LinkSelFiE: Link Selection and Fidelity Estimation in Quantum Networks

Reliable transmission of fragile quantum information requires one to efficiently select and utilize high-fidelity links among multiple noisy quantum links. However, the fidelity, a quality metric of quantum links, is unknown a priori. Uniformly estimating the fidelity of all links can be expensive, especially in networks with numerous links. To address this challenge, we formulate the link selection and fidelity estimation problem as a best arm identification problem and propose an algorithm named LinkSelFiE. The algorithm efficiently identifies the optimal link from a set of quantum links and provides an accurate fidelity estimate of that link with low quantum resource consumption. LinkSelFiE estimates link fidelity based on the feedback of a vanilla network benchmarking subroutine, and adaptively eliminates inferior links throughout the whole fidelity estimation process. This elimination leverages a novel confidence interval derived in this paper for the estimates from the subroutine, which theoretically guarantees that LinkSelFiE outputs the optimal link correctly with high confidence. We also establish a provable upper bound of cost complexity for LinkSelFiE. Moreover, we perform extensive simulations under various scenarios to corroborate that LinkSelFiE outperforms other existing methods in terms of both identifying the optimal link and reducing quantum resource consumption.