  We develop new routing algorithms for a quantum network with noisy quantum
devices such that each can store a small number of qubits. We thereby consider
two models for the operation of such a network. The first is a continuous
model, in which entanglement between a subset of the nodes is produced
continuously in the background. This can in principle allows the rapid creation
of entanglement between more distant nodes using the already pre-generated
entanglement pairs in the network. The second is an on-demand model, where
entanglement production does not commence before a request is made. Our
objective is to find protocols, that minimise the latency of the network to
serve a request to create entanglement between two distant nodes in the
network. We propose three routing algorithms and analytically show that as
expected when there is only a single request in the network, then employing
them on the continuous model yields a lower latency than on the on-demand one.
We study the performance of the routing algorithms in a ring, grid, and
recursively generated network topologies. We also give an analytical upper
bound on the number of entanglement swap operations the nodes need to perform
for routing entangled links between a source and a destination yielding a lower
bound on the end to end fidelity of the shared entangled state. We proceed to
study the case of multiple concurrent requests and show that in some of the
scenarios the on-demand model can outperform the continuous one. Using
numerical simulations on ring and grid networks we also study the behaviour of
the latency of all the routing algorithms. We observe that the proposed routing
algorithms behave far better than the existing classical greedy routing
algorithm. The simulations also help to understand the advantages and
disadvantages of different types of continuous models for different types of
demands.
