  We show a significant reduction of the number of quantum operations and the
improvement of the circuit depth for the realization of the Toffoli gate by
using qudits. This is done by establishing a general relation between the
dimensionality of qudits and their topology of connections for a scalable
multi-qudit processor, where higher qudit levels are used for substituting
ancillas. The suggested model is of importance for the realization of quantum
algorithms and as a method of quantum error correction codes for single-qubit
operations.
