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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.
Volume406
Pagination54-70
Date PublishedJUL
Type of ArticleArticle
ISSN0003-4916
KeywordsQuantum circuits, quantum computation, Qutrits, Universal gate sets
Abstract

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.

DOI10.1016/j.aop.2019.04.001