  The production system is a theoretical model of computation relevant to the
artificial intelligence field allowing for problem solving procedures such as
hierarchical tree search. In this work we explore some of the connections
between artificial intelligence and quantum computation by presenting a model
for a quantum production system. Our approach focuses on initially developing a
model for a reversible production system which is a simple mapping of Bennett's
reversible Turing machine. We then expand on this result in order to
accommodate for the requirements of quantum computation. We present the details
of how our proposition can be used alongside Grover's algorithm in order to
yield a speedup comparatively to its classical counterpart. We discuss the
requirements associated with such a speedup and how it compares against a
similar quantum hierarchical search approach.
