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arXiv · 2604.02301

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

Evgeny V. Anikin·Andrey Chuchalin·Dimitrii Donchenko·Olga Lakhmanskaya·Kirill Lakhmanskiy
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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.

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Evgeny V. Anikin, Andrey Chuchalin, Dimitrii Donchenko, Olga Lakhmanskaya, Kirill Lakhmanskiy. 2026-04-02. Lemniscate phase trajectories for high-fidelity GHZ state preparation in trapped-ion chains. https://doi.org/10.1103/t5s5-v6mf

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