Implementing the Deutsch--Jozsa algorithm by using Schrödinger cat states in cavity QED

We propose a scheme to implement the Deutsch--Jozsa algorithm by using Schr?dinger cat states in cavity quantum electron-dynamics (QED). The scheme is based on the Raman interaction of a degenerate three-level \Lambda -type atom with a coherent state in a cavity. By using Schr?dinger cat states, the atomic spontaneous emission can be minimized and the Hadamard transformation in our scheme is not needed.