  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.

Quantum Physics