Iterative classical superadiabatic algorithm for combinatorial optimization

Abstract: We consider a classical and superadiabatic version of an iterative quantum adiabatic algorithm to solve combinatorial optimization problems. This algorithm is deterministic because it is based on purely classical dynamics, that is, it does not rely on any stochastic approach to mimic quantum dynamics. Moreover, use of shortcuts to adiabaticity makes the algorithm independent of the annealing time. We apply this algorithm to a certain class of hard instances of the 3-SAT problem. We find that more than 90\% of such 64-bits hard instances can be resolved by a few iteration. Our approach can also be used to analyze properties of instances themselves apart from stochastic uncertainty and shortage of adiabaticity.