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 F≤1−(π/2)/(VτR), for interaction strength V and Rydberg lifetime τR. 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.
@article{arxiv.2605.19245,
title = {Entangling gate performance and fidelity limits with neutral atom F\"orster resonances},
author = {S. A. Norrell and Y. Shen and M. Saffman and M. Otten},
journal= {arXiv preprint arXiv:2605.19245},
year = {2026}
}