An overview of quantum computation models: quantum automata

Quantum automata, as theoretical models of quantum computers, include quantum finite automata (QFA), quantum sequential machines (QSM), quantum pushdown automata (QPDA), quantum Turing machines (QTM), quantum cellular automata (QCA), and the others, for example, automata theory based on quantum logic (orthomodular lattice-valued automata). In this paper, we try to outline a basic progress in the research on these models, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata. Also, other models closely relative to them are mentioned. In particular, based on the existing results in the literature, we finally address a number of problems to be studied in future.