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The aim of this paper is the study of the single-electron coherent propagation in a quantum-computing gate made of coupled quantum wires. The structure under investigation is based on a two-dimensional (2-D) electron gas realized in a modulation-doped GaAs-AlGaAs heterostructure. A number of surface electrodes are used to form one-dimensional channels. The profile of the conduction band at the heterojunction has been computed numerically by solving the three-dimensional Poisson equation on the whole structure at 300 mK. Finally, a single-electron wavefunction is propagated within the so-formed quantum wire geometry by means of a 2-D, time-dependent Schrödinger solver. Results are shown for a single-qubit rotation gate implementing a quantum-NOT transformation. This work is part of a feasibility study on a solid-state realization of a universal set of quantum gates.