



@article {2271,
	title = {Canonical forms for single-qutrit Clifford+T operators},
	journal = {Annals of Physics},
	volume = {406},
	year = {2019},
	month = {8/19/2019},
	pages = {54-70},
	abstract = {<p><span style="color: rgb(51, 51, 51); font-family: \&quot;Open Sans\&quot;, \&quot;Lucida Grande\&quot;, \&quot;Helvetica Neue\&quot;, Helvetica, Arial, sans-serif; font-size: 14px;">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.\&nbsp;</span></p>},
	doi = {https://doi.org/10.1016/j.aop.2019.04.001},
	url = {https://arxiv.org/abs/1803.05047},
	author = {Andrew N. Glaudell and Neil J. Ross and J. M. Taylor}
}
