Decoherence and dephasing errors caused by the dc Stark effect in rapid ion transport

We investigate the error due to the dc Stark effect for quantum information processing for trapped ion quantum computers using the scalable architecture proposed in D. Wineland et al. [J. Res. Natl. Inst. Stand. Technol. 103, 259 (1998)] and D. Kielpinski et al. [Nature (London) 417, 709 (2002)]. As the operational speed increases, dephasing and decoherence due to the dc Stark effect become prominent as a large electric field is applied for rapidly transporting ions. We estimate the relative significance of the decoherence and dephasing effects and find that the latter is dominant. We find that the minimum possible dephasing is quadratic in the length of a trap and an inverse cubic in the operational time scale. From these relations, we obtain the operational speed range at which the shifts, caused by the dc Stark effect, are no longer negligible, no matter on which trajectory the ion is transported. Without phase correction, the shortest time a qubit can be transferred across a 100-micrometer-long trap, without excessive error, is about 10 ns for a Ca-40(+) ion and 50 ps for a Be-9(+) ion. In practice, the accumulated error is difficult to track and to calculate; thus, our paper gives an estimate for the range of the speed limit imposed by the dc Stark effect.