  Many quantum dot qubits operate in regimes where the energy splittings
between qubit states are large and phonons can be the dominant source of
decoherence. The recently proposed charge quadrupole qubit, based on one
electron in a triple quantum dot, employs a highly symmetric charge
distribution to suppress the influence of charge noise. To study the effects of
phonons on the charge quadrupole qubit, we consider Larmor and Ramsey pulse
sequences to identify favorable operating parameters. We show that it is
possible to implement typical gates with $>99.99\%$ fidelity in the presence of
phonons and charge noise.
