  The discrete-time quantum walk (QW) is a quantum version of the random walk
(RW) and has been widely investigated for the last two decades. Some remarkable
properties of QW are well known. For example, QW has a ballistic spreading,
i.e., QW is quadratically faster than RW. For some cases, localization occurs:
a walker stays at the starting position forever. In this paper, we consider
stationary measures of two-state QWs on the line. It was shown that for any
space-homogeneous model, the uniform measure becomes the stationary measure.
However, the corresponding result for space-inhomogeneous model is not known.
Here, we present a class of space-inhomogeneous QWs on the line and cycles in
which the uniform measure is stationary. Furthermore, we briefly discuss a
difference between QWs and RWs.
