  We consider a version of Shor's quantum factoring algorithm such that the
quantum Fourier transform is replaced by an extremely simple one where
decomposition coefficients take only the values of $1,i,-1,-i$. In numerous
calculations which have been carried out so far, our algorithm has been
surprisingly stable and never failed. There are numerical indications that the
probability of period finding given by the algorithm is a slowly decreasing
function of the number to be factorized and is typically less than in Shor's
algorithm. On the other hand, quantum computer (QC), capable of implementing
our algorithm, will require a much less amount of resources and will be much
less error-sensitive than standard QC. We also propose a modification of
Coppersmith' Approximate Fast Fourier Transform. The numerical results show
that the probability is signifacantly amplified even in the first post integral
approximation. Our algorithm can be very useful at early stages of development
of quantum computer.
