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.

Brief Biography of the Speaker:
Satoshi Iriyama is an assistant professor in Tokyo University of Science in Japan. His main research topics are the Quantum Algorithm which is the algorithm of quantum computer, the Quantum Information and Bio-Informatics. He and Professor Ohya in Tokyo University of Science proposed the mathematical model of quantum Turing machine, called a Generalized Quantum Turing Machine(GQTM for short), which is one of mathematical model of quantum computation, and defined language classes defined by GQTM. They proved that there exists a GQTM solving SAT problem, one of NP complete problems, in polynomial time. The mathematical characterization of GQTM contains the discussion of computability in the quantum computer.
He is also a researcher in Quantum Bio-Informatics Center (QBIC) in the university. The main opportunity of this center is to construct a new paradigm of Quantum Theory and Bio-Informatics. He and Professor Ohya showed the quantum algorithm for multiple alignment of amino acid sequences which is known as a difficult problem in Bio-Informatics.