  This article is an attempt to generalize the classical theory of reversible
computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and
by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum
case. This is a fundamental step towards the construction of a quantum computer
because a time efficient quantum computation is a reversible physical process.
The paper is organized as follows. The first section reviews the classical
theory of reversible computing. In the second section it is showed that the
designs used in the classical framework to decrease the consumption of space
cannot be generalized to the quantum case; it is also suggested that quantum
computing is generally more demanding of space than classical computing. In the
last section a new model of fully quantum and reversible automaton is proposed.
The computational power of this automaton is at least equal to that of
classical automata. Some conclusion are drawn in the last section.
