Language Classes Defined by Generalized Quantum Turing Machine

Abstract

Ohya and Volovich proposed a quantum algorithm with chaotic amplification to solve the SAT problem, which went beyond the notion of the usual quantum algorithm. In this paper, we generalize quantum Turing machines by rewriting the usual quantum Turing automaton in terms of a channel transformation. Moreover, we define some computational classes of generalized quantum Turing machines and show that we can describe the Ohya-Volovich (OV) SAT algorithm with completely positive channels.