  We show that the time evolution of the wave function of a quantum mechanical
many particle system can be implemented very efficiently on a quantum computer.
The computational cost of such a simulation is comparable to the cost of a
conventional simulation of the corresponding classical system. We then sketch
how results of interest, like the energy spectrum of a system, can be obtained.
We also indicate that ultimately the simulation of quantum field theory might
be possible on large quantum computers.
  We want to demonstrate that in principle various interesting things can be
done. Actual applications will have to be worked out in detail also depending
on what kind of quantum computer may be available one day...
