In entanglement distribution networks, communication between two nodes necessitates the generation of end-to-end entanglement by entanglement swapping at intermediate nodes. Efficiently creating end-to-end entanglements over long distances is a key objective. In our prior study on asynchronous routing, we enhanced these entanglement rates by leveraging solely the local knowledge of the node's entanglement links. This was achieved by creating a tree structure, particularly a destination-oriented directed acyclic graph (DODAG) or a spanning tree, eliminating synchronous operations and conserving unused entanglement links. In this article, we present a multi-tree approach with multiple DODAGs designed to improve end-to-end entanglement rates in large-scale networks, specifically catering to a range of network topologies, including grids and barbells, as well as realistic topologies found in research testbeds like ESnet and Internet2. Our simulations show a marked improvement in end-to-end entanglement rates for specific topologies compared to the single-tree method. This study underscores the promise of asynchronous routing schemes in quantum networks, highlighting the effectiveness of asynchronous routing across different network topologies and proposing a superior routing tactic.
In entanglement distribution networks, communication between two nodes necessitates the generation of end-to-end entanglement by entanglement swapping at intermediate nodes. Efficiently creating end-to-end entanglements over long distances is a key objective. In our prior study on asynchronous routing, we enhanced these entanglement rates by leveraging solely the local knowledge of the node's entanglement links. This was achieved by creating a tree structure, particularly a destination-oriented directed acyclic graph (DODAG) or a spanning tree, eliminating synchronous operations and conserving unused entanglement links. In this article, we present a multi-tree approach with multiple DODAGs designed to improve end-to-end entanglement rates in large-scale networks, specifically catering to a range of network topologies, including grids and barbells, as well as realistic topologies found in research testbeds like ESnet and Internet2. Our simulations show a marked improvement in end-to-end entanglement rates for specific topologies compared to the single-tree method. This study underscores the promise of asynchronous routing schemes in quantum networks, highlighting the effectiveness of asynchronous routing across different network topologies and proposing a superior routing tactic.
In quantum networks, one way to communicate is to distribute entanglements through swapping at intermediate nodes. Most existing work primarily aims to create efficient two-party end-to-end entanglement over long distances. However, some scenarios also require remote multipartite entanglement for applications such as quantum secret sharing and multi-party computation. Our previous study improved end-to-end entanglement rates using an asynchronous, tree-based routing scheme that relies solely on local knowledge of entanglement links, conserving unused entanglement and avoiding synchronous operations. This article extends this approach to multipartite entanglements, particularly the three-party Greenberger-Horne-Zeilinger (GHZ) states. It shows that our asynchronous protocol outperforms traditional synchronous methods in entanglement rates, especially as coherence times increase. This approach can also be extended to four-party and larger multipartite GHZ states, highlighting the effectiveness and adaptability of asynchronous routing for multipartite scenarios across various network topologies.
With the emergence of the Quantum Internet, the need for advanced quantum networking techniques has significantly risen. Various models of quantum repeaters have been presented, each delineating a unique strategy to ensure quantum communication over long distances. We focus on repeaters that employ entanglement generation and swapping. This revolves around establishing remote end-to-end entanglement through repeaters, a concept we denote as the “quantum-native” repeaters (also called “first-generation” repeaters in some literature). The challenges in routing with quantum-native repeaters arise from probabilistic entanglement generation and restricted coherence time. Current approaches use synchronized time slots to search for entanglement-swapping paths, resulting in inefficiencies. Here, we propose a new set of asynchronous routing protocols for quantum networks by incorporating the idea of maintaining a dynamic topology in a distributed manner, which has been extensively studied in classical routing for lossy networks, such as using a destination-oriented directed acyclic graph or a spanning tree. The protocols update the entanglement-link topology asynchronously, identify optimal entanglement-swapping paths, and preserve unused direct-link entanglements. Our results indicate that asynchronous protocols achieve a larger upper bound with an appropriate setting and significantly higher entanglement rate than existing synchronous approaches, and the rate increases with coherence time, suggesting that it will have a much more profound impact on quantum networks as technology advances.
The effective routing of entanglement over a quantum network is a fundamental problem in quantum communication. The distribution and reshaping of multipartite entanglement over a quantum network requires scalable protocols that adapt to the underlying topology. Graph states provide a convenient framework for this challenging task, as they encode global entanglement in a structured way that can be locally manipulated to produce a variety of target states, without requiring additional long-distance quantum operations. In this article, we propose graph-state-based routing protocols for sharing GHZ states, achieving larger sizes than those achieved in the existing works for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier works. In particular, for grid networks, we show special constructions of such trees that achieve larger GHZ states than the prior works. Moreover, if the user nodes along which the entanglement is to be routed are pre-specified, a strategy is proposed to accomplish this routing.
We introduce the DODAG-X protocol for multipartite entanglement distribution in quantum networks. Leveraging the power of Destination Oriented Directed Acyclic Graphs (DODAGs), our protocol optimizes resource consumption and enhances robustness to noise in dynamic and lossy networks. Implementing a variation on the X-protocol within the DODAG, we minimize graph verification and path-finding calculations, significantly reducing computational overhead when compared to other entanglement routing schemes. Additionally, our benchmarks on grid lattice and small-world topologies reveal substantial measurement reduction compared to existing protocols. We demonstrate the success of DODAG-X for generating maximal three-party entanglement in arbitrary networks, and describe the potential for scaling to generic n-party entanglement. The DODAG-X protocol provides a scalable and efficient solution for entanglement routing, advancing current techniques for reliable quantum communication and network applications.
Distributing multipartite entanglement over a quantum network means routing it through a shared resource state. Existing measurement-based schemes search for a fresh path and re-verify the topology before every request, placing a network-wide classical exchange on the critical path of each one. We introduce DODAG-X, which removes it. A single destination-oriented directed acyclic graph spanning tree is computed once and reused across all requests, so each party's route is recovered by following parent pointers instead of by a new search. The per-request routing cost drops from O(N) to O(N) on symmetric grids and to O(logN) on small-world networks for N nodes, and only the N−1 tree links need be maintained under link loss. Routing on the sparse tree also shrinks the neighborhoods cleared to isolate the parties, lowering measurements per request by roughly 19\% on small-world graphs and up to 34\% on moderately dense, strongly rewired ones; on a fixed tree the two protocols use identical counts. We prove correctness for up to three parties with no restriction on topology, and prove a sufficient condition under which one application yields an n-party GHZ state for any n. We then delimit it, exhibiting requests outside the hypothesis whose output is multipartite entangled yet in a different local-Clifford class. Under a discrete-time Markov failure model the classical repair layer matches the reachability of full-graph re-search up to a failed-edge fraction of one half, and a coherence criterion relating tree depth to memory lifetime identifies the viable hardware platforms.
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.