  Temporal fluctuations in the Hadamard walk on circles are studied. A temporal
standard deviation of probability that a quantum random walker is positive at a
given site is introduced to manifest striking differences between quantum and
classical random walks. An analytical expression of the temporal standard
deviation on a circle with odd sites is shown and its asymptotic behavior is
considered for large system size. In contrast with classical random walks, the
temporal fluctuation of quantum random walks depends on the position and
initial conditions, since temporal standard deviation of the classical case is
zero for any site. It indicates that the temporal fluctuation of the Hadamard
walk can be controlled.
