Abstract: The simulated annealing method for was first proposed in the context of classical spin glasses and has become one of the most successful global optimization methods. The basic idea is that a Monte Carlo simulation with slowly decreasing temperature can explore the energy(cost-function) landscape of a complex system without getting trapped in local minimums. It is then natural to consider similar schemes based on slow reduction of quantum fluctuations in quantum annealing processes. Such schemes have been explored for some time, in theoretical model studies as well as in experiments on frustrated Ising spin systems. Quantum annealing has risen to particular prominence in the context of quantum computation, where there are now serious efforts to implement the method in actual devices, such as the D-wave quantum annealer. It is not yet clear whether true quantum annealing has been realized, however. Beyond this practical issue, a fundamental question is whether quantum annealing really is more efficient than classical simulated annealing for solving important optimization problems. I will discuss recent numerical work on this issue based on non-equilibrium quantum Monte Carlo simulations in imaginary time, in which a quantum Ising spin glass is brought toward a quantum-critical point on its way to reaching the classical optimum ground state energy.

Reference: C.-W. Liu, A. Polkovnikov, A. W. Sandvik, arXiv:1409.7192.