In many quantum information applications, ranging from computation to communication, a key step is the ability to engineer some states with given correlations on multipartite systems (or "quantum network"), where the interaction between the parts are limited by locality constraints and control capabilities. We here focus on two specific tasks and some robust, randomized protocols to achieve them. The first one is the symmetrization of the network state with respect to the subsystem permutation group: we show that this problem can be tackled with methods borrowed from classical "consensus" problems.
The second is the asymptotic preparation of a given entangled pure state: we provide a test to check if the task is feasible under the existing constraints, as well as randomized design methods for controlled open-system dynamics. Motivating examples and applications will be introduced. In both cases, asymptotic convergence to the target can be proved under minimal assumptions on the network topology and the way the local dynamics are selected.