Quantum utility routing raises mean path SKR by 193.2% over A* in CV-QKD networks while using 78.4% fewer nodes than Max–Min

QUR embeds transition-level composable finite-size secret key rates directly into the routing cost, letting routes trade bottleneck SKR against distance, relay use, hop count, movement away from the target, and detour through six configurable weights. Prior CV-QKD networking studies considered dynamic SKR-based routing, shortest-path selection, or composable end-to-end security in routing analyses; here transition-level composable finite-size SKRs are combined with explicit distance, relay, hop-count, and geometry penalties inside a single weighted search. Simulations use Waxman random graphs with 1000 nodes at a given radius and degree threshold, averaged over 50 independently generated graphs per parameter point; transition rates follow the composable finite-size security framework for Gaussian networks with untrusted relays under collective Gaussian attacks, and transitions with non-positive SKR are excluded.

At the default network configuration, QURgo increases mean path SKR by 193.2% relative to A*, while using 78.4% fewer nodes than Max–Min, and QURfw shows the same qualitative behavior. A* favors geometrically short routes that can contain weak quantum transitions, while Max–Min maximizes the weakest transition at the cost of substantially larger node use; QUR occupies the intermediate regime, improving bottleneck SKR and node efficiency together. The numbers come from the default-configuration simulation comparison; both QUR modes outperform the reference algorithms in the SKR-per-node comparison, the mean number of accepted paths is similar across methods, and QURgo matches the A* path count in 100.0% of tested graphs.

The machine-learned fixed-weight QURfw retains almost the same node saving and multipath behavior after giving up per-graph weight optimization, sacrificing only some SKR. This indicates that the useful QUR operating regime is not produced only by highly specialized weights for individual graphs; a common weight vector captures much of the routing behavior across the network ensemble, allowing the expensive optimization stage to be moved offline. QURfw uses a histogram-based gradient boosting model taking graph features and the six weights as input, trained on up to 50×8000 exact graph–weight evaluations; the fixed vector is selected from each graph's 500 highest-scoring vectors plus additional randomly sampled vectors.

Untrusted nodes can continue to support connectivity as public CV Bell measurement relays: at 76.3% untrusted nodes, QURgo still achieves 100.0% routing success and finds approximately 3.92 routes per graph, whereas at about 91.9% untrusted nodes routing success falls sharply. This frames the trust scan as a transition from a rate-limited regime to a trusted-connectivity-limited regime, showing that allowing untrusted Bell measurement relays substantially extends the former but cannot compensate indefinitely. The conclusion comes from simulations scanning the degree threshold, with nodes labeled untrusted when their degree exceeds the threshold; the authors note that at the most severe trust restriction the limiting factor is no longer only the SKR of relay-assisted transitions but also that remaining trusted nodes become too sparse to form a positive-SKR connection.

The framework applies to CV-QKD networks whose topology, node positions, link lengths, and trust status are known, where nodes are equipped with two-mode squeezed vacuum sources and the required measurement capabilities, trusted nodes form end-to-end routes through key forwarding, and untrusted nodes participate as public CV Bell measurement relays. It targets metropolitan-scale Waxman random-graph simulations with a default of 1000 nodes and up to five node-disjoint routes per graph, averaged over 50 independently generated graphs per parameter point; when the network radius is varied, the characteristic connection distance is maintained and only link lengths increase. For a network operator, the weight vector is a policy choice: the present score favors reduced node use while discouraging poor key rate, but could instead emphasize relay avoidance, higher key throughput, lower latency, multipath availability, or resilience. QURfw indicates that the expensive weight optimization can be moved offline, leaving only route search and transition rate updates during operation, which suits dynamic networks where channel transmissivity and available SKR vary with time.

The present results rest on Waxman random-graph simulations with specific parameter settings and have not been validated on real metropolitan networks or other topologies; the fixed weight vector is learned and evaluated on the same network ensemble, so transfer to unseen topologies remains to be tested. Composability is applied at the transition level here, and the authors note that recent work shows end-to-end composable security introduces a security–rate trade-off in which a total security budget must be distributed across all transitions of a route; this coupling is avoided by assigning a fixed and relatively strict security parameter to each transition, so the end-to-end security parameter is not fixed a priori but increases with the number of transitions in the selected route. The simulations also do not include heterogeneous equipment, time-dependent channels, or trust assignments based on ownership, location, or operational history, which remain directions for extension.