Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W4312441879', 'doi': 'https://doi.org/10.2139/ssrn.4236129', 'title': 'Time Complexity Analysis of Quantum Algorithms Via Linear Representations For Nonlinear Ordinary and Partial Differential Equations', 'display_name': 'Time Complexity Analysis of Quantum Algorithms Via Linear Representations For Nonlinear Ordinary and Partial Differential Equations', 'publication_year': 2022, 'publication_date': '2022-01-01', 'ids': {'openalex': 'https://openalex.org/W4312441879', 'doi': 'https://doi.org/10.2139/ssrn.4236129'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.2139/ssrn.4236129', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210172589', 'display_name': 'SSRN Electronic Journal', 'issn_l': '1556-5068', 'issn': ['1556-5068'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1318003438', 'host_organization_name': 'RELX Group (Netherlands)', 'host_organization_lineage': ['https://openalex.org/I1318003438'], 'host_organization_lineage_names': ['RELX Group (Netherlands)'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'http://arxiv.org/pdf/2209.08478', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5013079905', 'display_name': 'Shi Jin', 'orcid': 'https://orcid.org/0000-0003-0271-6021'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Jin, Shi', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5100645625', 'display_name': 'Nana Liu', 'orcid': 'https://orcid.org/0000-0002-8121-1744'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Liu, Nana', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5100397941', 'display_name': 'Yue Yu', 'orcid': 'https://orcid.org/0000-0001-5685-0117'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Yu, Yue', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.486, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 4, 'citation_normalized_percentile': {'value': 0.685436, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 80, 'max': 83}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10682', 'display_name': 'Quantum Computing Algorithms and Architecture', 'score': 0.9951, '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': 0.9951, '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': 0.9702, '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/T10622', 'display_name': 'Quantum Mechanics and Applications', 'score': 0.9365, '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/exponential-integrator', 'display_name': 'Exponential integrator', 'score': 0.41096267}], 'concepts': [{'id': 'https://openalex.org/C93779851', 'wikidata': 'https://www.wikidata.org/wiki/Q271977', 'display_name': 'Partial differential equation', 'level': 2, 'score': 0.54993874}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.5471016}, {'id': 'https://openalex.org/C51544822', 'wikidata': 'https://www.wikidata.org/wiki/Q465274', 'display_name': 'Ordinary differential equation', 'level': 3, 'score': 0.5027895}, {'id': 'https://openalex.org/C158622935', 'wikidata': 'https://www.wikidata.org/wiki/Q660848', 'display_name': 'Nonlinear system', 'level': 2, 'score': 0.50172424}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.47633415}, {'id': 'https://openalex.org/C122700484', 'wikidata': 'https://www.wikidata.org/wiki/Q16148845', 'display_name': 'Exponential integrator', 'level': 5, 'score': 0.41096267}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.393912}, {'id': 'https://openalex.org/C28826006', 'wikidata': 'https://www.wikidata.org/wiki/Q33521', 'display_name': 'Applied mathematics', 'level': 1, 'score': 0.3473838}, {'id': 'https://openalex.org/C78045399', 'wikidata': 'https://www.wikidata.org/wiki/Q11214', 'display_name': 'Differential equation', 'level': 2, 'score': 0.25022563}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.24962547}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.22662914}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.15016714}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.14763111}, {'id': 'https://openalex.org/C186219872', 'wikidata': 'https://www.wikidata.org/wiki/Q955889', 'display_name': 'Differential algebraic equation', 'level': 4, 'score': 0.12608898}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.2139/ssrn.4236129', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4210172589', 'display_name': 'SSRN Electronic Journal', 'issn_l': '1556-5068', 'issn': ['1556-5068'], 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1318003438', 'host_organization_name': 'RELX Group (Netherlands)', 'host_organization_lineage': ['https://openalex.org/I1318003438'], 