A two-qubit system made of electrons running along coupled pairs of quantum wires is described and numerically analyzed. A brief review of the basic gates is given first, based on preliminary investigations, followed by the description of the electron dynamics. A detailed analysis of a conditional phase shifter is carried out by means of a time-dependent Schrodinger solver applied to a two-particle system. A quantum network suitable for creating entanglement is simulated, and results are shown. The physical structure of the proposed network is within the reach of a solid-state implementation. The physical parameters used in the computations have been chosen with reference to silicon quantum wires embedded in silicon dioxide.