Quantum walk with one variable absorbing boundary

Quantum walks constitute a promising ingredient in the research on quantum algorithms; consequently, exploring different types of quantum walks is of great significance for quantum information and quantum computation. In this study, we investigate the progress of quantum walks with a variable absorbing boundary and provide an analytical solution for the escape probability (the probability of a walker that is not absorbed by the boundary). We simulate the behavior of escape probability under different conditions, including the reflection coefficient, boundary location, and initial state. Moreover, it is also meaningful to extend our research to the situation of continuous-time and high-dimensional quantum walks.