Expressiveness and Computational Complexity of Geometric Quantum Logic

Details Expressiveness and Computational Complexity of Geometric Quantum Logic Expressiveness and Computational Complexity of Geometric Quantum Logic

2010-04-10

arxiv.org/abs/1004.1696v1

Mathematics

Logic

Scientific paper

Quantum logic generalizes, and in dimension one coincides with, Boolean logic. We show that the satisfiability problem of quantum logic formulas is NP-complete in dimension two as well. For higher higher-dimensional spaces R^d and C^d with d>2 fixed, we establish quantum satisfiability to be polynomial time equivalent to the real feasibility of a multivariate quartic polynomial equation: a problem well-known complete for the counterpart of NP in the Blum-Shub-Smale model of computation lying (probably strictly) between classical NP and PSPACE. We finally investigate the problem over INdefinite finite dimensions and relate it to the real feasibility of quartic NONcommutative *-polynomial equations.

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