We study the problem of exact synthesis for the Clifford+R gate set and give the explicit structure of the underlying Bruhat-Tits building for this group. In this process, we also give an alternative proof of the arithmetic nature of the Clifford+R gate set.
@article{arxiv.2510.11526,
title = {Buildings for Synthesis with Clifford+R},
author = {Mark Deaconu and Nihar Gargava and Amolak Ratan Kalra and Michele Mosca and Jon Yard},
journal= {arXiv preprint arXiv:2510.11526},
year = {2026}
}