  Classical and quantum annealing is discussed for a kinetically constrained
chain of $N$ non-interacting asymmetric double wells, represented by Ising
spins in a longitudinal field $h$. It is shown that in certain cases, where the
kinetic constraints may arise from infinitely high but vanishingly narrow
barriers appearing in the relaxation path of the system, quantum annealing
exploiting the quantum-mechanical penetration of sufficiently narrow barriers
may be far more efficient than its thermal counterpart.
  We have used a semiclassical picture of scattering dynamics to do our
simulation for the quantum system.
