We introduce Quantum Tree Networks (QTN), an architecture for hierarchical
multi-flow entanglement routing. The network design is a k-ary tree where end
nodes are situated on the leaves and routers at the internal nodes, with each
node connected to k nodes in the child layer. The channel length between
nodes grows with a rate ak, increasing as one ascends from the leaf to the
root node. This construction allows for congestion-free and error-corrected
operation with qubit-per-node overhead to scale sublinearly with the number of
end nodes, N. The overhead for a k-ary QTN scales as O(Nlogkak⋅logkN) and is sublinear for all k with minimal
surface-covering end nodes. More specifically, the overhead of quarternary
(k=4) QTN is ∼O(N0.25⋅log4N). Alternatively, when
end nodes are distributed over a square lattice, the quaternary tree routing
gives the overhead ∼O(N⋅log4N). Our network-level
simulations demonstrate a size-independent threshold behavior of QTNs.
Moreover, tree network routing avoids the necessity for intricate multi-path
finding algorithms, streamlining the network operation. With these properties,
the QTN architecture satisfies crucial requirements for scalable quantum
networks.Comment: 13 pages, 5 figure