  A simple coined quantum walk in one dimension can be characterized by a
$SU(2)$ operator with three parameters which represents the coin toss. However,
different such coin toss operators lead to equivalent dynamics of the quantum
walker. In this manuscript we present the unitary equivalence classes of
quantum walks and show that all the nonequivalent quantum walks can be
distinguished by a single parameter. Moreover, we argue that the electric
quantum walks are equivalent to quantum walks with time dependent coin toss
operator.
