RELiQ: Scalable Entanglement Routing via Reinforcement Learning in Quantum Networks

TL;DR

Problem: entanglement routing in dynamic quantum networks is challenged by link fluctuations and probabilistic operations, and global topology is often unavailable. Approach: RELiQ employs multi-agent reinforcement learning with a recurrent graph neural network to build global representations from local, one-hop information and message exchanges, enabling scalable, topology-agnostic routing. Contributions: a decentralized framework that generalizes to varying node degrees and unseen topologies, a comprehensive evaluation against local and global baselines on synthetic and real networks, and an analysis of computational and monitoring overhead. Impact: enables fast, high-fidelity end-to-end entanglements in realistic quantum networks without retraining, supporting applications like distributed quantum computing and quantum networks.

Abstract

Quantum networks are becoming increasingly important because of advancements in quantum computing and quantum sensing, such as recent developments in distributed quantum computing and federated quantum machine learning. Routing entanglement in quantum networks poses several fundamental as well as technical challenges, including the high dynamicity of quantum network links and the probabilistic nature of quantum operations. Consequently, designing hand-crafted heuristics is difficult and often leads to suboptimal performance, especially if global network topology information is unavailable. In this paper, we propose RELiQ, a reinforcement learning-based approach to entanglement routing that only relies on local information and iterative message exchange. Utilizing a graph neural network, RELiQ learns graph representations and avoids overfitting to specific network topologies - a prevalent issue for learning-based approaches. Our approach, trained on random graphs, consistently outperforms existing local information heuristics and learning-based approaches when applied to random and real-world topologies. When compared to global information heuristics, our method achieves similar or superior performance because of its rapid response to topology changes.

Figures (16)

• Figure 1: Sample topologies used for training and evaluation.
• Figure 2: Illustration of entanglement swapping. Bell pairs are established between neighboring nodes (nodes 1 and 2, nodes 2 and 3). The intermediary node 2, containing two qubits, will play the role of a quantum repeater and perform the Bell State Measurement (BSM) on its qubits. The result is an entangled state between the remote qubits of node 1 and node 3.
• Figure 3: Decay of qubits in quantum memory depending on the number of decoupling pulses $n_{\text{dec}}$, reproduced from doi:10.1126/science.add9771.
• Figure 4: Visualization of the phases of our quantum network model. The quantum repeaters are depicted as the nodes of the graph, which are connected via fiber. If elementary links are available between two repeaters, each blue wavy line represents one of these links. The agent is represented as a red rectangle, which moves across the network in Phase 2. The currently planned path is depicted as a red line.
• Figure 5: Number of successfully created elementary links per second for different link lengths and attenuation constants $\alpha$. The number of successfully created elementary links decreases drastically with increasing link length.