Scalable Quantum Networks: Congestion-Free Hierarchical Entanglement Routing with Error Correction

• URL: http://arxiv.org/abs/2306.09216v2
• Date: Tue, 12 Sep 2023 21:45:47 GMT
• Title: Scalable Quantum Networks: Congestion-Free Hierarchical Entanglement Routing with Error Correction
• Abstract summary: Quantum Tree Networks (QTN) is an architecture for hierarchical multi-flow entanglement routing. Network design is a $k$-ary tree where end nodes are situated on the leaves and routers at the internal nodes. Our network-level simulations demonstrate a size-independent threshold behavior of QTNs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $a_k$, 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 $\mathcal{O}(N^{\log_k a_k} \cdot \log_k N)$ and is sublinear for all $k$ with minimal surface-covering end nodes. More specifically, the overhead of quarternary ($k=4$) QTN is $\sim \mathcal{O}(N^{0.25}\cdot\log_4 N)$. Alternatively, when end nodes are distributed over a square lattice, the quaternary tree routing gives the overhead $\sim \mathcal{O}(\sqrt{N}\cdot\log_4 N)$. 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.

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