TY - JOUR T1 - Canonical forms for single-qutrit Clifford+T operators JF - Annals of Physics Y1 - 2019 A1 - Andrew N. Glaudell A1 - Neil J. Ross A1 - J. M. Taylor AB -

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. 

VL - 406 U4 - 54-70 UR - https://arxiv.org/abs/1803.05047 U5 - https://doi.org/10.1016/j.aop.2019.04.001 ER -