**abstract:**
Recently, a formalism for discrete time open quantum walks (OQWs) was introduced 1. The formalism is similar to the formalism of quantum Markov chains and rests upon the implementation of appropriate completely positive maps. The class of OQWs includes classical random walks. It was shown that OQWs can perform universal dissipative quantum computation and state engineering 2.

Here, we present the microscopic derivation of OQWs. A walk on a graph is considered and transitions between vertices are mediated by the interaction of the walker with the shared bosonic environment. The reduced dynamics is described in terms of generalised master equations. The time discretization of the master equation gives raise to an OQW. Based on the class of microscopic models considered here possible physical implementations of dissipative quantum computing are discussed.

1 S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy, J. Stat. Phys. 147 (2012) 832. 2 I. Sinayskiy and F. petruccione, QIP 11 (2012) 1301.

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