Bayesian Optimization for Repeater Protocols

TL;DR

This paper introduces a Bayesian optimization framework to efficiently explore and identify optimal quantum repeater protocols for secret key distribution in quantum networks, considering experimental imperfections and large protocol spaces.

Contribution

The authors extend existing methods for calculating secret-key rates and apply Bayesian optimization to navigate complex protocol spaces, achieving near-optimal solutions efficiently.

Findings

Bayesian optimization reliably finds optimal repeater protocols.

The framework accurately validates against brute-force methods.

Insights are gained on maximizing protocol efficiency under various conditions.

Abstract

Efficiently distributing secret keys over long distances remains a critical challenge in the development of quantum networks. "First-generation" quantum repeater chains distribute entanglement by executing protocols composed of probabilistic entanglement generation, swapping and distillation operations. However, finding the protocol that maximizes the secret-key rate is difficult for two reasons. First, calculating the secretkey rate for a given protocol is non-trivial due to experimental imperfections and the probabilistic nature of the operations. Second, the protocol space rapidly grows with the number of nodes, and lacks any clear structure for efficient exploration. To address the first challenge, we build upon the efficient machinery developed by Li et al. [1] and we extend it, enabling numerical calculation of the secret-key rate for heterogeneous repeater chains with an arbitrary number of nodes. For navigating the large, unstructured space of repeater protocols, we implement a Bayesian optimization algorithm, which we find consistently returns the optimal result. Whenever comparisons are feasible, we validate its accuracy against results obtained through brute-force methods. Further, we use our framework to extract insight on how to maximize the efficiency of repeater protocols across varying node configurations and hardware conditions. Our results highlight the effectiveness of Bayesian optimization in exploring the potential of near-term quantum repeater chains.