{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T18:07:22Z","timestamp":1764785242291,"version":"3.41.2"},"reference-count":42,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:p> In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper [Patel and Wilde, Open Sys.\u00a0&amp; Info.\u00a0Dyn., 30:2350010 (2023)], we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent. <\/jats:p>","DOI":"10.1142\/s1230161223500142","type":"journal-article","created":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T02:43:41Z","timestamp":1699325021000},"source":"Crossref","is-referenced-by-count":9,"title":["Wave Matrix Lindbladization II: General Lindbladians, Linear Combinations, and Polynomials"],"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":[[2023,11,6]]},"reference":[{"first-page":"229","volume-title":"2009 24th Annual IEEE Conference on Computational Complexity","author":"Aaronson Scott","key":"S1230161223500142BIB001"},{"issue":"12","key":"S1230161223500142BIB002","doi-asserted-by":"crossref","first-page":"122202","DOI":"10.1063\/1.4838855","volume":"54","author":"Beigi Salman","year":"2013","journal-title":"Journal of Mathematical Physics"},{"first-page":"283","volume-title":"Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing","author":"Berry Dominic W.","key":"S1230161223500142BIB003"},{"issue":"9","key":"S1230161223500142BIB004","doi-asserted-by":"crossref","first-page":"090502","DOI":"10.1103\/PhysRevLett.114.090502","volume":"114","author":"Berry Dominic 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 Dominic W.","key":"S1230161223500142BIB005"},{"issue":"1","key":"S1230161223500142BIB006","doi-asserted-by":"crossref","first-page":"1","DOI":"10.26421\/QIC14.1-2-1","volume":"14","author":"Berry Dominic W.","year":"2014","journal-title":"Quantum Information and Computation"},{"key":"S1230161223500142BIB008","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1090\/conm\/305\/05215","volume":"305","author":"Brassard Gilles","year":"2002","journal-title":"Contemporary Mathematics"},{"volume-title":"The Theory of Open Quantum Systems","year":"2002","author":"Breuer Heinz-Peter","key":"S1230161223500142BIB009"},{"issue":"7","key":"S1230161223500142BIB010","doi-asserted-by":"crossref","first-page":"070503","DOI":"10.1103\/PhysRevLett.123.070503","volume":"123","author":"Campbell Earl","year":"2019","journal-title":"Physical Review Letters"},{"issue":"11","key":"S1230161223500142BIB012","doi-asserted-by":"crossref","first-page":"901","DOI":"10.26421\/QIC17.11-12-1","volume":"17","author":"Childs Andrew M.","year":"2017","journal-title":"Quantum Information and Computation"},{"issue":"11","key":"S1230161223500142BIB013","doi-asserted-by":"crossref","first-page":"901","DOI":"10.26421\/QIC12.11-12-1","volume":"12","author":"Childs Andrew M.","year":"2012","journal-title":"Quantum Information and Computation"},{"key":"S1230161223500142BIB014","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 Richard","year":"2017"},{"volume-title":"Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics","year":"2004","author":"Gardiner Crispin","key":"S1230161223500142BIB016"},{"issue":"5","key":"S1230161223500142BIB017","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1063\/1.522979","volume":"17","author":"Gorini Vittorio","year":"1976","journal-title":"Journal of Mathematical Physics"},{"issue":"9","key":"S1230161223500142BIB018","first-page":"5628","volume":"63","author":"Haah Jeongwan","year":"2017","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"S1230161223500142BIB019","doi-asserted-by":"crossref","first-page":"010320","DOI":"10.1103\/PRXQuantum.3.010320","volume":"3","author":"Kamakari Hirsh","year":"2022","journal-title":"PRX Quantum"},{"issue":"9","key":"S1230161223500142BIB020","doi-asserted-by":"crossref","first-page":"090502","DOI":"10.1103\/PhysRevLett.106.090502","volume":"106","author":"Kastoryano M. 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