  The search of a sweet spot, locus in qubit parameters where quantum control
is first-order insensitive to noises, is key to achieve high-fidelity quantum
gates. Efforts to search for such a sweet spot in conventional
double-quantum-dot singlet-triplet qubits where each dot hosts one electron
("two-electron singlet-triplet qubit"), especially for two-qubit operations,
have been unsuccessful. Here we consider singlet-triplet qubits allowing each
dot to host more than one electron, with a total of four electrons in the
double quantum dots ("four-electron singlet-triplet qubit"). We theoretically
demonstrate, using configuration-interaction calculations, that sweet spots
appear in this coupled qubit system. We further demonstrate that, under
realistic charge noise and hyperfine noise, two-qubit operation at the proposed
sweet spot could offer gate fidelities ($\sim99\%$) that are higher than
conventional two-electron singlet-triplet qubit system ($\sim90\%$). Our
results should facilitate realization of high-fidelity two-qubit gates in
singlet-triplet qubit systems.
