  We analyze the complexity of the quantum optimization algorithm based on
adiabatic evolution for the set partition problem. We introduce a cost function
defined on a logarithmic scale of the partition residues so that the total
number of values of the cost function is of the order of the problem size. We
simulate the behavior of the algorithm by numerical solution of the
time-dependent Schroedinger equation as well as the stationary equation for the
adiabatic eigenvalues. The numerical results for the time-dependent quantum
evolution indicate that the complexity of the algorithm scales exponentially
with the problem size.This result appears to contradict the recent numerical
results for complexity of quantum adiabatic algorithm applied to a different
NP-complete problem (Farhi et al, Science 292, p.472 (2001)).
