  We propose a quadrupolar exchange-only spin (QUEX) qubit that is highly
robust against charge noise and nuclear spin dephasing, the dominant
decoherence mechanisms in quantum dots. The qubit consists of four electrons
trapped in three quantum dots, and operates in a decoherence-free subspace to
mitigate dephasing due to nuclear spins. To reduce sensitivity to charge noise,
the qubit can be completely operated at an extended charge noise sweet spot
that is first-order insensitive to electrical fluctuations. Due to on-site
exchange mediated by the Coulomb interaction, the qubit energy splitting is
electrically controllable and can amount to several GHz even in the ``off"
configuration, making it compatible with conventional microwave cavities.
