Mathematical characterization of quantum algorithm

Authors:
Satoshi Iriyama;Masanori Ohya
Affiliations:
Tokyo University of Science, Department of Information Sciences, Yamasaki, Noda City, Chiba, Japan;Tokyo University of Science, Department of Information Sciences, Yamasaki, Noda City, Chiba, Japan
Venue:
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Year:
2009

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Abstract

We have studied quantum computation for many years, and defined the generalized quantum Turing machine by using completely positive channels and density operators on the Hilbert space. This mathematical model of quantum algorithm gives us the new language classes in which the class NP is included in a polynomial time class. It has also a possibility to expand the theory of computability which has philosophical significance. In this talk, we explain a definition of the model, the language classes, some theorems and applications.