Topological synchronization of quantum van der Pol oscillators

\"To observe synchronization in large networks of classical or quantum systems demands both excellent control of the interactions between nodes and very accurate preparation of initial conditions due to the involved nonlinearities and dissipation. This limits its applicability for future devices. We demonstrate a route toward significantly enhancing the robustness of synchronized behavior in open nonlinear systems that utilizes the power of topology. In nontrivial topological lattices of quantum van der Pol oscillators, boundary synchronization emerges in the classical mean field as well as the quantum regime. In addition to its robustness against disorder and initial state perturbations, the observed dynamics is independent of the underlying topological model provided the existence of topological zero-energy modes. Our work extends the notion of topology to the general nonlinear dynamics and open quantum system realm with applications to networks where specific nodes need special protection like power grids or quantum networks. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the \"\"https://creativecommons.org/licenses/by/4.0/\"\"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.\"