{"id":"https://openalex.org/W4313471940","doi":"https://doi.org/10.3390/e25010090","title":"Variational Quantum Process Tomography of Non-Unitaries","display_name":"Variational Quantum Process Tomography of Non-Unitaries","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4313471940","doi":"https://doi.org/10.3390/e25010090","pmid":"https://pubmed.ncbi.nlm.nih.gov/36673231"},"language":"en","primary_location":{"id":"doi:10.3390/e25010090","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25010090","pdf_url":"https://www.mdpi.com/1099-4300/25/1/90/pdf?version=1673514098","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/1/90/pdf?version=1673514098","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070693137","display_name":"Shichuan Xue","orcid":null},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shichuan Xue","raw_affiliation_strings":["Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101969072","display_name":"Yizhi Wang","orcid":"https://orcid.org/0000-0002-9232-7523"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yizhi Wang","raw_affiliation_strings":["Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"],"raw_orcid":"https://orcid.org/0000-0002-9232-7523","affiliations":[{"raw_affiliation_string":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100371138","display_name":"Yong Liu","orcid":"https://orcid.org/0000-0003-0523-6816"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Liu","raw_affiliation_strings":["Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101245716","display_name":"Weixu Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weixu Shi","raw_affiliation_strings":["Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090927549","display_name":"Junjie Wu","orcid":"https://orcid.org/0000-0001-5951-8988"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junjie Wu","raw_affiliation_strings":["Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China"],"raw_orcid":"https://orcid.org/0000-0001-5951-8988","affiliations":[{"raw_affiliation_string":"Institute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5090927549"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.994,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.79639896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"25","issue":"1","first_page":"90","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9975000023841858,"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/T11804","display_name":"Quantum many-body systems","score":0.9866999983787537,"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/quantum-tomography","display_name":"Quantum tomography","score":0.7629115581512451},{"id":"https://openalex.org/keywords/quantum-process","display_name":"Quantum process","score":0.6740056276321411},{"id":"https://openalex.org/keywords/quantum-circuit","display_name":"Quantum circuit","score":0.640771746635437},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.608923614025116},{"id":"https://openalex.org/keywords/quantum-machine-learning","display_name":"Quantum machine learning","score":0.5540348291397095},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5300212502479553},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.46356046199798584},{"id":"https://openalex.org/keywords/method-of-quantum-characteristics","display_name":"Method of quantum characteristics","score":0.45478713512420654},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.4463749825954437},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.4448186457157135},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4201088547706604},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.4154358506202698},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3466620445251465},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.19509881734848022}],"concepts":[{"id":"https://openalex.org/C166834278","wikidata":"https://www.wikidata.org/wiki/Q4218494","display_name":"Quantum tomography","level":4,"score":0.7629115581512451},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.6740056276321411},{"id":"https://openalex.org/C124148022","wikidata":"https://www.wikidata.org/wiki/Q2122210","display_name":"Quantum circuit","level":5,"score":0.640771746635437},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.608923614025116},{"id":"https://openalex.org/C2779094486","wikidata":"https://www.wikidata.org/wiki/Q18811578","display_name":"Quantum machine learning","level":4,"score":0.5540348291397095},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5300212502479553},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.46356046199798584},{"id":"https://openalex.org/C99669320","wikidata":"https://www.wikidata.org/wiki/Q6823722","display_name":"Method of quantum characteristics","level":5,"score":0.45478713512420654},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4463749825954437},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.4448186457157135},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4201088547706604},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4154358506202698},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3466620445251465},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.19509881734848022}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25010090","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25010090","pdf_url":"https://www.mdpi.com/1099-4300/25/1/90/pdf?version=1673514098","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:36673231","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36673231","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:0322864a9f334c56a119a08fa0eaeaa5","is_oa":true,"landing_page_url":"https://doaj.org/article/0322864a9f334c56a119a08fa0eaeaa5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 