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Quantum information will not only reformulate our view of the nature of computation and communication but will also open up fundamentally new possibilities for realizing high-performance computer architecture and telecommunication networks. Since our data will no longer remain safe in the traditional Internet when commercial quantum computers become fully available, 1, 2, 8, 15, 34 there will be a need for a fundamentally different network structure: the quantum Internet. 22, 25, 32, 33, 45, 47 While quantum computational supremacy refers to tasks and problems that quantum computers can solve but are beyond the capability of classical computers, the quantum supremacy of the quantum Internet identifies the properties and attributes that the quantum Internet offers but are unavailable in the traditional Internet. a