Multi-User Entanglement Routing Design over Quantum Internets

Quantum Internet has potential capabilities far beyond the traditional Internet and is thus a promising future platform for communication and computation. Entanglement is a cornerstone of quantum mechanics and forms the basis of numerous quantum applications in the quantum Internet. While existing studies primarily focus on two-user entanglement, a plethora of applications necessitates the leap to multi-user entanglement. This paper tackles the fundamental problem of multi-user entanglement routing in the quantum Internet, aiming to entangle multiple quantum users with a high entanglement rate. We abstract the problem as a novel graph routing problem, which is not readily addressed by existing graph problem solutions due to the unique characteristics of the quantum Internet. To address this problem, we first consider a sufficient condition ensuring a feasible solution's existence and design an algorithm with the optimal solution. Given the NP-Completeness and NP- Hardness of determining a feasible solution's existence and deriving an optimal solution in general cases, respectively, we propose two heuristic algorithms to offer efficient solutions, which are shown, via extensive simulations, to outperform the existing algorithms in terms of entanglement rates.