  We discuss a possibility of implementing a universal quantum XOR gate, by
using two coupled quantum dots subjected to external magnetic fields that are
parallel and slightly different. We consider this system in two different field
configurations. In the first case, parallel external fields with the intensity
difference at each spin being proportional to the time-dependent interaction
between the spins. General exact solution describing this system is presented
and analyzed to adjust parameters of the field. Then we consider parallel
fields with intensity difference at each spin being constant and the
interaction between the spins switching on and off adiabatically. In both cases
we adjust characteristics of the external fields (their intensities and
duration) in order to have the parallel pulse adequate for constructing the XOR
gate. In order to provide a complete theoretical description of all the cases,
we derive relations between the spin interaction, the inter-dot distance, and
the external field.