'host_organization_lineage_names': ['RELX Group (Netherlands)'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/2209.08478', 'pdf_url': 'http://arxiv.org/pdf/2209.08478', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/2209.08478', 'pdf_url': 'http://arxiv.org/pdf/2209.08478', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 62, 'referenced_works': ['https://openalex.org/W1492999010', 'https://openalex.org/W1555627060', 'https://openalex.org/W1563019883', 'https://openalex.org/W1566819357', 'https://openalex.org/W1871899311', 'https://openalex.org/W187557541', 'https://openalex.org/W1964694549', 'https://openalex.org/W1994388250', 'https://openalex.org/W1998217267', 'https://openalex.org/W2001888406', 'https://openalex.org/W2037291088', 'https://openalex.org/W2041506125', 'https://openalex.org/W2050334794', 'https://openalex.org/W2051247278', 'https://openalex.org/W2069525126', 'https://openalex.org/W2083916485', 'https://openalex.org/W2096334625', 'https://openalex.org/W2346499024', 'https://openalex.org/W2761673598', 'https://openalex.org/W2770725152', 'https://openalex.org/W2902420940', 'https://openalex.org/W2937013510', 'https://openalex.org/W2962907934', 'https://openalex.org/W3003292238', 'https://openalex.org/W3008698147', 'https://openalex.org/W3010833233', 'https://openalex.org/W3012790144', 'https://openalex.org/W3040128945', 'https://openalex.org/W3098280028', 'https://openalex.org/W3101151619', 'https://openalex.org/W3102764375', 'https://openalex.org/W3103487277', 'https://openalex.org/W3103800805', 'https://openalex.org/W3103836757', 'https://openalex.org/W3104433882', 'https://openalex.org/W3104901447', 'https://openalex.org/W3105798535', 'https://openalex.org/W3111297213', 'https://openalex.org/W3128324875', 'https://openalex.org/W3130923323', 'https://openalex.org/W3170298122', 'https://openalex.org/W3198880747', 'https://openalex.org/W3212990387', 'https://openalex.org/W3215685676', 'https://openalex.org/W4200633982', 'https://openalex.org/W4221152681', 'https://openalex.org/W4221153315', 'https://openalex.org/W4221159723', 'https://openalex.org/W4242279564', 'https://openalex.org/W4283013854', 'https://openalex.org/W4287599531', 'https://openalex.org/W4296984701', 'https://openalex.org/W4297199308', 'https://openalex.org/W4297958736', 'https://openalex.org/W4304782780', 'https://openalex.org/W4308827976', 'https://openalex.org/W4313304448', 'https://openalex.org/W4313447505', 'https://openalex.org/W4318979654', 'https://openalex.org/W4320485281', 'https://openalex.org/W4327942886', 'https://openalex.org/W4400486058'], 'related_works': ['https://openalex.org/W77016536', 'https://openalex.org/W4392238179', 'https://openalex.org/W3196497253', 'https://openalex.org/W3164276969', 'https://openalex.org/W3146600122', 'https://openalex.org/W2999616507', 'https://openalex.org/W2979449540', 'https://openalex.org/W2148488327', 'https://openalex.org/W2118964038', 'https://openalex.org/W1979864573'], 'abstract_inverted_index': {'Download': [0, 323], 'This': [1, 324, 469], 'Paper': [2, 8, 325, 347, 399, 411], 'Open': [3, 326], 'PDF': [4, 327], 'in': [5, 186, 328, 375, 416, 475], 'Browser': [6, 329], 'Add': [7], 'to': [9, 20, 57, 62, 67, 74, 195, 287, 300, 315, 340, 358, 390, 453], 'My': [10], 'Library': [11], 'Share:': [12], 'Permalink': [13], 'Using': [14], 'these': [15], 'links': [16], 'will': [17, 228], 'ensure': [18], 'access': [19], 'this': [21], 'page': [22, 470], 'indefinitely': [23], 'Copy': [24], 'URL': [25], 'Time': [26, 262], 'Complexity': [27, 263], 'Analysis': [28, 264], 'of': [29, 81, 212, 216, 265, 385], 'Quantum': [30, 244, 248, 266], 'Algorithms': [31, 267], 'Via': [32, 268], 'Linear': [33, 233, 269], 'Representations': [34, 270], 'For': [35, 271], 'Nonlinear': [36, 272], 'Ordinary': [37, 273], 'and': [38, 87, 101, 109, 120, 146, 161, 224, 256, 259, 274, 446, 456, 460], 'Partial': [39, 275], 'Differential': [40, 276], 'Equations': [41], '60': [42], 'Pages': [43, 404], 'Posted:': [44], '3': [45], 'Oct': [46], '2022': [47], 'See': [48], 'all': [49], 'articles': [50], 'by': [51, 473], 'Shi': [52, 255, 282], 'JinShi': [53], 'Jinaffiliation': [54], 'not': [55, 60, 65, 285, 298, 313], 'provided': [56, 61, 66, 286, 299, 314], 'SSRNNana': [58], 'Liuaffiliation': [59], 'SSRNYue': [63], 'Yuaffiliation': [64], 'SSRN': [68, 288, 301, 316, 359, 405, 408, 424, 433, 434], 'Abstract': [69, 351], 'We': [70, 137, 189, 450], 'construct': [71], 'quantum': [72, 140, 148, 178], 'algorithms': [73, 143], 'compute': [75], 'the': [76, 110, 117, 