Three-state quantum walks on cycles

Abstract

In this paper, on the basis of constructing a new shift operator [Formula: see text] and choosing the Grover coin [Formula: see text] as coin operator [Formula: see text], we get the standard evolution operator [Formula: see text] on cycles. Using [Formula: see text], we not only got the analytical expression of wavefunction [Formula: see text], but also obtained the conclusion that the limit distribution [Formula: see text] of [Formula: see text], which is not uniform distribution, regardless of [Formula: see text] is odd or even.