The Equivalence Between Quantum Mealy Automata and Quantum Moore Automata

The proposal of quantum algorithms for factorizing large numbers and of quantum searching algorithm has lead quantum computing to a new period of rapid development. Quantum automata theory has been a very active and fruitful research area, in which many meaningful results have been obtained over the past 10 years. In this paper, the authors firstly define the finite Fock space over an alphabet set, based on which, the definitions of quantum Mealy automata and quantum Moore automata are introduced. These definitions accord with quantum mechanics hypothesis. To consider a closed quantum system consisting of two kinds of automata without influence from the environments, based on the principle of quantum measurement, an investigation is made of the evolution of quantum Mealy automata and quantum Moore automata in detail. Then presented are the languages that are considered as quantum machine languages generated by quantum Mealy automata and quantum Moore automata utilizing the basic properties of density operator. It is well known that a complete measurement can always be represented as an unitary operation1and partial tracing. Considering this principle it is shown that quantum Mealy automata are equivalent to quantum Moore automata under the condition of the pure states.