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Quantum collision models are receiving increasing attention as they describemany nontrivial phenomena in dynamics of open quantum systems. In a generalscenario of both fundamental and practical interest, a quantum systemrepeatedly interacts with individual particles or modes forming a correlatedand structured reservoir; however, classical and quantum environmentcorrelations greatly complicate the calculation and interpretation of thesystem dynamics. Here we propose an exact solution to this problem based on thetensor network formalism. We find a natural Markovian embedding for the systemdynamics, where the role of an auxiliary system is played by virtual indices ofthe network. The constructed embedding is amenable to analytical treatment fora number of timely problems like the system interaction with two-photonwavepackets, structured photonic states, and one-dimensional spin chains. Wealso derive a time-convolution master equation and relate its memory kernelwith the environment correlation function, thus revealing a clear physicalpicture of memory effects in the dynamics. The results advance tensor-networkmethods in the fields of quantum optics and quantum transport.

Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks