Quantum and classical annealing in spin glasses and quantum computing

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.