A 'register' in quantum information processing is a composition of k quantum systems, 'qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have the possibility of preparing arbitrary entangled state of these k systems. Preparation and arbitrary transformations of states are possible with a universal set of quantum gates and for any d, this universal set may consist of gates acting only on single systems and neighbouring pairs. Here, we revisit methods of construction of Hamiltonians for such universal sets of gates and as a concrete new example, we consider the case with qutrits. Quantum tomography is also revisited briefly.