• quantum gates
• holonomies
• quantum transport

In recent years we are witnessing the birth of the first quantum computers: quantum devices that can harness the phenomena of quantum mechanics such as superposition, interference and entanglement to perform computational tasks that modern classical computers can not do in a reasonable time. The strong demand to develop even more powerful quantum computers is pushing the technological progress to invest in research for new control techniques in order to exploit the phenomena of quantum mechanics to our advantages. The key concept at the base of the computational power of a quantum computer is the qubit: the quantum analog of the classical bit represented by a superposition of two quantum states. Nowadays, the ability to manipulate such qubit states through quantum transformations, i.e. quantum gates, represents the hardest challenge to face. In this thesis it was proposed a spatial analog of the well-known Berry's phase mechanism to perform quantum gates, manipulating the quantum states of a non-relativistic electron, i.e. the qubit states, which moves in a scattering region. It was showed the possibility to perform quantum gates modulating adiabatically the geometric shape of the scattering region thanks to a set of control parameters. It were provided numerical examples to demonstrate the feasibility of the quantum transformations achievable with the adiabatic modulation, showing the correctness of numerical methods utilized.