  We investigate the error due to D.C. Stark effect for quantum information
processing for trapped ion quantum computers using the scalable architecture
proposed in J. Res. Natl. Inst. Stan. 103, 259 (1998) and Nature 417, 709
(2002). As the operation speed increases, dephasing and decoherence due to the
D.C. Stark effect becomes prominent as a large electric field is applied for
transporting ions rapidly. We estimate the relative significance of the
decoherence and dephasing effects and find that the latter is dominant. We find
that the minimum possible of dephasing is quadratic in the time of flight, and
an inverse cubic in the operational time scale. From these relations, we obtain
the operational speed-range at which the shifts caused by D.C. Stark effect, no
matter follow which trajectory the ion is transported, are no longer
negligible. Without phase correction, the maximum speed a qubit can be
transferred across a 100 micron-long trap, without excessive error, in about 10
ns for Calcium ion and 50 ps for Beryllium ion. In practice, the accumulated
error is difficult to be tracked and calculated, our work gives an estimation
to the range of speed limit imposed by D.C. Stark effect.
