Abstract
The $s_z=0$ spin configuration of two electrons confined at a double quantum dot (DQD) encodes the singlet-triplet qubit (STQ). We introduce the inverted STQ (ISTQ) that emerges from the setup of two quantum dots (QDs) differing significantly in size and out-of-plane magnetic fields. The strongly confined QD has a two-electron singlet ground state, but the weakly confined QD has a two-electron triplet ground state in the $s_z=0$ subspace. Spin-orbit interactions act nontrivially on the $s_z=0$ subspace and provide universal control of the ISTQ together with electrostatic manipulations of the charge configuration. GaAs and InAs DQDs can be operated as ISTQs under realistic noise conditions.
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