Classical and quantum satisfiability
Anderson de Ara\'ujo (University of S\~ao Paulo), Marcelo Finger, (University of S\~ao Paulo)
TL;DR
This paper introduces a linear algebraic and logical framework for QSAT, demonstrating that it is not a straightforward extension of classical SAT and highlighting implications for complexity class comparisons.
Contribution
It provides a new logical characterization of QSAT and proves it is not an extension of SAT, impacting the understanding of NP and QMA class relationships.
Findings
QSAT defined via linear algebraic and logical methods
Logical version of QSAT is not an extension of classical SAT
Implications for NP and QMA complexity classes
Abstract
We present the linear algebraic definition of QSAT and propose a direct logical characterization of such a definition. We then prove that this logical version of QSAT is not an extension of classical satisfiability problem (SAT). This shows that QSAT does not allow a direct comparison between the complexity classes NP and QMA, for which SAT and QSAT are respectively complete.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Computability, Logic, AI Algorithms