In the system with ions confined both in a linear trap and in a high-
Q single mode cavity, we present a simple quantum computing scheme by means of lasers and quantized cavity field, based on a previous proposal with bichromatic radiation [Phys. Rev. Lett.
82, 1971 (1999)]. The controlled-NOT gate operation can be performed by only three operations and it is independent of motional states of ions. Experimental feasibility for achieving our scheme is discussed.
Based on squeezed operators this paper has implemented an ideal unconventional geometric quantum gate (GQG) in ion trap-optical cavity system by radiating the trapped ions with the cavity field of frequency ω c and an external laser field of frequency ωL. It can ensure that the gate time is shorter than the coherence time for qubits and the decay time of the optical cavity by appropriately tuning the ionic transition frequency ω 0 , the frequencies of the cavity mode ω c and the vibrational mode ν. It has also realized the unconventional GQG under the influence of the cavity decay based on the squeezed-like operators and found that the present scheme works well for the smaller cavity decay by investigating the corresponding fidelity and success probability.