Characteristics and Implementation of B${}^{\alpha }$ Gates

Abstract

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.