Quantum collision models are state-of-the-art approaches to describe open quantum systems through repeated interactions with a coarse-grained environment [1]. Despite their wide-spread use -- for instance in quantum optics, quantum thermodynamics, or the study of non-Markovian dynamics -- these models don't allow for the fully certified treatment of system-environment interactions as no complete error bounds on the simulation of system observables are available.

In this talk, we will show that Markovian and non-Markovian collision models can be recovered analytically from chain mapping techniques starting from a general microscopic Hamiltonian [2]. We will see that this novel derivation reveals a new source of error -- induced by an unfaithful sampling of the environment -- in reduced dynamics obtained with collision models that can be larger than all the other errors in the dynamics. The complete characterization of this error finally enables the promotion of collision models to the class of numerically exact methods. Remarkably, this derivation gives a prescription on the absolute size of the time step that should be used in a non-Markovian collision models in order to ensure their validity, thus defining what is an adequate coarse-graining of the environment. Finally, we will discuss the consequences of the unveiled connection between collision models and techniques based on chain mapping in terms of further development of these two types of methods.

[1] Ciccarello, F.; Lorenzo, S.; Giovannetti, V.; Palma, G. M. Quantum Collision Models: Open System Dynamics from Repeated Interactions. Physics Reports 2022, 954, 1–70. https://doi.org/10.1016/j.physrep.2022.01.001.

[2] Lacroix, T.; Cilluffo, D.; Huelga, S. F.; Plenio, M. B. Making Collision Models Exact. In Preparation 2024.