Dynamically corrected gates for an exchange-only qubit

We provide analytical composite pulse sequences that perform dynamical decoupling concurrently with arbitrary rotations for a qubit coded in the spin state of a triple quantum dot. The sequences are designed to respect realistic experimental constraints such as strictly nonnegative couplings. Logical errors and leakage errors are simultaneously corrected. A short pulse sequence is presented to compensate nuclear noise and a longer sequence is presented to simultaneously compensate nuclear and charge noise. The capability developed in this work provides a clear prescription for combatting the relevant sources of noise that currently hinder exchange-only qubit experiments.