  This paper proposed a quantum analogue of classical queue automata by using
the definition of the quantum Turing machine and quantum finite-state automata.
However, quantum automata equipped with storage medium of a stack has been
considered, but the concept of quantum queue automata has not been introduced
so far. The classical Turing machines can be simulated by classical queue
automata. Motivated by the efficiency of the quantum Turing machine and nature
of classical queue automata, we have introduced the notion of quantum queue
automata using unitary criteria. Our contributions are as follows. We have also
introduced a generalization of real-time deterministic queue automata, the
real-time quantum queue automata which work in real-time i.e. the input head
can move towards the right direction only and takes exactly one step per input
symbol. We have shown that real-time quantum queue automata is more superior
than its real-time classical variants by using quantum transitions. We have
proved the existence of the language that can be recognized by real-time
quantum queue automata and cannot be recognized by real-time deterministic
(reversible) queue automata. Further, we have shown that there is a language
that can be recognized by real-time quantum queue automata but not by real-time
non-deterministic queue automata.
