In this paper we introduce classically time-controlled quantum automata or CTQA, which is a slight but reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution operators and a scheduler defining how long each operator will run. Surprisingly enough, time-dependent evolutions provide a significant change in the computational power of quantum automata with respect to a discrete quantum model. Furthermore, CTQA presents itself as a new model of computation that provides a different approach to a formal study of “classical control, quantum data” schemes in quantum computing.CONACYT – Consejo Nacional de Ciencia y TecnologíaPROCIENCIA