The capacity of classical neurocomputers is limited by the number of c
lassical degrees of freedom, which is roughly proportional to the size
of the computer. By contrast, a hypothetical quantum neurocomputer ca
n implement an exponentially larger number of the degrees of freedom w
ithin the same size. In this paper an attempt is made to reconcile the
linear reversible structure of quantum evolution with nonlinear irrev
ersible dynamics for neural nets.