Unary Quantum Finite State Automata with Control Language

We study quantum finite automata with control language (qfcs), a theoretical model for finite memory hybrid systems coupling a classical computational framework with a quantum component. We constructively show how to simulate measure-once, measure-many, reversible, and Latvian qfas by qfcs, emphasizing the size cost of such simulations. Next, we prove the decidability of testing the periodicity of the stochastic events induced by a given qfc. Thanks to our qfa simulations, we can extend such a decidability result to measure-once, measure-many, reversible, and Latvian qfas as well. Finally, we focus on comparing the size efficiency of quantum and classical finite state automata on unary regular language recognition. We show that unary regular languages can be recognized by isolated cut point qfcs for which the size is generally quadratically smaller than the size of equivalent dfas.