Exchange interaction between distant spins mediated by a multielectron quantum dot*

We demonstrate coherent exchange interactions between two separated electron spins in a GaAs heterostructure, mediated by a central multielectron quantum dot. We observe three different regimes of spin exchange. First, long-range superexchange, mediated my virtual occupations of the multielectron dot. Second, direct exchange, induced by moving one of the electrons onto the multielectron dot. Finally, on-site exchange, with both electrons transferred to the multielectron dot. Using independent readout of both spins, we further show that this interaction mechanism can be used for a fast and high-fidelity square-root-SWAP entangling gate for single electronic spins.