Real 3-qubit gate decompositions via triality
Quantum Physics
2026-02-17 v2 Group Theory
Abstract
We show that any unimodular real 3-qubit gate can be expressed as the product of at most 14 CNOT gates plus single-qubit gates, improving on the bound of 16 CNOTs due to Wei and Di. Our method uses the exotic triality symmetry of , and we explore some of the useful properties of this map in relation to the study of real 3-qubit gates.
Cite
@article{arxiv.2512.18049,
title = {Real 3-qubit gate decompositions via triality},
author = {Brendan Pawlowski},
journal= {arXiv preprint arXiv:2512.18049},
year = {2026}
}