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Solid state quantum computing proposals rely on adiabatic operations of theexchange gate among localized spins in nanostructures. We study corrections tothe Heisenberg interaction between lateral semiconductor quantum dots in anexternal magnetic field. Using exact diagonalization we obtain the regime ofvalidity of the adiabatic approximation. We also find qualitative correctionsto the Heisenberg model at high magnetic fields and in looped arrays of spins.Looped geometries of localized spins generate flux dependent, multi-spin termswhich go beyond the basic Heisenberg model.Comment: 13 pages, 8 figure

Exchange gate in solid-state spin-quantum computation: The applicability of the Heisenberg model