Classical-quantum mixing in the random 2-satisfiability problem

Ionut-Dragos Potirniche, C. R. Laumann, S. L. Sondhi
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
Classical satisfiability (SAT) and quantum satisfiability (QSAT) are complete problems for the complexity classes NP and QMA which are believed to be intractable for classical and quantum computers, respectively. Statistical ensembles of instances of these problems have been studied previously in an attempt to elucidate their typical, as opposed to worst case, behavior. In this paper we introduce a new statistical ensemble that interpolates between classical and quantum. For the simplest
more » ... -QSAT ensemble we find the exact boundary that separates SAT and UNSAT instances. We do so by establishing coincident lower and upper bounds, in the limit of large instances, on the extent of the UNSAT and SAT regions, respectively.
doi:10.1103/physreva.92.040301 fatcat:e7od6gm56jggnp4fyjhbxmtdjm