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

TL;DR

This paper explores the SAT-UNSAT transition in convex continuous satisfaction problems, comparing classical and quantum models, revealing different universality classes and the impact of quantum fluctuations.

Contribution

It introduces a model that incorporates quantum fluctuations into the SAT-UNSAT transition analysis, highlighting differences from classical models and discussing the effects of a random field.

Findings

Classical and quantum models have different critical exponents.

Quantum fluctuations influence the universality class.

Brief discussion on the effects of the random field.

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.