Ohya and Volovich have proposed a new quantum computation model with chaotic amplification to solve the SAT problem, which went beyond usual quantum algorithm. In this paper, we generalize quantum Turing machine, and we show in this general quantum Turing machine (GQTM) that we can treat the Ohya-Volovich (OV) SAT algorithm.
Ohya and Volovich found the quantum algorithm with a chaos dynamics, called the OV SAT algorithm which enabled to solve NP-Complete problem in polynomial time. It is proved that the unitary operator of the quantum algorithm can be constructed by a product of so called fundamental gates. To discuss the computational complexity rigorously, we introduced a generalized quantum Turing machine(GQTM) where the computational process is given by quantum channels including a dispative dynamics and the configuration is represented by density operators. In this paper, we explain the GQTM and the OV SAT algorithm, then we discuss the computational complexity of OV SAT algorithm. Finally, we introduce some resent results and topics by use of GQTM.
Ohya and Volovich found the quantum algorithm with a chaos dynamics, called the OV SAT algorithm which enabled to solve NP-Complete problem in polynomial time. It is proved that the unitary operator of the quantum algorithm can be constructed by a product of so called fundamental gates. To discuss the computational complexity rigorously, we intro- duced a generalized quantum Turing machine(GQTM) where the computational process is given by quantum channels including a dispative dynamics and the configuration is represented by density operators. In this paper, we explain the GQTM and the OV SAT algorithm, then we discuss the computational complexity of OV SAT algorithm. Finally, we introduce some resent results and topics by use of GQTM.