Efficient quantum algorithm for dissipative nonlinear differential equations
Jin-Peng Liu, University of Maryland - College Park
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.
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Meeting link: https://umd.zoom.us/j/91027995597?pwd=MDNPQWNRZVdGSTlFQUdyUStlTE80QT09
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This virtual seminar is jointly sponsored by the Institute for Quantum Computing and the Joint Center for Quantum Information and Computer Science.
If you are interested in presenting at a future seminar, please email either Daniel Grier (daniel.grier@uwaterloo.ca) or Hakop Pashayan (hpashaya@uwaterloo.ca).