  The main goal of this paper is to give a rigorous mathematical description of
systems for processing quantum information. To do it authors consider abstract
state machines as models of classical computational systems. This class of
machines is refined by introducing constrains on a state structure, namely, it
is assumed that state of computational process has two components: a control
unit state and a memory state. Then authors modify the class of models by
substituting the deterministic evolutionary mechanism for a stochastic
evolutionary mechanism. This approach can be generalized to the quantum case:
one can replace transformations of a classical memory with quantum operations
on a quantum memory. Hence the authors come to the need to construct a
mathematical model of an operation on the quantum memory. It leads them to the
notion of an abstract quantum automaton. Further the authors demonstrate that a
quantum teleportation process is described as evolutionary process for some
abstract quantum automaton.
