{"id":"https://openalex.org/W2107957354","doi":null,"title":"Quantum algorithms for approximating the effective resistances of electrical networks.","display_name":"Quantum algorithms for approximating the effective resistances of electrical networks.","publication_year":2013,"publication_date":"2013-11-08","ids":{"openalex":"https://openalex.org/W2107957354","mag":"2107957354"},"language":"en","primary_location":{"id":"mag:2107957354","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1311.1851","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1311.1851","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101477058","display_name":"Guoming Wang","orcid":"https://orcid.org/0000-0003-3131-6916","observed_orcids":["https://orcid.org/0000-0003-3131-6916"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Guoming Wang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-3131-6916","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5101477058"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"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":0.9883000254631042,"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":0.9883000254631042,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.010200000368058681,"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/T11476","display_name":"Graph theory and applications","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-algorithms","display_name":"quantum algorithms","score":0.972000002861023},{"id":"https://openalex.org/keywords/effective-resistance","display_name":"effective resistance","score":0.9890000224113464},{"id":"https://openalex.org/keywords/electrical-networks","display_name":"electrical networks","score":0.9950000047683716},{"id":"https://openalex.org/keywords/electrical-flow","display_name":"electrical flow","score":0.7549999952316284},{"id":"https://openalex.org/keywords/graph-expansion","display_name":"graph expansion","score":0.8240000009536743},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.699999988079071},{"id":"https://openalex.org/keywords/approximation-algorithms","display_name":"approximation algorithms","score":0.5220000147819519},{"id":"https://openalex.org/keywords/graph-laplacian","display_name":"graph Laplacian","score":0.6100000143051147}],"concepts":[{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6445127129554749},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.5515605211257935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5262462496757507},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5118746161460876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46581152081489563},{"id":"https://openalex.org/C196796808","wikidata":"https://www.wikidata.org/wiki/Q132629","display_name":"Electrical network","level":2,"score":0.4634515941143036},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4469345510005951},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4450991749763489},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4388716220855713},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.43623432517051697},{"id":"https://openalex.org/C157469704","wikidata":"https://www.wikidata.org/wiki/Q2585642","display_name":"Maximum flow problem","level":2,"score":0.4332149028778076},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.415849506855011},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40154707431793213},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34434592723846436},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1302889883518219},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12786653637886047},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"mag:2107957354","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1311.1851","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.767.3463","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.767.3463","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1311.1851.pdf","raw_type":"text"}],"best_oa_location":{"id":"mag:2107957354","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1311.1851","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W127744604","https://openalex.org/W1485224727","https://openalex.org/W1492999010","https://openalex.org/W1537532043","https://openalex.org/W1561344775","https://openalex.org/W1564709644","https://openalex.org/W1576866980","https://openalex.org/W1578099820","https://openalex.org/W1741741009","https://openalex.org/W1751325145","https://openalex.org/W1980669364","https://openalex.org/W1985671429","https://openalex.org/W2009281933","https://openalex.org/W2045107949","https://openalex.org/W2048572907","https://openalex.org/W2079692740","https://openalex.org/W2084652510","https://openalex.org/W2098948451","https://openalex.org/W2109154425","https://openalex.org/W2109882328","https://openalex.org/W2121981260","https://openalex.org/W2122780600","https://openalex.org/W2125664420","https://openalex.org/W2128550154","https://openalex.org/W2133352257","https://openalex.org/W2153441719","https://openalex.org/W2156652176","https://openalex.org/W2962738101","https://openalex.org/W3101636216"],"related_works":["https://openalex.org/W2963277272","https://openalex.org/W4383468647","https://openalex.org/W4401587585","https://openalex.org/W2949753501","https://openalex.org/W4410119152","https://openalex.org/W4287123691","https://openalex.org/W4225508562","https://openalex.org/W2796365873","https://openalex.org/W4379115809","https://openalex.org/W4297688350"],"abstract_inverted_index":{"The":[0],"theory":[1],"of":[2,64,88,106,113,120,132,221,237,242,258],"electrical":[3,24,28,85,212],"network":[4],"has":[5],"many":[6],"applications":[7],"in":[8,83,94,273],"algorithm":[9,202],"design":[10],"and":[11,30,51,99,135,145,149],"analysis.":[12],"It":[13,263],"is":[14,61,103,109,117,129,137,151,161,185,264],"an":[15,84],"important":[16],"task":[17],"to":[18,38,45,123,210,232],"compute":[19,39],"the":[20,52,62,76,104,110,114,118,121,124,130,133,138,176,180,211,234,247,250,256,259],"basic":[21],"quantities":[22],"about":[23],"networks,":[25],"such":[26],"as":[27,33,35,197],"flows":[29],"effective":[31,77],"resistances,":[32],"quickly":[34],"possible.":[36],"Classically,":[37],"these":[40],"quantities,":[41],"one":[42,241],"basically":[43],"need":[44],"solve":[46,167],"a":[47,188,198,205],"Laplacian":[48,248],"linear":[49],"system,":[50],"best":[53],"known":[54],"algorithms":[55,73,154,165,191,225,269],"take":[56],"O\u0303(m)":[57],"time,":[58],"where":[59,101],"m":[60],"number":[63,105],"edges.":[65],"In":[66,141,158],"this":[67,168],"paper,":[68],"we":[69,173],"present":[70],"two":[71,81,216],"quantum":[72,206,230,268],"for":[74],"approximating":[75],"resistance":[78],"between":[79,214],"any":[80,215],"vertices":[82],"network.":[86],"Both":[87],"them":[89,243],"have":[90],"time":[91],"complexity":[92],"polynomial":[93,177],"logn,":[95],"d,":[96],"c,":[97],"1/\u03c6":[98],"1/\u03b5,":[100],"n":[102],"vertices,":[107,115,217],"d":[108,144],"maximum":[111],"degree":[112],"c":[116,146],"ratio":[119],"largest":[122],"smallest":[125],"edge":[126],"resistance,":[127],"\u03c6":[128,150],"expansion":[131,182],"network,":[134],"\u03b5":[136],"relative":[139],"error.":[140],"particular,":[142],"when":[143],"are":[147,226],"small":[148],"large,":[152],"our":[153,190,200],"run":[155],"very":[156,170],"fast.":[157,171],"contrast,":[159],"it":[160],"unknown":[162],"whether":[163],"classical":[164],"can":[166,270],"case":[169],"Furthermore,":[172],"prove":[174],"that":[175,266],"dependence":[178],"on":[179,228,245,253],"inverse":[181],"(i.e.":[183],"1/\u03c6)":[184],"necessary.":[186],"As":[187],"consequence,":[189],"cannot":[192],"be":[193,220,271],"significantly":[194],"improved.":[195],"Finally,":[196],"by-product,":[199],"second":[201],"also":[203],"produces":[204],"state":[207],"approximately":[208],"proportional":[209],"flow":[213],"which":[218],"might":[219],"independent":[222],"interest.":[223],"Our":[224],"based":[227],"using":[229],"tools":[231],"analyze":[233],"algebraic":[235],"properties":[236],"graph-related":[238],"matrices.":[239],"While":[240],"relies":[244,252],"inverting":[246],"matrix,":[249],"other":[251],"projecting":[254],"onto":[255],"kernel":[257],"weighted":[260],"incidence":[261],"matrix.":[262],"hopeful":[265],"more":[267],"developed":[272],"similar":[274],"way.":[275],"1":[276]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}