Stopping time of a one-dimensional bounded quantum walk

Luo Hao¹, Zhan Xiang², Zhang Peng¹, Xue Peng^{2, †,}

P^(X_d)(T_s) for QW ((a) and (c)) and RW ((b) and (d)) with X_d = 10 ((a) and (b)) and X_d = 40 ((c) and (d)). Because X_d is even in our cases, we have P^(X_d)(T_s) = 0 for odd steps T_s = ±1, ±3, ±5, …. Hence, we have only shown P^(X_d)(T_s) for T_s = 0, ±2, ±4, ….