Quantum computing defines the use of quantum mechanics in the computation process. Given that Moore's law is about to reach its physical limits, it is natural to search for new technologies and computation models. The need for mechanisms and verification processes for infinite quantum computation will draw the attention of the research community. Potential applications of the proposed automata concern the verification of quantum systems and the design of appropriate quantum circuits. In the present work we define a quantum version of ω-automata, the periodic quantum automata that are able to efficiently recognize ω-languages of the form (ab), where m is a finite number. We present our definitions through examples and figures. Even if our definition is simple, yet it has several interesting and useful properties. For example, they seem to be space efficient for periodic ω-languages of the form (ab).
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