{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T18:05:56Z","timestamp":1764785156465,"version":"3.41.2"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"National Science Foundation","award":["1907615"],"award-info":[{"award-number":["1907615"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:p> Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator [Formula: see text] is encoded into a quantum state [Formula: see text]. Then, given access to [Formula: see text] copies of the state [Formula: see text], the task is to simulate the corresponding Markovian dynamics for time [Formula: see text]. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses [Formula: see text] samples of [Formula: see text] to achieve the target dynamics, with an approximation error of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1230161223500105","type":"journal-article","created":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T09:04:01Z","timestamp":1689584641000},"source":"Crossref","is-referenced-by-count":14,"title":["Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics"],"prefix":"10.1142","volume":"30","author":[{"given":"Dhrumil","family":"Patel","sequence":"first","affiliation":[{"name":"Department of Computer Science, Cornell University, Ithaca, New York 14850, USA"}]},{"given":"Mark M.","family":"Wilde","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, USA"}]}],"member":"219","published-online":{"date-parts":[[2023,7,20]]},"reference":[{"first-page":"229","volume-title":"2009 24th Annual IEEE Conference on Computational Complexity","author":"Aaronson S.","key":"S1230161223500105BIB001"},{"first-page":"283","volume-title":"Proceedings of the Annual ACM Symposium on Theory of Computing","author":"Berry D. W.","key":"S1230161223500105BIB002"},{"issue":"9","key":"S1230161223500105BIB003","doi-asserted-by":"crossref","first-page":"090502","DOI":"10.1103\/PhysRevLett.114.090502","volume":"114","author":"Berry D. W.","year":"2014","journal-title":"Physical Review Letters"},{"first-page":"792","volume-title":"2015 IEEE 56th Annual Symposium on Foundations of Computer Science","author":"Berry D. W.","key":"S1230161223500105BIB004"},{"issue":"1","key":"S1230161223500105BIB005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.26421\/QIC14.1-2-1","volume":"14","author":"Berry D. W.","year":"2014","journal-title":"Quantum Information and Computation"},{"issue":"7671","key":"S1230161223500105BIB007","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/nature23474","volume":"549","author":"Biamonte J.","year":"2016","journal-title":"Nature"},{"volume-title":"The Theory of Open Quantum Systems","year":"2002","author":"Breuer H.-P.","key":"S1230161223500105BIB008"},{"issue":"11","key":"S1230161223500105BIB009","first-page":"901","volume":"17","author":"Childs A. M.","year":"2016","journal-title":"Quantum Information and Computation"},{"key":"S1230161223500105BIB010","series-title":"Leibniz International Proceedings in Informatics (LIPIcs)","first-page":"17:1","volume-title":"44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)","volume":"80","author":"Cleve R.","year":"2017"},{"issue":"6","key":"S1230161223500105BIB011","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF02650179","volume":"21","author":"Feynman R. P.","year":"1982","journal-title":"International Journal of Theoretical Physics"},{"volume-title":"Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics","year":"2004","author":"Gardiner C.","key":"S1230161223500105BIB012"},{"issue":"1","key":"S1230161223500105BIB013","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1103\/RevModPhys.86.153","volume":"86","author":"Georgescu I. M.","year":"2014","journal-title":"Reviews of Modern Physics"},{"issue":"5","key":"S1230161223500105BIB014","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1063\/1.522979","volume":"17","author":"Gorini V.","year":"2008","journal-title":"Journal of Mathematical Physics"},{"issue":"1","key":"S1230161223500105BIB015","doi-asserted-by":"crossref","first-page":"010320","DOI":"10.1103\/PRXQuantum.3.010320","volume":"3","author":"Kamakari H.","year":"2022","journal-title":"PRX Quantum"},{"issue":"3","key":"S1230161223500105BIB016","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s00220-016-2641-8","volume":"344","author":"Kastoryano M. J.","year":"2014","journal-title":"Communications in Mathematical Physics"},{"issue":"9","key":"S1230161223500105BIB017","doi-asserted-by":"crossref","first-page":"090502","DOI":"10.1103\/PhysRevLett.106.090502","volume":"106","author":"Kastoryano M. J.","year":"2011","journal-title":"Physical Review Letters"},{"issue":"1","key":"S1230161223500105BIB018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41534-017-0013-7","volume":"3","author":"Kimmel S.","year":"2017","journal-title":"npj