  The exploration of new problem classes for quantum computation is an active
area of research. An essentially completely unexplored topic is the use of
quantum algorithms and computing to explore and ask questions \textit{about}
the functional dynamics of neural networks. This is a component of the
still-nascent topic of applying quantum computing to the modeling and
simulations of biological and artificial neural networks. In this work, we show
how a carefully constructed set of conditions can use two foundational quantum
algorithms, Grover and Deutsch-Josza, in such a way that the output
measurements admit an interpretation that guarantees we can infer if a simple
representation of a neural network (which applies to both biological and
artificial networks) after some period of time has the potential to continue
sustaining dynamic activity. Or whether the dynamics are guaranteed to stop
either through 'epileptic' dynamics or quiescence.
