Quantum Computation with Trapped Ions in an Optical Cavity

Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup and commonly addressed by laser fields. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the quantum Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation.

Figure 1

Atomic levels of the two atoms and laser and cavity couplings with their detunings. The qubits $1$, $2$ and the auxiliary states $|\sigma ⟩$ are depicted.

Figure 2

Adiabatic evolution for $\Gamma =0.1g$ and $\kappa =0.1g$. The population of the state $|11⟩$ is completely transferred to the state $|A⟩$ with success rate $P_0=0.852$ and fidelity $F=0.999$. For this transition the overall time of the adiabatic procedure, which is performed with linear ramp for the laser pulse, is $T=5\times {10}^4/g$.

Figure 3

The fidelity for the adiabatic transfer of population for $\Gamma =0.1g$ and $k=0.1g$. We observe maximum at $\Omega =0.0145g$ and $\Delta \approx 0.024g$ with fidelity $F=0.999$.

Figure 4

The probability for no photon emissions for the adiabatic transfer with $\Gamma =0.1g$ and $k=0.1g$. We observe maximum for $\Omega =0.0145g$ and any $\Delta$ with $P_0=0.858$. This coincides with the range the fidelity is also maximum.

Figure 5

Application of the proposed scheme to the calcium ion ${\mathrm{C}\mathrm{a}}^{+}$.