  We consider a new quantum gate mechanism based on electron spins in coupled
semiconductor quantum dots. Such gates provide a general source of spin
entanglement and can be used for quantum computers. We determine the exchange
coupling J in the effective Heisenberg model as a function of magnetic (B) and
electric fields, and of the inter-dot distance (a) within the Heitler-London
approximation of molecular physics. This result is refined by using
sp-hybridization, and by the Hund-Mulliken molecular-orbit approach which leads
to an extended Hubbard description for the two-dot system that shows a
remarkable dependence on B and a due to the long-range Coulomb interaction. We
find that the exchange J changes sign at a finite field (leading to a
pronounced jump in the magnetization) and then decays exponentially. The
magnetization and the spin susceptibilities of the coupled dots are calculated.
We show that the dephasing due to nuclear spins in GaAs can be strongly
suppressed by dynamical nuclear spin polarization and/or by magnetic fields.
