  In this brief report, we discuss the characteristics of B$^{\alpha}$ gates.
We provide the conditions for the two-qubit gates generated by two applications
of a B$^{\alpha}$ gate. We propose an experimental scheme to implement
B$^{\alpha}$ gates in ion-trap system. In this scheme, we assume that only a
single vibrational mode contributes to spin-spin coupling. This scheme is an
extension of a recently proposed scheme to realize XY-type interaction in
ion-trap system. With the successful implementation of this scheme,
B$^{\alpha}$ gates can be used for doing quantum computation in ion-trap
quantum computers.
