Classical-Quantum Mixing in the Random 2-Satisfiability Problem

TL;DR

This paper introduces a new statistical ensemble that interpolates between classical and quantum satisfiability problems, providing exact boundaries for SAT and UNSAT instances in the 2-SAT/2-QSAT case.

Contribution

It develops a novel ensemble bridging classical and quantum satisfiability, and precisely characterizes the SAT/UNSAT boundary for 2-SAT/2-QSAT.

Findings

Exact SAT/UNSAT boundary for 2-SAT/2-QSAT ensemble

Established bounds on SAT and UNSAT regions in large instances

Unified framework for classical and quantum satisfiability analysis

Abstract

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 2-SAT/2-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.