  We developed a non-Hermitian quantum optimization algorithm to find the
ground state of the ferromagnetic Ising model with up to 1024 spins (qubits).
Our approach leads to significant reduction of the annealing time. Analytical
and numerical results demonstrate that the total annealing time is proportional
to ln N, where N is the number of spins. This encouraging result is important
in using classical computers in combination with quantum algorithms for the
fast solutions of NP-complete problems. Additional research is proposed for
extending our dissipative algorithm to more complicated problems.
