Novel Support Routing Algorithm for Quantum Satellite Networks with Finite Quantum Memory.

Quantum memories are a critical component of entanglement-based quantum networks, enabling the storage and synchronisation of quantum states across dynamic links. However, current quantum memories have significantly lower capacity than the rate at which entanglement can be generated, making memory saturation a key bottleneck that reduces network efficiency and hinders the scaling of quantum networks. This problem is especially pronounced in dynamic satellite-based quantum networks, where short visibility windows constrain link availability. In this paper, we present a support entanglement-swapping algorithm that utilises leftover entanglement in quantum memories, thereby alleviating memory saturation and increasing network connectivity. Our algorithm combines two mathematical concepts, line graphs and maximum-cardinality matching, to select independent entanglement swap pairs without sharing any entanglement between concurrent swaps. This property ensures that the resulting changes to the network remain local and mutually independent, making the algorithm easy to integrate alongside any existing routing schemes without requiring network-wide coordination. We evaluate the algorithm through simulations on both static fibre-based networks and dynamic satellite networks. Across most configurations, our algorithm increases both the mean and the total number of entanglements shared between end nodes, while also increasing the network's long-range connectivity. The 'SwapWithToUse' algorithm variant consistently provides the greatest improvements, with gains increasing as entanglement-generation rate increases.