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arXiv:2609.16198

Utility-Based Path Selection and Configuration in Quantum Networks via Layered Shortest Paths

Leonardo Bacciottini, Subhransu Maji, Don Towsley, Gayane Vardoyan

quant-phcs.NISubmitted Sep 14, 2026• Announced Sep 16, 2026• 0 citations
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Abstract

A path in a quantum network is a chain of repeaters that distributes entanglement between two users. Selecting a path requires balancing the rate and quality (e.g., fidelity) of the delivered entanglement, but these quantities, unlike standard routing metrics, compose non-additively. The problem is compounded by link-level configuration choices (e.g., distillation rounds or emitter brightness tuning), each trading rate against fidelity, so that a path's performance depends jointly on its route and its per-link settings. We cast this joint path selection and configuration problem as a shortest path computation on a layered graph whose layers track discretized end-to-end fidelity. A single run returns the full rate fidelity Pareto frontier, from which the path maximizing any nondecreasing utility function of rate and fidelity can be selected. We prove that for certain utility functions (including the secret key rate of BB84), the method is a fully polynomial time approximation scheme, returning a near-optimal path within a specified tolerance. We further characterize exactly when cheaper scalarization-based routing suffices: it is optimal for utility functions with convex fidelity profiles, but can be arbitrarily suboptimal otherwise (e.g., for step-like, sigmoidal utilities), whereas the layered method remains reliable in all cases.

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A path in a quantum network is a chain of repeaters that distributes entanglement between two users. Selecting a path requires balancing the rate and quality (e.g., fidelity) of the delivered entanglement, but these quantities, unlike standard routing metrics, compose non-additively. The problem is compounded by link-level configuration choices (e.g., distillation rounds or emitter brightness tuning), each trading rate against fidelity, so that a path's performance depends jointly on its route and its per-link settings. We cast this joint path selection and configuration problem as a shortest path computation on a layered graph whose layers track discretized end-to-end fidelity. A single run returns the full rate fidelity Pareto frontier, from which the path maximizing any nondecreasing utility function of rate and fidelity can be selected. We prove that for certain utility functions (including the secret key rate of BB84), the method is a fully polynomial time approximation scheme, returning a near-optimal path within a specified tolerance. We further characterize exactly when cheaper scalarization-based routing suffices: it is optimal for utility functions with convex fidelity profiles, but can be arbitrarily suboptimal otherwise (e.g., for step-like, sigmoidal utilities), whereas the layered method remains reliable in all cases.
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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.
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Distributed quantum computation requires many entangled pairs to be available simultaneously, so routing must optimize fidelity from a fixed, short-lived set of network resources rather than the rate of pairs accumulated over time. We formulate this one-shot routing problem for heterogeneous Werner-state links and jointly optimize path selection and the schedule of entanglement swapping and distillation. We show that the common purify-then-swap ordering is not optimal network-wide and that exact schedule enumeration requires mΘ(m)m^{Θ(m)}mΘ(m) time. We introduce Fidelity-Optimizing Local Detours (FOLD), a heuristic that starts from the highest-fidelity path and merges a detour only when distillation improves on both routes and raises end-to-end fidelity. FOLD runs in polynomial time, recovers almost all of the optimal fidelity on tractable instances, and is four orders of magnitude faster than exact optimization at circuit rank 555. On the Internet topologies where any strategy improves on shortest-path routing, FOLD achieves the highest mean end-to-end fidelity among the polynomial baselines. We further extend the formulation to links whose fidelities are known only as distributions, where uncertainty, rather than the effort spent routing, limits the fidelity delivered. Through an example of requests competing for the same links, we show that coordination becomes a condition for feasibility, and that a shared path budget controls the fidelity trade-off between them.