Decomposition of Clifford Gates
Quantum Physics
2023-04-12 v1 Information Theory
math.IT
Abstract
In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a product of Clifford transvections. The algorithm can be directly used for finding all Pauli matrices that commute with any given Clifford gate. To achieve this goal, we exploit the structure of the symplectic group with a novel graphical approach.
Cite
@article{arxiv.2102.11380,
title = {Decomposition of Clifford Gates},
author = {Tefjol Pllaha and Kalle Volanto and Olav Tirkkonen},
journal= {arXiv preprint arXiv:2102.11380},
year = {2023}
}