We present a polynomial quantum algorithm for the Abelian stabilizer problem
which includes both factoring and the discrete logarithm. Thus we extend famous
Shor's results. Our method is based on a procedure for measuring an eigenvalue
of a unitary operator. Another application of this
procedure is a polynomial quantum Fourier transform algorithm for an arbitrary
finite Abelian group. The paper also contains a rather detailed introduction
to the theory of quantum computation.