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Quantum communication brings radically new capabilities that are provably impossible to attain in any classical network. Here, we take the first step from a physics experiment to a quantum internet system. We propose a functional allocation of a quantum network stack, and construct the first physical and link layer protocols that turn ad-hoc physics experiments producing heralded entanglement between quantum processors into a well-defined and robust service. This lays the groundwork for designing and implementing scalable control and application protocols in platform-independent software. To design our protocol, we identify use cases, as well as fundamental and technological design considerations of quantum network hardware, illustrated by considering the state-of-the-art quantum processor platform available to us (Nitrogen-Vacancy (NV) centers in diamond). Using a purpose built discrete-event simulator …