{"id":"https://openalex.org/W4383907991","doi":"https://doi.org/10.22331/q-2023-07-11-1052","title":"\"Proper\" Shift Rules for Derivatives of Perturbed-Parametric Quantum Evolutions","display_name":"\"Proper\" Shift Rules for Derivatives of Perturbed-Parametric Quantum Evolutions","publication_year":2023,"publication_date":"2023-07-11","ids":{"openalex":"https://openalex.org/W4383907991","doi":"https://doi.org/10.22331/q-2023-07-11-1052"},"language":"en","primary_location":{"id":"doi:10.22331/q-2023-07-11-1052","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22331/q-2023-07-11-1052","pdf_url":"https://quantum-journal.org/papers/q-2023-07-11-1052/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2023-07-11-1052/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070611630","display_name":"Dirk Oliver Theis","orcid":"https://orcid.org/0000-0002-9362-0748"},"institutions":[{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE"],"is_corresponding":true,"raw_author_name":"Dirk Oliver Theis","raw_affiliation_strings":["Theoretical Computer Science, University of Tartu, Estonia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science, University of Tartu, Estonia","institution_ids":["https://openalex.org/I56085075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070611630"],"corresponding_institution_ids":["https://openalex.org/I56085075"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.3173,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61537103,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"7","issue":null,"first_page":"1052","last_page":"1052"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9940000176429749,"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/T10382","display_name":"Quantum and electron transport phenomena","score":0.9923999905586243,"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/algorithm","display_name":"Algorithm","score":0.532504677772522},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5009210109710693},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4791007339954376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3824378252029419},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.27650412917137146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24879291653633118}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.532504677772522},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5009210109710693},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4791007339954376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3824378252029419},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27650412917137146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24879291653633118}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2023-07-11-1052","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22331/q-2023-07-11-1052","pdf_url":"https://quantum-journal.org/papers/q-2023-07-11-1052/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:doaj.org/article:5a242c4e3413417b94cd11a25b393e8e","is_oa":true,"landing_page_url":"https://doaj.org/article/5a242c4e3413417b94cd11a25b393e8e","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":"Quantum, Vol 7, p 1052 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2023-07-11-1052","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22331/q-2023-07-11-1052","pdf_url":"https://quantum-journal.org/papers/q-2023-07-11-1052/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/G1737039731","display_name":"Secure Quantum Technology","funder_award_id":"PRG946","funder_id":"https://openalex.org/F4320321090","funder_display_name":"Eesti Teadusagentuur"}],"funders":[{"id":"https://openalex.org/F4320321090","display_name":"Eesti Teadusagentuur","ror":"https://ror.org/00jjeja18"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4383907991.pdf"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W3242376","https://openalex.org/W576816927","https://openalex.org/W1558239788","https://openalex.org/W1568345435","https://openalex.org/W2036655429","https://openalex.org/W2071461214","https://openalex.org/W2227304090","https://openalex.org/W2578080479","https://openalex.org/W2790388700","https://openalex.org/W2794444783","https://openalex.org/W2949954357","https://openalex.org/W2980446414","https://openalex.org/W3027746348","https://openalex.org/W3101122608","https://openalex.org/W3104396616","https://openalex.org/W3125913056","https://openalex.org/W3178013591","https://openalex.org/W3186049801","https://openalex.org/W4226056990","https://openalex.org/W4281561414","https://openalex.org/W4287215222","https://openalex.org/W4289115890","https://openalex.org/W4388747517","https://openalex.org/W6948079120","https://openalex.org/W6948411473","https://openalex.org/W6967142185"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051058708","https://openalex.org/W154868527","https://openalex.org/W1494268238","https://openalex.org/W1983207144","https://openalex.org/W2490706771","https://openalex.org/W2480116122","https://openalex.org/W1976468483","https://openalex.org/W1516574938","https://openalex.org/W2563912921"],"abstract_inverted_index":{"Banchi":[0,71],"&amp;":[1,72],"Crooks":[2],"(Quantum,":[3],"2021)":[4],"have":[5],"given":[6],"methods":[7,37,183],"to":[8,44,68,167,190],"estimate":[9],"derivatives":[10,83],"of":[11,84,88,103,143,151,158,170,177],"expectation":[12,86],"values":[13,87],"depending":[14],"on":[15,140,193],"a":[16,24,93,149],"parameter":[17],"that":[18,47,95,184],"enters":[19],"via":[20],"what":[21],"we":[22,91,131],"call":[23],"\"perturbed\"":[25],"quantum":[26,105,145],"evolution":[27],"<mml:math":[28,55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>x</mml:mi><mml:mo":[29],"stretchy=\"false\">&amp;#x21A6;</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow":[30],"class=\"MJX-TeXAtom-ORD\"><mml:mi>i</mml:mi><mml:mo":[31],"stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:mo":[32],"stretchy=\"false\">)</mml:mo><mml:mrow":[33],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mi":[34],"class=\"MJX-variant\">&amp;#x210F;</mml:mi></mml:mrow></mml:msup></mml:math>.":[35],"Their":[36],"require":[38],"modifications,":[39],"beyond":[40],"merely":[41],"changing":[42],"parameters,":[43,99],"the":[45,51,54,65,82,104,125,133,152,178],"unitaries":[46],"appear.":[48],"Moreover,":[49],"in":[50,148,156,163],"case":[52],"when":[53],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>B</mml:mi></mml:math>-term":[56],"is":[57,113],"unavoidable,":[58],"no":[59,100],"exact":[60,114],"method":[61,74,94,112],"(unbiased":[62],"estimator)":[63],"for":[64,80],"derivative":[66],"seems":[67],"be":[69],"known:":[70],"Crooks's":[73],"gives":[75,117],"an":[76],"approximation.In":[77],"this":[78,89],"paper,":[79],"estimating":[81],"parameterized":[85],"type,":[90],"present":[92],"only":[96],"requires":[97],"shifting":[98],"other":[101],"modifications":[102],"evolutions":[106],"(a":[107],"\"proper\"":[108],"shift":[109,137,154,172],"rule).":[110],"Our":[111],"(i.e.,":[115],"it":[116,123],"analytic":[118],"derivatives,":[119],"unbiased":[120],"estimators),":[121],"and":[122,188],"has":[124],"same":[126],"worst-case":[127],"variance":[128],"as":[129],"Banchi-Crooks's.Moreover,":[130],"discuss":[132],"theory":[134],"surrounding":[135],"proper":[136,153,171],"rules,":[138],"based":[139,192],"Fourier":[141,160],"analysis":[142],"perturbed-parametric":[144],"evolutions,":[146],"resulting":[147],"characterization":[150],"rules":[155,173],"terms":[157],"their":[159],"transforms,":[161],"which":[162],"turn":[164],"leads":[165],"us":[166],"non-existence":[168],"results":[169],"with":[174],"exponential":[175],"concentration":[176],"shifts.":[179],"We":[180],"derive":[181],"truncated":[182],"exhibit":[185],"approximation":[186],"errors,":[187],"compare":[189],"Banchi-Crooks's":[191],"preliminary":[194],"numerical":[195],"simulations.":[196]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
