Lemniscate phase trajectories for high-fidelity GHZ state preparation in trapped-ion chains

TL;DR

This paper introduces an amplitude and phase-modulated 'echoed lemniscate pulse' that significantly reduces GHZ state preparation infidelity in trapped-ion chains by canceling out higher-order Lamb-Dicke effects.

Contribution

The authors propose a novel pulse shape, the 'echoed lemniscate pulse', which improves GHZ state fidelity by scaling infidelity as η^6 instead of η^4, outperforming traditional pulses.

Findings

Lemniscate pulse achieves infidelity as low as 10^{-4} for 20-ion chains.

The phase trajectory follows a figure-eight curve, enabling error cancellation.

The method improves fidelity scaling from η^4 to η^6, reducing out-of-Lamb-Dicke effects.

Abstract

In trapped-ion chains, multipartite GHZ states can be prepared natively with the help of a single bichromatic laser pulse. However, higher-order terms in the expansion in the Lamb-Dicke parameter $\eta$ limit the GHZ state preparation infidelity for rectangular and bell-like pulses to the order of $\eta^4$. For tens of ions, the infidelity caused by out-of-Lamb-Dicke effects can reach several percents. We propose an amplitude and phase-modulated pulse shape, an "echoed lemniscate pulse", which cancels this contribution into error in the leading order. For the proposed pulse, the infidelity scales as $\eta^6$. The improved scaling is achieved because of a special phase trajectory of a collective motional mode following the figure-eight curve (lemniscate). We demonstrate that the lemniscate pulse allows achieving lower infidelity than bell-like pulses, which can be as low as $10^{-4}$ for $20$-ion chains.