  Quantum annealing is a generic algorithm using quantum-mechanical
fluctuations to search for the solution of an optimization problem. The present
paper first reviews the fundamentals of quantum annealing and then reports on
preliminary results for an alternative method. The review part includes the
relationship of quantum annealing with classical simulated annealing. We next
propose a novel quantum algorithm which might be available for hard
optimization problems by using a classical-quantum mapping as well as the
Jarzynski equality introduced in nonequilibrium statistical physics.