121, 128, 133, 139, 147, 157, 162, 167, 173, 177, 183, 192, 197, 201, 209, 213, 217, 222, 225, 376, 386], 'solution': [77], 'and/or': [78], 'physical': [79], 'observables': [80], 'nonlinear': [82, 88, 99, 123], 'ordinary': [83], 'differential': [84, 104], 'equations': [85, 90, 105], '(ODEs)': [86], 'Hamilton-Jacobi': [89], '(HJE)': [91], 'via': [92], 'linear': [93, 102, 118, 141, 170, 245], 'representations': [94, 119], 'or': [95, 132, 379], 'exact': [96], 'mappings': [97], 'between': [98, 116, 221], 'ODEs/HJE': [100], 'partial': [103], '(the': [106], 'Liouville': [107, 198, 226, 236], 'equation': [108, 199], 'Koopman-von': [111, 238], 'Neumann': [112, 239], 'equation).': [113], 'The': [114], 'connection': [115], 'original': [122], 'system': [124], 'is': [125], 'established': [126], 'through': [127], 'Dirac': [129], 'delta': [130], 'function': [131], 'level': [134], 'set': [135], 'mechanism.': [136], 'compare': [138], 'systems': [142, 246], 'based': [144], 'methods': [145, 150, 180], 'simulation': [149, 179, 249], 'arising': [151], 'from': [152], 'different': [153, 169], 'numerical': [154], 'approximations,': [155], 'including': [156], 'finite': [158], 'difference': [159], 'discretisations': [160, 165], 'Fourier': [163], 'spectral': [164], 'for': [166, 200], 'two': [168], 'representations,': [171], 'with': [172], 'result': [174], 'showing': [175], 'that': [176, 336], 'usually': [181], 'give': [182], 'best': [184], 'performance': [185], 'time': [187], 'complexity.': [188], 'also': [190, 229], 'propose': [191], 'Schrodinger': [193, 218, 223, 242], 'framework': [194, 227], 'solve': [196], 'HJE,': [202], 'since': [203], 'it': [204], 'can': [205], 'be': [206, 230], 'recast': [207], 'as': [208], 'semiclassical': [210], 'limit': [211], 'Wigner': [214], 'transform': [215], 'equation.': [219], 'Comparsion': [220], 'made.': [231], 'Keywords:': [232], 'representation': [234], 'methods,': [235], 'representation,': [237, 240], 'Semiclassical': [241], 'equation,': [243], 'algorithms,': [247], 'Suggested': [250, 252], 'Citation:': [251], 'Citation': [253], 'Jin,': [254], 'Liu,': [257], 'Nana': [258, 295], 'Yu,': [260], 'Yue,': [261], 'Equations.': [277], 'Available': [278, 294, 307, 322], 'at': [279], 'SSRN:': [280], 'https://ssrn.com/abstract=4236129': [281], 'Jin': [283], 'affiliation': [284, 297, 312], '(': [289, 302, 317], 'email': [290, 303, 318], ')': [291, 304, 319], 'No': [292, 305, 320], 'Address': [293, 306, 321], 'Liu': [296], 'Yue': [308], 'Yu': [309], '(Contact': [310], 'Author)': [311], 'Do': [330], 'you': [331, 337, 366], 'have': [332], 'a': [333, 398], 'job': [334], 'opening': [335], 'would': [338], 'like': [339], 'promote': [341], 'on': [342], 'SSRN?': [343], 'Place': [344], 'Job': [345], 'Opening': [346], 'statistics': [348], 'Downloads': [349], '2': [350], 'Views': [352], '6': [353], 'PlumX': [354], 'Metrics': [355], 'Feedback': [356, 357, 360], '(required)': [361, 363], 'Email': [362], 'Submit': [364, 397], 'If': [365], 'need': [367], 'immediate': [368], 'assistance,': [369], 'call': [370], '877-SSRNHelp': [371], '(877': [372], '777': [373], '6435)': [374], 'United': [377, 387], 'States,': [378, 388], '+1': [380], '212': [381], '448': [382], '2500': [383], 'outside': [384], '8:30AM': [389], '6:00PM': [391], 'U.S.': [392], 'Eastern,': [393], 'Monday': [394], '-': [395], 'Friday.': [396], 'Section': [400], '508': [401], 'Text': [402], 'Only': [403], 'Quick': [406], 'Links': [407], 'Solutions': [409], 'Research': [410], 'Series': [412], 'Conference': [413], 'Papers': [414, 427], 'Partners': [415], 'Publishing': [417], 'Jobs': [418], '&': [419], 'Announcements': [420, 440], 'Newsletter': [421], 'Sign': [422], 'Up': [423], 'Rankings': [425], 'Top': [426, 428, 430], 'Authors': [429], 'Organizations': [431], 'About': [432], 'Objectives': [435], 'Network': [436], 'Directors': [437], 'Presidential': [438], 'Letter': [439], 'Contact': [441], 'us': [442], 'FAQs': [443], 'Copyright': [444], 'Terms': [445], 'Conditions': [447], 'Privacy': [448], 'Policy': [449], 'use': [451], 'cookies': [452], 'help': [454], 'provide': [455], 'enhance': [457], 'our': [458], 'service': [459], 'tailor': [461], 'content.': [462], 'To': [463], 'learn': [464], 'more,': [465], 'visit': [466], 'Cookie': [467], 'Settings.': [468], 'was': [471], 'processed': [472], 'aws-apollo-5dc': [474], '0.266': [476], 'seconds': [477]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4312441879', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 3}], 'updated_date': '2024-12-29T11:44:57.573585', 'created_date': '2023-01-04'}