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Developing strategies to effectively discriminate between different quantum states is a fundamental issue in quantum information and communication. The actual realization of generally optimal protocols in this task is often limited by the need of supplemental resources and very complex receivers. We have experimentally implemented two discrimination schemes in a minimum-error scenario based on a receiver featured by a network structure and a dynamical processing of information. The first protocol implemented in our experiment, directly inspired to a recent theoretical proposal, achieves binary optimal discrimination, while the second one provides a novel approach to multi-state quantum discrimination, relying on the dynamical features of the network-like receiver. This strategy exploits the arrival time degree of freedom as an encoding variable, achieving optimal results, without the need for supplemental systems or devices. Our results further reveal the potential of dynamical approaches to quantum state discrimination tasks, providing a possible starting point for efficient alternatives to current experimental strategies.