  Routing in a quantum network presents unique challenges due to its acquired
properties of quantum mechanics like no-cloning, link failure, and
entanglement. This study explores an approach to routing in quantum networks,
which targets practical scenarios for quantum networks, mirroring real-world
classical networks. Thus, it consists of access networks with users acting as
sources and destinations, interconnected through a core network of nodes
cooperating to establish end-to-end entanglement between them. By addressing
practical constraints, we examine the impact of heterogeneous nodes with mixed
efficiency figures on quantum network performance. In particular, we focus on
some key parameters in an operational quantum network such as the fraction of
nodes with a higher efficiency (called high-quality), path establishment order,
end-to-end fidelity, i.e., a measure of the quality of the end-to-end
entanglement established. Our simulations show that incorporating knowledge of
node quality not only helps boost the fidelity of some of the routing paths but
also reduces the number of blocked paths in the quantum network. The study also
highlights the critical role of the fraction of high-quality nodes in
end-to-end fidelity and explores the trade-offs between upgrading all nodes to
high quality or retaining a subset of lower-quality nodes.
