%0 Journal Article %J Annals of Physics %D 2019 %T Canonical forms for single-qutrit Clifford+T operators %A Andrew N. Glaudell %A Neil J. Ross %A J. M. Taylor %X

We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for this operator. The algorithm runs in time linear in the number of T gates. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits. 

%B Annals of Physics %V 406 %P 54-70 %8 8/19/2019 %G eng %U https://arxiv.org/abs/1803.05047 %R https://doi.org/10.1016/j.aop.2019.04.001