{"id":"https://openalex.org/W3032861285","doi":"https://doi.org/10.22331/q-2021-03-15-412","title":"Quantum Circuits for Sparse Isometries","display_name":"Quantum Circuits for Sparse Isometries","publication_year":2021,"publication_date":"2021-03-15","ids":{"openalex":"https://openalex.org/W3032861285","doi":"https://doi.org/10.22331/q-2021-03-15-412","mag":"3032861285"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-03-15-412","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-412","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-412/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-03-15-412/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Emanuel Malvetti","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Emanuel Malvetti","raw_affiliation_strings":["Department of Chemistry, Technische Universit\u00e4t M\u00fcnchen, Lichtenbergstra\u00dfe 4, 85747 Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Technische Universit\u00e4t M\u00fcnchen, Lichtenbergstra\u00dfe 4, 85747 Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Raban Iten","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Raban Iten","raw_affiliation_strings":["ETH Z\u00fcrich, 8093 Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"ETH Z\u00fcrich, 8093 Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":null,"display_name":"Roger Colbeck","orcid":"https://orcid.org/0000-0003-3591-0576"},"institutions":[{"id":"https://openalex.org/I52099693","display_name":"University of York","ror":"https://ror.org/04m01e293","country_code":"GB","type":"education","lineage":["https://openalex.org/I52099693"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Roger Colbeck","raw_affiliation_strings":["Department of Mathematics, University of York, YO10 5DD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of York, YO10 5DD, UK","institution_ids":["https://openalex.org/I52099693"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":3.7789,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.94163106,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"5","issue":null,"first_page":"412","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9742000102996826,"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":0.9742000102996826,"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":0.0052999998442828655,"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":0.0035000001080334187,"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/focus","display_name":"Focus (optics)","score":0.5742999911308289},{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.5604000091552734},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.511900007724762},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5047000050544739},{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.4422999918460846},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.42750000953674316},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.4034999907016754},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.40049999952316284},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.3968000113964081}],"concepts":[{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5742999911308289},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.5604000091552734},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5582000017166138},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.511900007724762},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5047000050544739},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4943000078201294},{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.4422999918460846},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.42750000953674316},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.4034999907016754},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.40049999952316284},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.3517000079154968},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3231000006198883},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.32030001282691956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3109000027179718},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.30219998955726624},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3000999987125397},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.2874000072479248},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.27959999442100525},{"id":"https://openalex.org/C58849907","wikidata":"https://www.wikidata.org/wiki/Q2118982","display_name":"Quantum gate","level":4,"score":0.2689000070095062},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26489999890327454},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.25290000438690186},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.2513999938964844}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2021-03-15-412","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-412","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-412/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.00016","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.00016","pdf_url":"https://arxiv.org/pdf/2006.00016","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":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:461019f564324954922545e780c42c13","is_oa":true,"landing_page_url":"https://doaj.org/article/461019f564324954922545e780c42c13","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 412 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-03-15-412","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-03-15-412","pdf_url":"https://quantum-journal.org/papers/q-2021-03-15-412/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2505040309","display_name":null,"funder_award_id":"EP/M013472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3245899752","display_name":"UK Quantum Technology Hub for Quantum Communications Technologies","funder_award_id":"EP/M013472/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4164594981","display_name":"The EPSRC Quantum Communications Hub","funder_award_id":"EP/T001011/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G87932940","display_name":null,"funder_award_id":"EP/T001011/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8963509774","display_name":null,"funder_award_id":"200020-165843","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3032861285.pdf","grobid_xml":"https://content.openalex.org/works/W3032861285.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1605974080","https://openalex.org/W1749786511","https://openalex.org/W1988900139","https://openalex.org/W2035915021","https://openalex.org/W2046761109","https://openalex.org/W2065516801","https://openalex.org/W2066229005","https://openalex.org/W2092590148","https://openalex.org/W2102008187","https://openalex.org/W2104590612","https://openalex.org/W2146532505","https://openalex.org/W2226110723","https://openalex.org/W2524198841","https://openalex.org/W2746214559","https://openalex.org/W2986416691"],"related_works":[],"abstract_inverted_index":{"We":[0,54,82],"consider":[1],"the":[2,21,49,69,77,85,96],"task":[3],"of":[4,23,51,79,88,98],"breaking":[5],"down":[6],"a":[7,39],"quantum":[8],"computation":[9],"given":[10],"as":[11],"an":[12,63],"isometry":[13,65],"into":[14],"C-NOTs":[15],"and":[16,91],"single-qubit":[17],"gates,":[18],"while":[19],"keeping":[20],"number":[22],"C-NOT":[24],"gates":[25],"small.":[26],"Although":[27],"several":[28],"decompositions":[29],"are":[30],"known":[31],"for":[32],"general":[33],"isometries,":[34],"here":[35],"we":[36],"focus":[37],"on":[38,42],"method":[40,60,70,90],"based":[41],"Householder":[43],"reflections":[44],"that":[45,68],"adapts":[46],"well":[47],"in":[48,76,95],"case":[50,78,97],"sparse":[52,80,99,108],"isometries.":[53,81],"show":[55],"how":[56],"to":[57,61,73,105],"use":[58],"this":[59,89],"decompose":[62],"arbitrary":[64],"before":[66],"illustrating":[67],"can":[71],"lead":[72],"significant":[74],"improvements":[75],"also":[83],"discuss":[84],"classical":[86],"complexity":[87],"illustrate":[92],"its":[93],"effectiveness":[94],"state":[100],"preparation":[101],"by":[102],"applying":[103],"it":[104],"randomly":[106],"chosen":[107],"states.":[109]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2020-06-05T00:00:00"}
