,109,166],"(quantum)":[22],"over":[24],"graph":[26,42],"makes":[27],"the":[28,31,38,41,63,66,113,139,150,172,187],"efficiency":[29],"of":[30,40,52,65,87,95,107,112,149,154,174],"algorithm":[32],"be":[34,181],"closely":[35],"dependent":[36],"on":[37,58,130,152,183],"properties":[39],"itself.":[43],"In":[44],"this":[45],"work,":[46],"we":[47],"present":[48],"complete":[50],"implementation":[51],"quantum":[54,143,176],"walk":[55],"procedure":[57],"Johnson":[59,184],"graphs,":[60,185],"speeding":[61],"up":[62],"solution":[64],"Subset":[67],"Sum":[68],"Problem,":[69],"well-known":[71],"computational":[72],"with":[74,189],"applications":[75],"in":[76,93],"resource":[77],"allocation,":[78],"scheduling,":[79],"and":[80,100,103,127,156],"cryptanalysis.":[81],"We":[82,134],"provide":[83],"detailed":[85],"design":[86,164],"each":[88],"sub-circuit,":[89],"quantifying":[90],"their":[91],"costs":[92],"terms":[94,153],"gate":[96],"count,":[97],"circuit":[98,132],"depth,":[99],"qubit":[101,125],"width,":[102],"exhibit":[104],"all":[105],"figures":[106],"merit":[108],"function":[111],"parameters.":[115],"Our":[116],"approach":[117],"includes":[118],"two":[119],"distinct":[120],"implementations:":[121],"one":[122],"that":[123,179],"minimizes":[124],"usage":[126],"another":[128],"focused":[129],"optimizing":[131],"depth.":[133],"compare":[135],"our":[136],"solutions":[137],"against":[138],"unstructured":[140],"Grover":[141],"based":[142],"algorithm,":[145],"demonstrating":[146],"reduction":[148],"cost":[151],"T-count":[155],"T-depth,":[157],"for":[158,171],"practically":[159],"solvable":[160],"instances.":[161],"The":[162],"proposed":[163],"serves":[165],"foundational":[168],"building":[169],"block":[170],"development":[173],"efficient":[175],"can":[180],"modeled":[182],"bridging":[186],"gap":[188],"existing":[190],"theoretical":[191],"complexity":[192],"analyses.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-12-12T23:16:27.785689","created_date":"2025-10-28T00:00:00"}