RSS icon
Twitter icon
Facebook icon
Vimeo icon
YouTube icon

Canonical forms for single-qutrit Clifford plus T operators

TitleCanonical forms for single-qutrit Clifford plus T operators
Publication TypeJournal Article
Year of Publication2019
AuthorsA. N. Glaudell, N. J. Ross, and J. M. Taylor
JournalAnn. Phys.
Date PublishedJUL
Type of ArticleArticle
KeywordsQuantum circuits, quantum computation, Qutrits, Universal gate sets

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. (C) 2019 Elsevier Inc. All rights reserved.