  We calculate the effect of an inhomogeneous magnetic field, which is
invariably present in an experimental environment, on the exchange energy of a
double quantum dot artificial molecule, projected to be used as a 2-qubit
quantum gate in the proposed quantum dot quantum computer. We use two different
theoretical methods to calculate the Hilbert space structure in the presence of
the inhomogeneous field: the Heitler-London method which is carried out
analytically and the molecular orbital method which is done computationally.
Within these approximations we show that the exchange energy J changes slowly
when the coupled dots are subject to a magnetic field with a wide range of
inhomogeneity, suggesting swap operations can be performed in such an
environment as long as quantum error correction is applied to account for the
Zeeman term. We also point out the quantum interference nature of this slow
variation in exchange.
