We present an approach to purification and entanglement routing on complex quantum network architectures, that is, how a quantum network equipped with imperfect channel fidelities and limited memory storage time can distribute entanglement between users. We explore how network parameters influence the performance of path-finding algorithms necessary for optimizing routing and, in particular, we explore the interplay between the bandwidth of a quantum channels and the choice of purification protocol. Finally, we demonstrate multi-path routing on various network topologies with resource constraints, in an effort to inform future design choices for quantum network configurations. Our work optimizes both the choice of path over the quantum network and the choice of purification schemes used between nodes. We consider not only pair-production rate, but optimize over the fidelity of the delivered entangled state. We introduce effective heuristics enabling fast path-finding algorithms for maximizing entanglement shared between two nodes on a quantum network, with performance comparable to that of a computationally-expensive brute-force path search.
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