Decoherence and dephasing errors caused by D.C. Stark effect in rapid ion transport

TL;DR

This paper analyzes how D.C. Stark effect-induced errors impact rapid ion transport in quantum computers, estimating speed limits and error magnitudes for different ion species to inform scalable quantum architecture design.

Contribution

It provides a quantitative analysis of decoherence and dephasing errors due to D.C. Stark effect during fast ion transport, establishing speed limits and error estimates for scalable ion-trap quantum computing.

Findings

Dephasing is the dominant error over decoherence.

Minimum dephasing scales quadratically with transport time.

Maximum transfer speeds are approximately 10 ns for Calcium and 50 ps for Beryllium ions.

Abstract

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.