Queued quantum collision models

Collision models describe the sequential interactions of a system with independent ancillas. Motivated by recent advances in neutral atom arrays, in this Letter 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.