  The discrete-time quantum walk (QW) is determined by a unitary matrix whose
component is complex number. Konno (2015) extended the QW to a walk whose
component is quaternion.We call this model quaternionic quantum walk (QQW). The
probability distribution of a class of QQWs is the same as that of the QW. On
the other hand, a numerical simulation suggests that the probability
distribution of a QQW is different from the QW. In this paper, we clarify the
difference between the QQW and the QW by weak limit theorems for a class of
QQWs.
