Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators
Abstract
Matsumoto and Amano (2008) showed that every single-qubit Clifford+T operator can be uniquely written of a particular form, which we call the Matsumoto-Amano normal form. In this mostly expository paper, we give a detailed and streamlined presentation of Matsumoto and Amano's results, simplifying some proofs along the way. We also point out some corollaries to Matsumoto and Amano's work, including an intrinsic characterization of the Clifford+T subgroup of SO(3), which also yields an efficient T-optimal exact single-qubit synthesis algorithm. Interestingly, this also gives an alternative proof of Kliuchnikov, Maslov, and Mosca's exact synthesis result for the Clifford+T subgroup of U(2).
Keywords
Cite
@article{arxiv.1312.6584,
title = {Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators},
author = {Brett Giles and Peter Selinger},
journal= {arXiv preprint arXiv:1312.6584},
year = {2019}
}
Comments
13 pages. Changes in v2: minor typos corrected, small updates to introduction