In this paper, we introduce 2-way quantum nite state automata (2qfa's), which are the quantum analogue of deterministic, nondeterministic and probabilistic 2-way nite state automata (2dfa's, 2nfa's and 2pfa's). We prove the following facts regarding 2qfa's. 1. For any > 0, there exists a 2qfa M which recognizes the non-regular language L = fa m b m j m 1g with (one-sided) error bounded by , and which halts in polynomial time. Speciically, M accepts any string in L with probability 1 and rejectsâ€¦Â CONTINUE READING