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.
@article{arxiv.1909.08973,
title = {Scalable quantum computing with qudits on a graph},
author = {E. O. Kiktenko and A. S. Nikolaeva and Peng Xu and G. V. Shlyapnikov and A. K. Fedorov},
journal= {arXiv preprint arXiv:1909.08973},
year = {2020}
}