Classically time-controlled quantum automata: definition and properties

In this paper, we introduce classically time-controlled quantum automata or classically time-controlled quantum automaton (CTQA), which is a reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution and a 'scheduler' defining how long each Hamiltonian will run. Surprisingly enough, time-dependent evolution provides a significant change in the computational power of quantum automata with respect to a discrete quantum model. Indeed, we show that if a scheduler is not computationally restricted, then a CTQA could even decide the Halting problem. In order to unearth the computational capabilities of CTQAs, we study the case of a computationally restricted scheduler. In particular, we showed that depending on the type of restriction imposed on the scheduler, a CTQA can (i) recognize non-regular languages with cut-point, even in the presence of Karp-Lipton advice, and (ii) recognize non-regular promise languages with bounded-error. Furthermore, we study the cutpoint-union of cutpoint languages by introducing a new model of Moore-Crutchfield quantum finite automata with a rotating tape head. 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.