Anderson de Araújo,  Marcelo Finger. 

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.

http://www.lbd.dcc.ufmg.br/colecoes/lsfa/2011/006.pdf

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