{"id":"https://openalex.org/W7225810393","doi":"https://doi.org/10.26434/chemrxiv.15011974/v1","title":"Gradient ascent pulse engineering (GRAPE)\u2013a primer on quality functions and pulse shape penalties","display_name":"Gradient ascent pulse engineering (GRAPE)\u2013a primer on quality functions and pulse shape penalties","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225810393","doi":"https://doi.org/10.26434/chemrxiv.15011974/v1"},"language":"en","primary_location":{"id":"doi:10.26434/chemrxiv.15011974/v1","doi":"https://doi.org/10.26434/chemrxiv.15011974/v1","is_oa":true,"landing_page_url":"https://doi.org/10.26434/chemrxiv.15011974/v1","pdf_url":null,"source":{"id":"https://openalex.org/S4393918830","display_name":"ChemRxiv","issn_l":"2573-2293","issn":["2573-2293"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.26434/chemrxiv.15011974/v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060704531","display_name":"Armin J. R\u00f6mer","orcid":"https://orcid.org/0009-0001-8498-8452","observed_orcids":["https://orcid.org/0009-0001-8498-8452"]},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Armin J. R\u00f6mer","raw_affiliation_strings":["Institute of Energy Technologies (IET-1), Forschungszentrum J\u00fclich GmbH, J\u00fclich, Germany","Institute of Technical and Macromolecular Chemistry, RWTH Aachen University, Aachen, Germany"],"raw_orcid":"https://orcid.org/0009-0001-8498-8452","affiliations":[{"raw_affiliation_string":"Institute of Energy Technologies (IET-1), Forschungszentrum J\u00fclich GmbH, J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]},{"raw_affiliation_string":"Institute of Technical and Macromolecular Chemistry, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029944987","display_name":"Josef Granwehr","orcid":"https://orcid.org/0000-0002-9307-1101","observed_orcids":["https://orcid.org/0000-0002-9307-1101"]},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Josef Granwehr","raw_affiliation_strings":["Institute of Energy Technologies (IET-1), Forschungszentrum J\u00fclich GmbH, J\u00fclich, Germany","Institute of Technical and Macromolecular Chemistry, RWTH Aachen University, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Energy Technologies (IET-1), Forschungszentrum J\u00fclich GmbH, J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]},{"raw_affiliation_string":"Institute of Technical and Macromolecular Chemistry, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031236316","display_name":"S. Kocher","orcid":"https://orcid.org/0000-0001-9501-1703","observed_orcids":["https://orcid.org/0000-0001-9501-1703"]},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]},{"id":"https://openalex.org/I2800875726","display_name":"Fritz Haber Institute of the Max Planck Society","ror":"https://ror.org/03k9qs827","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I2800875726"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Simone S. K\u00f6cher","raw_affiliation_strings":["Fritz Haber Institute of the Max Planck Society","Institute of Energy Technologies (IET-1), Forschungszentrum J\u00fclich GmbH, J\u00fclich, Germany"],"raw_orcid":"https://orcid.org/0000-0001-9501-1703","affiliations":[{"raw_affiliation_string":"Fritz Haber Institute of the Max Planck Society","institution_ids":["https://openalex.org/I2800875726"]},{"raw_affiliation_string":"Institute of Energy Technologies (IET-1), Forschungszentrum J\u00fclich GmbH, J\u00fclich, Germany","institution_ids":["https://openalex.org/I171892758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.7064999938011169,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.7064999938011169,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.11169999837875366,"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":0.042399998754262924,"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":[],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8278999924659729},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6775000095367432},{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.5605999827384949},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5256999731063843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46639999747276306},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.45879998803138733},{"id":"https://openalex.org/C2984281365","wikidata":"https://www.wikidata.org/wiki/Q906781","display_name":"Quantum control","level":3,"score":0.45660001039505005},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.4066999852657318},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.39570000767707825},{"id":"https://openalex.org/C2909374376","wikidata":"https://www.wikidata.org/wiki/Q2726733","display_name":"Nanodevice","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33799999952316284},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32899999618530273},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29919999837875366},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28369998931884766},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C182155053","wikidata":"https://www.wikidata.org/wiki/Q7259682","display_name":"Pulse sequence","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2711000144481659},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2667999863624573},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.25940001010894775}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.26434/chemrxiv.15011974/v1","doi":"https://doi.org/10.26434/chemrxiv.15011974/v1","is_oa":true,"landing_page_url":"https://doi.org/10.26434/chemrxiv.15011974/v1","pdf_url":null,"source":{"id":"https://openalex.org/S4393918830","display_name":"ChemRxiv","issn_l":"2573-2293","issn":["2573-2293"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.26434/chemrxiv.15011974/v1","doi":"https://doi.org/10.26434/chemrxiv.15011974/v1","is_oa":true,"landing_page_url":"https://doi.org/10.26434/chemrxiv.15011974/v1","pdf_url":null,"source":{"id":"https://openalex.org/S4393918830","display_name":"ChemRxiv","issn_l":"2573-2293","issn":["2573-2293"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"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],"optimal":[1,16],"control":[2,17],"is":[3,98,152],"a":[4],"versatile,":[5],"powerful":[6],"method":[7],"to":[8,72,112,132],"tailor":[9],"quantum":[10,15,84],"experiments.":[11],"In":[12],"NMR,":[13],"numerical":[14],"algorithms":[18],"such":[19],"as":[20,121],"the":[21,36,52,62,74,101,113,128,158],"gradient":[22,89,145],"ascent":[23],"pulse":[24,33,39],"engineering":[25],"(GRAPE)":[26],"algorithm":[27],"have":[28],"sparked":[29],"many":[30,53],"developments":[31],"in":[32,69],"shaping,":[34],"pushing":[35],"limits":[37],"of":[38,47,88],"selectivity":[40],"and":[41,51,82,90,103,146],"robustness.":[42],"To":[43],"provide":[44],"an":[45],"overview":[46],"its":[48,60],"core":[49],"principles":[50],"expansions":[54],"it":[55],"has":[56],"undergone":[57],"ever":[58],"since":[59],"introduction,":[61],"most":[63,129,159],"common":[64,130],"quality":[65],"functions":[66],"are":[67,93,139],"benchmarked":[68],"their":[70,143],"ability":[71],"guide":[73,133],"spin":[75,116,125],"state":[76],"transfer":[77],"for":[78,157],"facilitating":[79],"excitation,":[80],"inversion,":[81],"maximum":[83],"coherence.":[85],"Explicit":[86],"derivations":[87,107],"Hessian":[91,147],"formulas":[92],"given,":[94],"both":[95],"summarizing":[96],"what":[97],"known":[99],"from":[100],"literature":[102],"complementing":[104],"it.":[105],"The":[106,150],"also":[108],"give":[109],"due":[110],"consideration":[111],"fact":[114],"that":[115],"states":[117],"can":[118],"be":[119],"represented":[120],"density":[122],"operators":[123],"or":[124],"operators.":[126],"Analogously,":[127],"penalties":[131],"optimization":[134,162],"toward":[135],"experimentally":[136],"feasible":[137],"controls":[138],"discussed":[140],"along":[141],"with":[142],"explicit":[144],"formula":[148],"derivations.":[149],"discussion":[151],"complemented":[153],"by":[154],"thorough":[155],"benchmarking":[156],"commonly":[160],"used":[161],"algorithms.":[163]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}