  Quantum annealing method has been widely attracted attention in statistical
physics and information science since it is expected to be a powerful method to
obtain the best solution of optimization problem as well as simulated
annealing. The quantum annealing method was incubated in quantum statistical
physics. This is an alternative method of the simulated annealing which is
well-adopted for many optimization problems. In the simulated annealing, we
obtain a solution of optimization problem by decreasing temperature (thermal
fluctuation) gradually. In the quantum annealing, in contrast, we decrease
quantum field (quantum fluctuation) gradually and obtain a solution. In this
paper we review how to implement quantum annealing and show some quantum
fluctuation effects in frustrated Ising spin systems.
