Generalized Quantum Turing Machine and Its Application for SAT Problem

正直 小澤

Satoshi Iriyama, Masanori Ohya

Ohya and Volovich discussed a quantum algorithm for the SAT problem with a chaos amplification process (OMV SAT algorithm) and showed that the number of steps it performed was polynomial in input size. In this paper, we define a generalized quantum Turing machine (GQTM) and related computational complexity. Then we show that there exists a GQTM which recognizes the SAT problem in polynomial time. Moreover, we discuss the problem of finding the quantum algorithm for a partial recursive function.

Satoshi Iriyama, Masanori Ohya

Ryuichi Sawae, Hiroshi Takeuchi, Tadahito Harima

Satoshi Iriyama, Masanori Ohya

Abstract: 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 by rewriting usual quantum Turing machine in terms of channel transformation. Moreover, we define some computational classes of generalized quantum Turing machine and show that we can treat the Ohya-Volovich (OV) SAT algorithm.

Satoshi Iriyama, Masanori Ohya

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.