  The model of open quantum systems is adopted to describe the non-local
dynamical behaviour of qubits processed by entangling gates. The analysis gets
to the conclusion that a distinction between evaluation steps and task-oriented
computing steps is justified only within classical computation. In fact, the
use of entangling gates permits to reduce two steps (evaluation and
calculation) to a single computational one, and this determines an effective
computational speed-up. The application of the open quantum systems model
suggests that the reduction to one-computational step is strongly related to
the existence of Universal Dynamical Maps describing the evolution of component
systems of two-qubits gates. As the description in terms of Universal Dynamical
Map is possible only in the presence of a separable initial state, it turns out
that the internal reduced dynamics with respect to entangling gates is neither
unitary nor Markovian. The fact imposes a holistic vision on the structure of
the algorithm, where the entangling gates shall remain indivisible unities, or
black boxes, in order to preserve computational speed as well as reversibility.
This fact suggests to adopt a perspective on computation which is completely
non-classical: the whole algorithm turns out not to be the sequence of its
temporal parts.
