Criteria for universality of quantum gates

Adam Sawicki, Katarzyna Karnas

Published 2016-10-03Version 1

We consider the problem of deciding if a set of quantum one-qudit gates $\mathcal{S}=\{U_1,\ldots,U_n\}$ is universal. We provide compact form criteria that involve spectra of the gates and linear equations whose coefficients are polynomial in entries of the gates and their complex conjugates. Moreover, for non-universal $\mathcal{S}$ our criteria indicate what type of gates can be added to $\mathcal{S}$ to turn it into a universal set.