Routing in Non-Isotonic Quantum Networks

TL;DR

This paper introduces advanced algorithms for routing in quantum networks with non-isotonic utility functions, improving efficiency over exhaustive search and enabling better path quality and computational tradeoffs.

Contribution

It presents new best-first-search and metaheuristic algorithms tailored for non-isotonic quantum network routing, surpassing traditional methods.

Findings

Proposed algorithms outperform exhaustive search in speed and efficiency.

Best-first-search algorithms find optimal or near-optimal paths.

Metaheuristics enable balancing path quality with computational cost.

Abstract

Optimal routing in quantum-repeater networks requires finding the best path that connects a pair of end nodes. Most previous work on routing in quantum networks assumes utility functions that are isotonic, meaning that the ordering of two paths does not change when extending both with the same edge. However, we show that utility functions that take into account both the rate and quality of the entanglement generation (e.g., the secret-key rate) are often non-isotonic. This makes pathfinding difficult as classical algorithms such as Dijkstra's become unsuitable, with the state of the art for quantum networks being an exhaustive search over all possible paths. In this work we present improved algorithms. First, we present two best-first-search algorithms that use destination-aware merit functions for faster convergence. One of these provably finds the best path, while the other uses heuristics to achieve an effectively sublinear scaling of the query count in the network size while in practice always finding a close-to-optimal path. Second, we present metaheuristic algorithms (simulated annealing and a genetic algorithm) that enable tuning a tradeoff between path quality and computational overhead. While we focus on swap-ASAP quantum repeaters for concreteness, our algorithms are readily generalized to different repeater schemes and models.