Stability thresholds and calculation techniques for fast entangling gates on trapped ions

TL;DR

This paper analyzes the stability and calculation methods for fast entangling gates on trapped ions, focusing on the effects of pulse number and laser stability on gate fidelity.

Contribution

It provides a detailed analysis of the challenges in implementing fast entangling gates, including the stability of the rotating wave approximation and pulse stability requirements.

Findings

RWA remains stable regardless of pulse number

Laser pulse instability affects gate fidelity with increasing pulses

Bounds on pulse stability are established for high-fidelity gates

Abstract

Fast entangling gates have been proposed for trapped ions that are orders of magnitude faster than current implementations. We present here a detailed analysis of the challenges involved in performing a successful fast gate. We show that the RWA is a stable approximation with respect to pulse numbers: the timescale on which we can neglect terms rotating at the atomic frequency is negligibly affected by the number of pulses in the fast gate. In contrast, we show that the laser pulse instability does give rise to a pulse-number dependent effect; the fast gate infidelity is compounded with the number of applied imperfect pulses. Using a dimensional reduction method presented here, we find bounds on the pulse stability required to achieve two-qubit gate fidelity thresholds.