Characterizing gate operations near the sweet spot of an exchange-only qubit

Optimal working points or ``sweet spots'' have arisen as an important tool for mitigating charge noise in quantum dot logical spin qubits. The exchange-only qubit provides an ideal system for studying this effect because Z rotations are performed directly at the sweet spot, while X rotations are not. Here, we quantify the ability of the sweet spot to mitigate charge noise by treating X and Z rotations on an equal footing. Specifically, we optimize X rotations and determine an upper bound on their fidelity. We find that sweet spots offer a fidelity improvement factor of at least 20 for typical GaAs devices, and more for Si devices.