In the last thirty years, we have seen the evolution and the development of the semiconductor devices and large scale applications to realize computational instruments using the quantum rules. The science community has been enormously interested in the study of new devices and laws to apply in this new computer era, the quantum computation. The quantum computation comes as a combination of the classical information theory and the quantum physics. The semiconductor quantum dot device is one of the most promising candidate for quantum computation applications. In this work the electronic properties of laterally coupled quantum dots are studied, analytically and numerically. In particular is highlighted the role of the spin-orbit interactions for the possible realization of an elementary gate operation. An effective analytical model, which describes appropriately the system, is derived and tested in realistic cases, using experimental parameters. Furthermore we describe in more details the numerical method used to investigate the system and how is implemented.