# Efficient quantum algorithm for dissipative nonlinear differential equations

@article{Liu2021EfficientQA, title={Efficient quantum algorithm for dissipative nonlinear differential equations}, author={Jin-Peng Liu and Herman Oie Kolden and Hari Krovi and Nuno F. Loureiro and Konstantina Trivisa and Andrew M. Childs}, journal={Proceedings of the National Academy of Sciences}, year={2021}, volume={118} }

Significance Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a…

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