03676nas a2200121 4500008004100000245004100041210004100082260001500123520334200138100002003480700001703500856003703517 2017 eng d00aSubstochastic Monte Carlo Algorithms0 aSubstochastic Monte Carlo Algorithms c2017/04/283 a

In this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization algorithms in their own right. In SSMC, a population of walkers is initialized according to a known distribution on an arbitrary search space and varied into the solution of some optimization problem of interest. The first argument of this paper shows how an existing classical algorithm, "Go-With-The-Winners" (GWW), is a limiting case of SSMC when restricted to binary search and particular driving dynamics. 
Although limiting to GWW, SSMC is more general. We show that (1) GWW can be efficiently simulated within the SSMC framework, (2) SSMC can be exponentially faster than GWW, (3) by naturally incorporating structural information, SSMC can exponentially outperform the quantum algorithm that first inspired it, and (4) SSMC exhibits desirable search features in general spaces. Our approach combines ideas from genetic algorithms (GWW), theoretical probability (Fleming-Viot processes), and quantum computing. Not only do we demonstrate that SSMC is often more efficient than competing algorithms, but we also hope that our results connecting these disciplines will impact each independently. An implemented version of SSMC has previously enjoyed some success as a competitive optimization algorithm for Max-k-SAT.

1 aJarret, Michael1 aLackey, Brad uhttps://arxiv.org/abs/1704.09014