  It is shown that evolution of wave functions in nonintegrable quantum systems
is unpredictable for a long time T because of rapid growth of number of
elementary computational operations $\mathcal O(T)\sim T^\alpha$. On the other
hand, the evolution of wave functions in integrable systems can be predicted by
the fast algorithms $\mathcal O(T)\sim (log_2 T)^\beta$ for logarithmically
short time and thus there is an algorithmic "compressibility" of their
dynamics. The difference between integrable and nonintegrable systems in our
approach looks identically for classical and quantum systems. Therefore the
minimal number of bit operations $\mathcal O(T)$ needed to predict a state of
system for time interval T can be used as universal sign of chaos.
