The sz=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 sz=0 subspace. Spin-orbit
interactions act nontrivially on the sz=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.Comment: 10 pages, 4 figure