High-Speed Geometric Quantum Computation with Trapped Thermal Ions via Vibrational Mode Decay

We utilize the general displacement operator proposed recently [C.Y. Chen, et al., Phys. Rev. A 74 (2006) 032328] to investigate a high-speed geometric quantum computation via vibrational mode decay of two trapped thermal ions. We find that, under some special conditions, the geometric phase gating is somewhat faster in the heating case than in the ideal case. We also investigate analytically the influence from the vibrational mode heating on the fidelity and the success probability of the implementation. (general)