Thermal, quantum and simulated quantum annealing: analytical comparisons for simple models

We study various annealing dynamics, both classical and quantum, for simple mean-field models and explain how to describe their behavior in the thermodynamic limit in terms of differential equations. In particular we emphasize the differences between quantum annealing (i.e. evolution with Schr\"odinger equation) and simulated quantum annealing (i.e. annealing of a Quantum Monte Carlo simulation).