Differential equations are ubiquitous throughout mathematics, natural and social science, and engineering. There has been extensive previous work on efficient quantum algorithms for linear differential equations. However, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics. We give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to the nonlinearity and the inhomogeneity. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Finally, we discuss potential applications of this approach to problems arising in biology as well as in fluid and plasma dynamics.
ArXiv link: https://arxiv.org/abs/2011.03185
Topic: IQC-QuICS Math and Computer Science Seminar
Time: Apr 8, 2021 03:00 PM Eastern Time (US and Canada)
Join Zoom Meeting
https://umd.zoom.us/j/91027995597?pwd=MDNPQWNRZVdGSTlFQUdyUStlTE80QT09
Meeting ID: 910 2799 5597
Passcode: 360060
One tap mobile
+13017158592,,91027995597# US (Washington DC)
+19294362866,,91027995597# US (New York)
Dial by your location
+1 301 715 8592 US (Washington DC)
+1 929 436 2866 US (New York)
+1 312 626 6799 US (Chicago)
+1 253 215 8782 US (Tacoma)
+1 346 248 7799 US (Houston)
+1 669 900 6833 US (San Jose)
Meeting ID: 910 2799 5597
Find your local number: https://umd.zoom.us/u/admT3X8vUS
Join by SIP
91027995597@zoomcrc.com
Join by H.323
162.255.37.11 (US West)
162.255.36.11 (US East)
115.114.131.7 (India Mumbai)
115.114.115.7 (India Hyderabad)
213.19.144.110 (Amsterdam Netherlands)
213.244.140.110 (Germany)
103.122.166.55 (Australia Sydney)
103.122.167.55 (Australia Melbourne)
149.137.40.110 (Singapore)
64.211.144.160 (Brazil)
69.174.57.160 (Canada Toronto)
65.39.152.160 (Canada Vancouver)
207.226.132.110 (Japan Tokyo)
149.137.24.110 (Japan Osaka)
Meeting ID: 910 2799 5597
Passcode: 360060