Impact of Topology on Multipartite Entanglement Distribution Protocols in Quantum Networks

Abstract

Quantum networks will rely on entanglement distribution to enable multi-user applications such as distributed quantum computing and cryptography. While multipartite entanglement distribution routing protocols have been extensively studied on idealised grid topologies, less is understood about how real network structure shapes their performance and resource requirements. We present a systematic study of four routing protocols for multipartite entanglement distribution, each characterised by the number of paths (single-path and multi-path) and routing strategy (star-based and tree-based), over 81 real network topologies. We identified four distinct topology-dependent performance regimes, where: (i) all protocols perform poorly, (ii) tree-based protocols dominate, (iii) multi-path protocols dominate, or (iv) all protocols perform well. By correlating clusters with graph metrics, we also provide structural explanations for the varied performance of specific protocols. Additionally, motivated by the anticipated high cost of repeaters, we investigated the impact of repeater trimming on the performance of multi-path protocols. Topology strongly governs how far repeater nodes can be removed from the network while maintaining a given performance (distribution rate). For instance, in networks where only 80% of nodes operate as repeaters, well-performing topologies are able to retain over 90% of the distribution rate; whereas sparse, weakly connected graphs exhibit rapid performance degradation, retaining less than half of the distribution rate. Our results provide a topology-aware framework for protocol selection and infrastructure optimisation in future quantum networks, bridging routing design with cost-aware deployment strategies.

Figures (14)

• Figure 1: Examples of routing solutions upon termination of each protocol on GERMANY50 and CONUS75. The resulting routing solution is always identical for single-path protocols, but possibly different upon rerunning of multi-path protocols.
• Figure 2: Entanglement swapping used to establish a long-distance entanglement link, by performing BSMs on the qubits held at circled nodes.
• Figure 3: Illustration of entanglement swapping and fusion to combine 8 Bell pairs into a $|\text{GHZ}_4\rangle$ state between user nodes. Blue dashed lines between two nodes represent shared Bell pairs, and a star-shaped configuration with $N$ arms represents entanglement between $N$ qubits in a $\ket{\text{GHZ}_N}$ state.
• Figure 4: Example of the repeater trimming process on a simple graph. User nodes are coloured green. The number (between 0 and 1) on each node is the fraction of Monte Carlo runs (out of 5000) that utilises the repeater.
• Figure 5: Repeater trimming process for MPT on topology CORONET (Cluster 4). Hue of blue corresponds to repeater usage for a given (possibly trimmed) topology. A darker hue indicates higher usage and unused repeaters are white. Each trimming step (arrow) involves trimming of least used active repeaters, and 5000 Monte Carlo simulations on the newly trimmed topology. This topology has no redundant repeaters.