Geometric representations of braid and Yang-Baxter gates
Abstract
Brick-wall circuits composed of the Yang-Baxter gates are integrable. It becomes an important tool to study the quantum many-body system out of equilibrium. To put the Yang-Baxter gate on quantum computers, it has to be decomposed into the native gates of quantum computers. It is favorable to apply the least number of native two-qubit gates to construct the Yang-Baxter gate. We study the geometric representations of all X-type braid gates and their corresponding Yang-Baxter gates via the Yang-Baxterization. We find that the braid and Yang-Baxter gates can only exist on certain edges and faces of the two-qubit tetrahedron. We identify the parameters by which the braid and Yang-Baxter gates are the Clifford gate, the matchgate, and the dual-unitary gate. The geometric representations provide the optimal decompositions of the braid and Yang-Baxter gates in terms of other two-qubit gates. We also find that the entangling powers of the Yang-Baxter gates are determined by the spectral parameters. Our results provide the necessary conditions to construct the braid and Yang-Baxter gates on quantum computers.
Keywords
Cite
@article{arxiv.2406.08320,
title = {Geometric representations of braid and Yang-Baxter gates},
author = {Kun Zhang and Kun Hao and Kwangmin Yu and Vladimir Korepin and Wen-Li Yang},
journal= {arXiv preprint arXiv:2406.08320},
year = {2024}
}
Comments
Published version, 27 pages, 7 figures, 2 tables