Stochastic Dynamics and Control with Applications to Quantum Queueing Networks

M. Yanagisawa

Karim S. Elsayed, Olga Izyumtseva, Wasiur R. KhudaBukhsh +1 more

We present a queueing model for a quantum communication network consisting of a primary queue and a service queue in which Bell pairs are formed and stored. The Bell pairs are inherently extremely short-lived rendering the service queue (the quantum queue) much faster than the primary queue. We study the asymptotic behaviour of this multi-scale queueing system via a stochastic averaging principle. We prove a Functional Law of Large Numbers (FLLN) and a Functional Central Limit Theorem (FCLT) for the standard queue averaging the dynamics of the fast service queue.

Kunio Yasue

Sergio A Albeverio, Ph. Blanchard, D. Testard

Nicolò Lo Piparo, William J. Munro, Kae Nemoto

We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing memory decoherence, while entanglement requests arrive according to Poisson and bursty ON--OFF processes. Using a queueing-theoretic framework, we couple physical-layer memory dynamics with congestion-dependent service behavior to analyze stability, delay, and fidelity trade-offs. Operating regimes are characterized in terms of the load parameter, showing that fixed cutoff policies impose a fundamental fidelity--latency trade-off together with strict stability limits. Queue-aware adaptive control strategies are then introduced that dynamically adjust memory cutoff times and the number of parallel entanglement-generation channels. Cutoff adaptation restores stability near critical load by trading fidelity for service capacity, whereas resource scaling increases capacity without degrading entanglement quality. Under bursty traffic, joint adaptation suppresses delay spikes while activating additional channels only during congestion periods. The framework is further extended to a two-user shared-resource scenario in which independent traffic flows compete for a common resource pool. Stability is determined by aggregate load, while adaptive resource redistribution stabilizes queues that diverge under fixed partitioning. These results provide a queue-aware congestion-control perspective for adaptive resource management in quantum networks.

Guilherme Fiusa, Gabriel Teixeira Landi

Collision models describe the sequential interactions of a system with independent ancillas. Motivated by recent advances in neutral atom arrays, here we investigate a model where the ancillas are governed by a classical controller that allows them to queue up while they wait for their turn to interact with the system. The ancillas can undergo individual open dynamics while they wait, which could cause them to, e.g., decohere. The system, which plays the role of the server in the queue, can also undergo its own open dynamics whenever it is idle. We show that this framework greatly generalizes existing approaches for quantum collision models, recovering the deterministic and stochastic formulations in the appropriate limits. Next, we show how the combination of queueing dynamics with quantum collisions introduces rich dynamical phenomena, including phase transitions and a sharp dependence on the queue statistics.