  We study the effect of the spin-orbit interaction on quantum gate operations
based on the spin exchange coupling where the qubit is represented by the
electron spin in a quantum dot or a similar nanostructure. Our main result is
the exact cancellation of the spin-orbit effects in the sequence producing the
quantum XOR gate for the ideal case where the pulse shapes of the exchange and
spin-orbit interactions are identical. For the non-ideal case, the two pulse
shapes can be made almost identical and the gate error is strongly suppressed
by two small parameters, the spin-orbit constant and the deviation of the two
pulse shapes. We show that the dipole-dipole interaction leads only to very
small errors in the XOR gate.
