Theory of Quantum Annealing of an Ising Spin Glass
  Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. Comparing classical and quantum Monte Carlo annealing protocols on the random two-dimensional Ising model we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing, based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power which makes it faster 
Giuseppe E. Santoro (1), Roman Martonak (2 and 3), Erio Tosatti (1 and   4), and Roberto Car (5) ((1) SISSA and INFM, Triest...