  The fidelity of entangling operations is a key figure of merit in quantum
information processing, especially in the context of quantum error correction.
High-fidelity entangling gates in neutral atoms have seen remarkable
advancement recently. A full understanding of error sources and their
respective contributions to gate infidelity will enable the prediction of
fundamental limits on quantum gates in neutral atom platforms with realistic
experimental constraints. In this work, we implement the time-optimal Rydberg
CZ gate, design a circuit to benchmark its fidelity, and achieve a fidelity,
averaged over symmetric input states, of 0.9971(5), setting a new
state-of-the-art for neutral atoms. The remaining infidelity is explained by an
ab initio error model, consistent with our experimental results over a range of
gate speeds, with varying contributions from different error sources. Further,
we develop a linear response formalism to efficiently predict infidelity from
laser noise with non-trivial power spectral densities and derive scaling laws
of infidelity with gate speed. Besides its capability of predicting gate
fidelity, we also utilize the linear response formalism to compare and optimize
gate protocols, to learn laser frequency noise, and to study the noise response
for quantum simulation tasks. Finally, we predict that a CZ gate fidelity of
${\gtrsim} 0.999$ is feasible with realistic experimental upgrades.
