关键词: 量子算法, 量子行走, 开放量子系统, 击中时

Abstract: As a basic tool of quantum searching algorithms, quantum walk is an important reseach subject. Meanwhile, hitting time is a standard which measures a speed about quantum walk reaching some target vertex. It has been widely used to study quantum algorithms. In an open quantum environment, four definitions of hitting time are introduced for open quantum walk：single hitting time, parallel hitting time, average hitting time and limit hitting time. These four hitting times are distinguished. The related facts show that the first two are used to describe a case of locally reaching the target vertex while the latter two are used to describe a case of reaching the target vertex from an overall and limitation situation. For homogenous open quantum walk, non-homogenous open quantum walk and nested open quantum walk, their calculations of four hitting times are respectively given.

Key words: quantum algorithm, quantum walk, open quantum system, hitting time