  The universal quantum computation model based on quantum walk by Childs has
opened the door for a new way of studying the limitations and advantages of
quantum computation, as well as for its intermediate-term simulation. In recent
years, the growing interest in noisy intermediate-scale quantum computers
(NISQ) has lead to intense efforts being directed at understanding the
computational advantages of open quantum systems. In this work, we extend the
quantum walk model to open noisy systems in order to provide such a tool for
the study of NISQ computers. Our method does not use explicit purification, and
allows to ignore the environment degrees of freedom and get direct and much
more efficient access to the entanglement properties of the system. In our
representation, the quantum walk amplitudes represent elements in a density
matrix rather than the wavefunction of a pure state. Despite the non-trivial
manifestation of the normalization requirement in this setting, we model the
application of general unitary gates and nonunitary channels, with an explicit
implementation protocol for channels that are commonly used in noise models.
