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 towards significantly enhancing the robustness of synchronized behavior in open nonlinear systems that utilizes the power of topology. In lattices of quantum van der Pol oscillators with topologically motivated couplings, 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.