  Entanglement routing establishes remote entanglement connection between two
arbitrary nodes, which is one of the most important functions in quantum
networks. The existing routing mechanisms mainly improve the robustness and
throughput facing the failure of entanglement generations, which, however,
rarely include the considerations on the most important metric to evaluate the
quality of connection, entanglement fidelity. To solve this problem, we propose
purification-enabled entanglement routing designs to provide fidelity guarantee
for multiple Source-Destination (SD) pairs in quantum networks. In our
proposal, we first consider the single S-D pair scenario and design an
iterative routing algorithm, Q-PATH, to find the optimal purification decisions
along the routing path with minimum entangled pair cost. Further, a
low-complexity routing algorithm using an extended Dijkstra algorithm, Q-LEAP,
is designed to reduce the computational complexity by using a simple but
effective purification decision method. Then we consider the common scenario
with multiple S-D pairs and design a greedy-based algorithm considering
resource allocation and rerouting process for multiple routing requests. To
verify the effectiveness and superiority of the proposed algorithms, extensive
simulations are conducted, and the simulation results show that the proposed
algorithms not only can provide fidelity-guarantee routing solutions, but also
has superior performance in terms of throughput, fidelity of end-to-end
entanglement connection, and resource utilization ratio, compared with the
existing routing scheme.