Quantum Information"},{"issue":"6","key":"S1230161223500105BIB019","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1070\/RM1997v052n06ABEH002155","volume":"52","author":"Kitaev A. Y.","year":"1997","journal-title":"Russian Mathematical Surveys"},{"issue":"4","key":"S1230161223500105BIB020","doi-asserted-by":"crossref","first-page":"042307","DOI":"10.1103\/PhysRevA.78.042307","volume":"78","author":"Kraus B.","year":"2008","journal-title":"Physical Review A"},{"key":"S1230161223500105BIB021","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF01609396","volume":"40","author":"Lindblad G.","year":"1975","journal-title":"Communications in Mathematical Physics"},{"issue":"2","key":"S1230161223500105BIB022","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/BF01608499","volume":"48","author":"Lindblad G.","year":"1976","journal-title":"Communications in Mathematical Physics"},{"issue":"5278","key":"S1230161223500105BIB023","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1126\/science.273.5278.1073","volume":"273","author":"Lloyd S.","year":"1996","journal-title":"Science"},{"issue":"9","key":"S1230161223500105BIB024","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1038\/nphys3029","volume":"10","author":"Lloyd S.","year":"2014","journal-title":"Nature Physics"},{"issue":"1","key":"S1230161223500105BIB025","doi-asserted-by":"crossref","first-page":"010501","DOI":"10.1103\/PhysRevLett.118.010501","volume":"118","author":"Low G. H.","year":"2017","journal-title":"Physical Review Letters"},{"issue":"1","key":"S1230161223500105BIB026","doi-asserted-by":"crossref","first-page":"012324","DOI":"10.1103\/PhysRevA.87.012324","volume":"87","author":"Magesan E.","year":"2013","journal-title":"Physical Review A"},{"issue":"6","key":"S1230161223500105BIB027","doi-asserted-by":"crossref","first-page":"061118","DOI":"10.1103\/PhysRevE.86.061118","volume":"86","author":"Manzano D.","year":"2012","journal-title":"Physical Review E"},{"volume-title":"Charge and Energy Transfer Dynamics in Molecular Systems","year":"2008","author":"May V.","key":"S1230161223500105BIB028"},{"issue":"1","key":"S1230161223500105BIB030","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1038\/s43588-022-00374-2","volume":"3","author":"Miessen A.","year":"2022","journal-title":"Nature Computational Science"},{"key":"S1230161223500105BIB031","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198529798.001.0001","volume-title":"Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems","author":"Nitzan A.","year":"2006"},{"issue":"2","key":"S1230161223500105BIB032","doi-asserted-by":"crossref","first-page":"020403","DOI":"10.1103\/PhysRevLett.109.020403","volume":"109","author":"Olmos B.","year":"2012","journal-title":"Physical Review Letters"},{"issue":"1","key":"S1230161223500105BIB033","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1103\/RevModPhys.70.101","volume":"70","author":"Plenio M. B.","year":"1998","journal-title":"Reviews of Modern Physics"},{"issue":"21","key":"S1230161223500105BIB034","doi-asserted-by":"crossref","first-page":"217206","DOI":"10.1103\/PhysRevLett.106.217206","volume":"106","author":"Prosen T.","year":"2011","journal-title":"Physical Review Letters"},{"issue":"4","key":"S1230161223500105BIB035","doi-asserted-by":"crossref","first-page":"040501","DOI":"10.1103\/PhysRevLett.117.040501","volume":"117","author":"Reiter F.","year":"2016","journal-title":"Physical Review Letters"},{"issue":"2","key":"S1230161223500105BIB036","doi-asserted-by":"crossref","first-page":"023216","DOI":"10.1103\/PhysRevResearch.4.023216","volume":"4","author":"Schlimgen A. W.","year":"2022","journal-title":"Physical Review Research"},{"key":"S1230161223500105BIB037","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.22331\/q-2023-05-15-1002","volume":"7","author":"Suri N.","year":"2023","journal-title":"Quantum"},{"issue":"9","key":"S1230161223500105BIB038","doi-asserted-by":"crossref","first-page":"633","DOI":"10.1038\/nphys1342","volume":"5","author":"Verstraete F.","year":"2009","journal-title":"Nature Physics"},{"key":"S1230161223500105BIB039","doi-asserted-by":"publisher","DOI":"10.1142\/12402"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161223500105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T09:08:36Z","timestamp":1689584916000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1230161223500105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6]]},"references-count":37,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["10.1142\/S1230161223500105"],"URL":"https:\/\/doi.org\/10.1142\/s1230161223500105","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"type":"print","value":"1230-1612"},{"type":"electronic","value":"1793-7191"}],"subject":[],"published":{"date-parts":[[2023,6]]},"article-number":"2350010"}}