# Computational Complexity of Quantum Satisfiability

@article{Herrmann2011ComputationalCO, title={Computational Complexity of Quantum Satisfiability}, author={Christian Herrmann and Martin Ziegler}, journal={2011 IEEE 26th Annual Symposium on Logic in Computer Science}, year={2011}, pages={175-184} }

Quantum logic generalizes, and in dimension one coincides with, Boolean propositional logic. We introduce the weak and strong satisfiability problem for quantum logic formulas, and show both NP-complete in dimension two as well. For higher-dimensional spaces R^d and C^d with d>2 fixed, on the other hand, we show the problem to be complete for the nondeterministic Blum-Shub-Smale model of real computation. This provides a unified view on both Turing and real BSS complexity theory, and adds (a…

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