Traditional simulated annealing uses thermal fluctuations for convergence i
n optimization problems. Quantum tunneling provides a different mechanism f
or moving between states, with the potential for reduced time scales. Therm
al and quantum annealing are compared in a model disordered magnet, where t
he effects of quantum mechanics can be tuned by varying an applied magnetic
field. The results indicate that quantum annealing hastens convergence to
the optimum state.