Imagine a Quantum Internet where people can freely establish physically secure communication channels or migrate quantum programs between anywhere in the world. What would it look like? Despite the very exciting recent advances around building prototypes of quantum networks, little is known about how lab-scale prototypes can be expanded into a global infrastructure that is as capacitated, robust, and cost-efficient as the digital Internet right now. Part of the difficulty lies in our lack of understanding of how the structure of a quantum network affects its capacity and performance when serving multi-commodity quantum communication demands. This article studies the problem of designing high-performance network topologies for the quantum Internet. Utilizing abstract models of the basic quantum network operations and an optimal entanglement distribution protocol, we characterize the capacity and performance of various candidate topologies for the quantum Internet, in terms of the rate of entanglement distribution between source-destination pairs and the fidelity of entangled pairs, respectively. We discuss the implications of our preliminary results, and propose directions for further investigation. As the feasibility of largescale quantum network deployment continues to increase, we hope this article can draw attention to these macroscopic design problems, such as topology design, which potentially have a profound influence on how the entire technology evolves, just as we have observed with the digital Internet in the past decades.
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