On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates
Abstract
We study the operator entanglement of local operators in one-dimensional brickwork circuits whose two-site gate satisfies the braid relation; throughout this work, we call such a gate a Yang--Baxter gate. We establish upper bounds for several structured, overlapping classes of Yang--Baxter gates. We show that the operator Schmidt rank remains uniformly bounded in time for all qubit Yang--Baxter gates and, in arbitrary local dimension, for permutation gates obtained from non-degenerate Yang--Baxter maps. We also show that it grows at most polynomially for involutive dual-unitary Yang--Baxter gates and for arbitrary phase dressings of permutation gates obtained from non-degenerate Yang--Baxter maps. These results imply, respectively, constant and logarithmic upper bounds on the operator entanglement. Conversely, we construct a seven-state involutive Yang--Baxter gate without dual unitarity and a one-site operator whose exact operator Schmidt rank grows exponentially, although the corresponding operator entropies remain undetermined. Entanglement growth in the general Yang--Baxter case remains open. All proofs and selected examples were constructed by ChatGPT 5.6 Sol.
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BibTeX
@misc{pozsgay2026growth,
title = {{On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates}},
author = {Balázs Pozsgay},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.05121},
eprint = {2609.05121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05121},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates
AU - Balázs Pozsgay
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.05121
UR - https://arxiv.org/abs/2609.05121
AB - We study the operator entanglement of local operators in one-dimensional brickwork circuits whose two-site gate satisfies the braid relation; throughout this work, we call such a gate a Yang--Baxter gate. We establish upper bounds for several structured, overlapping classes of Yang--Baxter gates. We show that the operator Schmidt rank remains uniformly bounded in time for all qubit Yang--Baxter gates and, in arbitrary local dimension, for permutation gates obtained from non-degenerate Yang--Baxter maps. We also show that it grows at most polynomially for involutive dual-unitary Yang--Baxter gates and for arbitrary phase dressings of permutation gates obtained from non-degenerate Yang--Baxter maps. These results imply, respectively, constant and logarithmic upper bounds on the operator entanglement. Conversely, we construct a seven-state involutive Yang--Baxter gate without dual unitarity and a one-site operator whose exact operator Schmidt rank grows exponentially, although the corresponding operator entropies remain undetermined. Entanglement growth in the general Yang--Baxter case remains open. All proofs and selected examples were constructed by ChatGPT 5.6 Sol.
ER -