Basic Properties of Quantum Automata

Daowen Qiu, Mingsheng Ying

Mika Hirvensalo

In this paper, a model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum automata can be simulated by the open quantum evolution automata without increasing the number of the states.

Mika Hirvensalo

In this paper, a model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum automata can be simulated by the open quantum evolution automata without increasing the number of the states.

David Z. Albert

Songsong Dai

Quaternionic quantum theory is a generalization of the standard complex quantum theory. Inspired by this, we study the quaternionic quantum computation using quaternions. We first develop a theory of quaternionic quantum automata as a model of quaternionic quantum computation. Quaternionic quantum automata also can be seen as an extension of complex quantum automata. Then we introduce some operations of quaternionic quantum automata and establish some of their basic properties.

Asher Peres