 Nonlocality is a fundamental feature of quantum mechanics and its exploitation has led to the development of powerful quantum algorithms. In particular, nonlocality enables the efficient solution of certain computational problems, such as non-adaptive measurement-based quantum computing, NMQC, where the goal is to output a multivariate function. By analyzing NMQC from an information theoretical perspective, it was found that quantum correlations can compute all Boolean functions using at most n-1 qubits, while local hidden variables, LHVs, are restricted to linear functions. Here, we extend these results to NMQC with quits and prove that quantum correlations enable the computation of all three-valued logic functions using the generalized Kutrick-Greenburger Horns-Elinger, GHz, state as a resource and at most n-1 quits. This yields a corresponding generalized GHz-type paradox for any three-valued logic function that LHVs cannot compute. Furthermore, we show that not all functions can be computed efficiently with Kutrick-NMQC by providing a counter-example. This article was authored by Yelena Macaprang, Daniel Batty, Matty J. Hoban, and others. We are article.tv, links in the description below.