Column Generation for the Optimization of Switching in Repeaterless Quantum Networks

TL;DR

This paper presents a novel graph-based linear programming approach with column generation to optimize switching strategies in repeaterless quantum networks, improving scalability and network performance.

Contribution

It introduces a new graph formulation and column generation method for efficient, scalable optimization of switching configurations in quantum communication networks.

Findings

The method scales well with network size.

The approach provides a practical algorithm for network optimization.

Empirical tests confirm the framework's effectiveness.

Abstract

Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant challenge due to the combinatorial complexity. We introduce a novel graph formulation to model the physical and logical structure of repeaterless quantum networks, enabling the systematic optimization of switching strategies. The problem is posed as a linear program and solved using a column generation approach. This method enables scalable computation despite the exponential number of possible network configurations. Our results not only provide a formal foundation but also a practical algorithm for the optimization of switching. Empirical tests confirm the solver's scalability with network size, demonstrating the framework's effectiveness and laying the groundwork for future optimization of quantum network control.