Learning Best Paths in Quantum Networks

Quantum networks (QNs) transmit delicate quantum information across noisy quantum channels. Crucial applications, like quantum key distribution (QKD) and distributed quantum computation (DQC), rely on efficient quantum information transmission. Learning the best path between a pair of end nodes in a QN is key to enhancing such applications. This paper addresses learning the best path in a QN in the online learning setting. We explore two types of feedback: "link-level" and "path-level". Link-level feedback pertains to QNs with advanced quantum switches that enable link-level benchmarking. Path-level feedback, on the other hand, is associated with basic quantum switches that permit only path-level benchmarking. We introduce two online learning algorithms, BeQuP-Link and BeQuP-Path, to identify the best path using link-level and path-level feedback, respectively. To learn the best path, BeQuP-Link benchmarks the critical links dynamically, while BeQuP-Path relies on a subroutine, transferring path-level observations to estimate link-level parameters in a batch manner. We analyze the quantum resource complexity of these algorithms and demonstrate that both can efficiently and, with high probability, determine the best path. Finally, we perform NetSquid-based simulations and validate that both algorithms accurately and efficiently identify the best path.