  1-way quantum finite automata are deterministic and reversible in nature,
which greatly reduces its accepting property. In fact the set of languages
accepted by 1-way quantum finite automata is a proper subset of regular
languages. In this paper we replace the tape head of 1-way quantum finite
automata with DNA double strand and name the model Watson-Crick quantum finite
automata. The non-injective complementarity relation of Watson-Crick automata
introduces non-determinism in the quantum model. We show that this introduction
of non-determinism increases the computational power of 1-way Quantum finite
automata significantly. We establish that Watson-Crick quantum finite automata
can accept all regular languages and that it also accepts some languages not
accepted by any multihead deterministic finite automata. Exploiting the
superposition property of quantum finite automata we show that Watson-Crick
quantum finite automata accept the language L=ww where w belongs to {a,b}*.
