Open quantum walks (OQWs) were introduced as quantum analogs to classical Markov chains. In contrast to unitary quantum walks, OQWs are driven by the dissipative interaction with the environment and are formulated in the language of open quantum systems. OQWs demonstrates rich dynamical behavior and can be used to perform efficient dissipative quantum computation and state engineering. Another benefit of OQWs is in the well-defined classical limit. The unitary quantum walks are gaining computational power from the quantum interference between the nodes of a walk, and the asymptotic behavior of them is highly non- gaussian.

In this talk, I will review the latest status of the OQW research and introduce a generalization of the QWs, which includes OQWs and unitary quantum walks as limiting cases. In this generalization, one can naturally identify an order parameter P = (characteristic time)/(characteristic length) and perform a “thermodynamic” limit in the characteristic parameters, while keeping P a constant. As a result, the asymptotic distribution of the position of the walker for the small values of P corresponds to a unitary quantum walk and for the large values of P to an OQWs, respectively.