{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T02:34:22Z","timestamp":1769567662072,"version":"3.49.0"},"reference-count":49,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"\n We establish improved complexity estimates of quantum algorithms for linear dissipative ordinary differential equations (ODEs) and show that the time dependence can be fast-forwarded to be sub-linear. Specifically, we show that a quantum algorithm based on truncated Dyson series can prepare history states of dissipative ODEs up to time\n \n T<\/mml:mi>\n <\/mml:math>\n with cost\n \n \n \n \n O<\/mml:mi>\n <\/mml:mrow>\n &#x007E;<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n (<\/mml:mo>\n log<\/mml:mi>\n &#x2061;<\/mml:mo>\n (<\/mml:mo>\n T<\/mml:mi>\n )<\/mml:mo>\n (<\/mml:mo>\n log<\/mml:mi>\n &#x2061;<\/mml:mo>\n (<\/mml:mo>\n 1<\/mml:mn>\n \n \/<\/mml:mo>\n <\/mml:mrow>\n &#x03F5;<\/mml:mi>\n )<\/mml:mo>\n \n )<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:math>\n , which is an exponential speedup over the best previous result. For final state preparation at time\n \n T<\/mml:mi>\n <\/mml:math>\n , we show that its complexity is\n \n \n \n \n O<\/mml:mi>\n <\/mml:mrow>\n &#x007E;<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n (<\/mml:mo>\n \n T<\/mml:mi>\n <\/mml:msqrt>\n (<\/mml:mo>\n log<\/mml:mi>\n &#x2061;<\/mml:mo>\n (<\/mml:mo>\n 1<\/mml:mn>\n \n \/<\/mml:mo>\n <\/mml:mrow>\n &#x03F5;<\/mml:mi>\n )<\/mml:mo>\n \n )<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:math>\n , achieving a polynomial speedup in\n \n T<\/mml:mi>\n <\/mml:math>\n . We also analyze the complexity of simpler lower-order quantum algorithms, such as the forward Euler method and the trapezoidal rule, and find that even lower-order methods can still achieve\n \n \n \n \n O<\/mml:mi>\n <\/mml:mrow>\n &#x007E;<\/mml:mo>\n <\/mml:mover>\n <\/mml:mrow>\n (<\/mml:mo>\n \n T<\/mml:mi>\n <\/mml:msqrt>\n )<\/mml:mo>\n <\/mml:math>\n cost with respect to time\n \n T<\/mml:mi>\n <\/mml:math>\n for preparing final states of dissipative ODEs. As applications, we show that quantum algorithms can simulate dissipative non-Hermitian quantum dynamics and heat processes with fast-forwarded complexity sub-linear in time.\n <\/jats:p>","DOI":"10.22331\/q-2026-01-27-1986","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T14:55:46Z","timestamp":1769525746000},"page":"1986","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Fast-forwarding quantum algorithms for linear dissipative differential equations"],"prefix":"10.22331","volume":"10","author":[{"given":"Dong","family":"An","sequence":"first","affiliation":[{"name":"Beijing International Center for Mathematical Research (BICMR), Peking University, Beijing, China"},{"name":"Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, MD, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akwum","family":"Onwunta","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gengzhi","family":"Yang","sequence":"additional","affiliation":[{"name":"Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, MD, USA"},{"name":"Department of Mathematics, University of Maryland, College Park, MD, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Dominic W. 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