Quantum logic gates with single trapped ions could be implemented for arbitrary Lamb-Dicke parameters

Controlled-NOT gate for manipulating photonic polarization states in a two-mode optical cavity

“…The direct realization of a C-NOT gate, however, is more favorable to avoid the undesired operation complexity and decoherence processes. Many different schemes for such a purpose has been explored with traveling atoms [16,17] and trapped ions [18,19] in optical cavities or with trapped atoms in the free space [20,21].…”

Simplified approach to generate controlled-NOT gates with single trapped ions for arbitrary Lamb–Dicke parameters

“…Besides the requirement of an auxiliary atomic level, the present proposal for implementing the standard CNOT gate is really simpler than many previous ones, including that proposed recently in Ref. [12]. Here, the so-called standard CNOT gate between the external and internal degrees of freedom of the ion reads [4]…”

“…Theoretically, condition ( 10) is always satisfied for arbitrary-selected LD parameters by properly selecting the values of the integers n, m = 1, 2, 3, .... As a consequence, the two-qubit operation ( 9) could be, in principle, implemented for arbitrary LD parameters by properly setting the durations of the applied carrier laser pulse. However, because the practical existence of decoherence, as we discussed in [12], the duration of the present pulse should be shorter than the decoherence times of both the atomic and motional states of the ion [16,17]. This limits that the integers n could not take arbitrary large values to let Eq.…”

Quantum Manipulations of Single Trapped-Ions beyond the Lamb-Dicke Limit

“…(27), Table 3. Parameters for generating high-fidelity CNOT gates with arbitrarily selected LD parameters from 0.17 to 0.95 (27). Here ϑ 1 = −ϑ 3 = π/2, and t 1 = t 3 .…”