Entangling gate performance and fidelity limits with neutral atom F\"orster resonances

TL;DR

This paper models and improves the fidelity limits of neutral-atom entangling gates near F"orster resonances by developing a two-eigenstate approach and proposing a protocol that saturates the fidelity bound.

Contribution

It introduces a two-eigenstate model for F"orster resonance regimes and presents a gate protocol that reaches the fidelity bound, enhancing previous limits.

Findings

Fidelity bound is $oxed{ ext{F} \, \leq \, 1 - (\pi/2)/(V \tau_R)}$ near F"orster resonances.

A new gate protocol saturates the fidelity bound in the large-Rabi-frequency limit.

Retaining exchange dynamics can increase predicted fidelities by up to two orders of magnitude.

Abstract

Neutral-atom entangling gates are commonly analyzed with a single effective Rydberg-pair state, but near F\"orster resonances the pair manifold contains resonantly coupled interaction channels that change both the control landscape and the achievable fidelity. We develop a two-eigenstate model for this regime and show that when allowing for coupling to both pair states in the resonance, the gate fidelity is bounded by $\mathcal{F}\leq 1-(\pi/2)/(V\tau_R)$, for interaction strength $V$ and Rydberg lifetime $\tau_R$. We construct a gate protocol that saturates this bound in the large-Rabi-frequency limit, improving the existing fidelity limit by approximately $40\%$. We also evaluate common gate protocols near F\"orster resonances and find that retaining the exchange dynamics increases predicted fidelities by up to two orders of magnitude over earlier treatments.