We give the quantum subset construction of orthomodular lattice-valued finite
automata, then we show the equivalence between orthomodular lattice-valued
finite automata, orthomodular lattice-valued deterministic finite automata and
orthomodular lattice-valued finite automata with empty string-moves. Based on
these equivalences, we study the algebraic operations on orthomodular
lattice-valued regular languages, then we establish Kleene theorem in the frame
of quantum logic