We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{U_1,...,U_n\}$ is universal. We provide the compact-form criteria leading to a simple algorithm that allows deciding the universality of any given set of gates in a finite number of steps. Moreover, for a nonuniversal $\mathcal{S}$ our criteria indicate what types of gates can be added to $\mathcal{S}$ to turn it into a universal set.

• Received 27 October 2016

DOI:https://doi.org/10.1103/PhysRevA.95.062303