Universality of classical and quantum SAT-UNSAT transitions of convex continuous satisfaction problems

Abstract

Here we investigate the single-layer linearized perceptron near the SAT-UNSAT transition point as a prototypical model of the convex continuous satisfaction problems. The simplicity of the model allows us to take into account the effects of the quantum fluctuation, which have not been fully investigated before. We found that the classical and quantum models have different critical exponents and thus have different universality classes. We also briefly discuss the effects of the random field.