  Finding the optimal solution to a complex optimization problem is of great
importance in practically all fields of science, technology, technical design
and econometrics. We demonstrate that a modified Grover's quantum algorithm can
be applied to real problems of finding a global minimum using modest numbers of
quantum bits. Calculations of the global minimum of simple test functions and
Lennard-Jones clusters have been carried out on a quantum computer simulator
using a modified Grover's algorithm. The number of function evaluations $N$
reduced from O(N) in classical simulation to $O(\sqrt{N})$ in quantum
simulation. We also show how the Grover's quantum algorithm can be combined
with the classical Pivot method for global optimization to treat larger
systems.
