Quantum walks on N-cycles with an absorbing wall

Abstract

In this paper, we analyze quantum walks on cycles with an absorbing wall. We set the absorbing wall on cycles with N vertices (where N is an even number), and divide [Formula: see text] into two parts, [Formula: see text] and [Formula: see text]. Due to the periodicity of the cycles, the condition [Formula: see text] (or [Formula: see text]) is applied to [Formula: see text] and [Formula: see text], then the transmission probability [Formula: see text] and reflection probability [Formula: see text] at the absorbing wall [Formula: see text] at time t are obtained. Furthermore, we show that over time, the absorbing wall absorbs less and less.