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.