1, p 90 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/1/90/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25010090","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 25; Issue 1; Pages: 90","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9858050","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9858050","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25010090","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25010090","pdf_url":"https://www.mdpi.com/1099-4300/25/1/90/pdf?version=1673514098","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5497429695","display_name":null,"funder_award_id":"62061136011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5679267432","display_name":null,"funder_award_id":"61632021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4313471940.pdf"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W1532834996","https://openalex.org/W1574447377","https://openalex.org/W1598056440","https://openalex.org/W1965928854","https://openalex.org/W1999423794","https://openalex.org/W2008302279","https://openalex.org/W2030467629","https://openalex.org/W2032609902","https://openalex.org/W2049737808","https://openalex.org/W2051669075","https://openalex.org/W2078439793","https://openalex.org/W2090368878","https://openalex.org/W2125882885","https://openalex.org/W2136265395","https://openalex.org/W2140336578","https://openalex.org/W2167614492","https://openalex.org/W2170620327","https://openalex.org/W2482126025","https://openalex.org/W2754868542","https://openalex.org/W2755255888","https://openalex.org/W2811032035","https://openalex.org/W2897579646","https://openalex.org/W2903221501","https://openalex.org/W2915616721","https://openalex.org/W2972223037","https://openalex.org/W2982169647","https://openalex.org/W2989257188","https://openalex.org/W2996599572","https://openalex.org/W3004824513","https://openalex.org/W3020346240","https://openalex.org/W3033312235","https://openalex.org/W3037687232","https://openalex.org/W3096057304","https://openalex.org/W3098268180","https://openalex.org/W3100111077","https://openalex.org/W3101155683","https://openalex.org/W3101479050","https://openalex.org/W3103715576","https://openalex.org/W3104481216","https://openalex.org/W3106331386","https://openalex.org/W3111162498","https://openalex.org/W3132743969","https://openalex.org/W3173713405","https://openalex.org/W3173899054","https://openalex.org/W3176707359","https://openalex.org/W3181153658","https://openalex.org/W3198395576","https://openalex.org/W4221078204","https://openalex.org/W4226128736","https://openalex.org/W6635642861","https://openalex.org/W6652613850"],"related_works":["https://openalex.org/W4221078204","https://openalex.org/W3187574809","https://openalex.org/W4309470286","https://openalex.org/W2331376410","https://openalex.org/W2906136444","https://openalex.org/W2996599572","https://openalex.org/W4297091330","https://openalex.org/W4313471940","https://openalex.org/W4323076536","https://openalex.org/W3176232175"],"abstract_inverted_index":{"Quantum":[0],"process":[1,24,63,80,174,185],"tomography":[2,25,64,186],"is":[3,13,159],"a":[4,60,82],"fundamental":[5],"and":[6,9,34,89,120,145],"critical":[7],"benchmarking":[8],"certification":[10],"tool":[11],"that":[12,134],"capable":[14],"of":[15,32,42,114,125,155,164,170,181],"fully":[16],"characterizing":[17,189],"an":[18,28],"unknown":[19,77],"quantum":[20,23,62,70,79,87,102,118,136,149,173,184],"process.":[21],"Standard":[22],"suffers":[26],"from":[27],"exponentially":[29],"scaling":[30],"number":[31,154],"measurements":[33],"complicated":[35],"data":[36],"post-processing":[37],"due":[38],"to":[39,105],"the":[40,45,68,76,100,111,115,121,126,153,168,171,179,182],"curse":[41],"dimensionality.":[43],"On":[44],"other":[46],"hand,":[47],"non-unitary":[48,78,101,190],"operators":[49],"are":[50],"more":[51],"realistic":[52],"cases.":[53],"In":[54],"this":[55],"work,":[56],"we":[57,94],"put":[58],"forward":[59],"variational":[61,183],"method":[65,97,187],"based":[66],"on":[67],"supervised":[69],"machine":[71],"learning":[72],"framework.":[73],"It":[74],"approximates":[75],"utilizing":[81],"relatively":[83],"shallow":[84,146],"depth":[85,147],"parametric":[86,148],"circuit":[88],"fewer":[90],"input":[91,156],"states.":[92],"Numerically,":[93],"verified":[95],"our":[96],"by":[98],"reconstructing":[99],"mappings":[103],"up":[104],"eight":[106],"qubits":[107],"in":[108,188],"two":[109,162],"cases:":[110],"weighted":[112],"sum":[113],"randomly":[116],"generated":[117],"circuits":[119,150],"imaginary":[122],"time":[123],"evolution":[124],"Heisenberg":[127],"XXZ":[128],"spin":[129],"chain":[130],"Hamiltonian.":[131],"Results":[132],"show":[133],"those":[135],"processes":[137],"could":[138],"be":[139],"reconstructed":[140],"with":[141],"high":[142],"fidelities":[143],"(>99%)":[144],"(d\u22648),":[151],"while":[152],"states":[157],"required":[158],"at":[160],"least":[161],"orders":[163],"magnitude":[165],"less":[166],"than":[167],"demands":[169],"standard":[172],"tomography.":[175],"Our":[176],"work":[177],"shows":[178],"potential":[180],"operators.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}