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Classical-Quantum Mixing in the Random 2-Satisfiability Problem
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.Comment: Updated reference
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