Recorded 24 January 2022. Andrew Childs of the University of Maryland presents "Efficient quantum algorithm for dissipative nonlinear differential equations" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: While there has been extensive previous work on efficient quantum algorithms for linear differential equations, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics. Despite this obstacle, we develop a quantum algorithm for initial value problems described by dissipative quadratic n-dimensional ordinary differential equations.... We achieve this improvement using the method of Carleman linearization, for which we give a novel convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for R=sqrt(2). Finally, we discuss potential applications of this approach to problems arising in biology as well as in fluid and plasma dynamics. Based on joint work with Jin-Peng Liu, Herman Kolden, Hari Krovi, Nuno Loureiro, and Konstantina Trivisa. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/quantum-numerical-linear-algebra/?tab=schedule