How fast can Yang–Baxter circuits grow in complexity?

Bounds for selected gate families

The abstract reports that operator Schmidt rank remains uniformly bounded in time for all qubit Yang–Baxter gates. It also gives a uniform bound, in arbitrary local dimension, for permutation gates obtained from non-degenerate Yang–Baxter maps.

For two other stated families, the rank grows at most polynomially in time: involutive dual-unitary Yang–Baxter gates, and arbitrary phase dressings of permutation gates obtained from non-degenerate Yang–Baxter maps. The abstract says these results imply, respectively, constant and logarithmic upper bounds on operator entanglement.

These are bounds for specified, overlapping classes of gates. They do not establish one growth rule for all Yang–Baxter gates.

One example beyond the bounds

The preprint also constructs a seven-state involutive Yang–Baxter gate that is not dual-unitary, along with a one-site operator whose exact operator Schmidt rank grows exponentially. This is a result about that particular gate and operator; it does not, by itself, establish a broader rule for other dimensions or gates. The abstract says the corresponding operator entropies remain undetermined.

The overall question—how operator entanglement grows in the general Yang–Baxter case—remains open, according to the abstract.

What the source can establish here

The available evidence is the abstract, not the full paper. It therefore does not provide enough detail to assess the proof techniques, assumptions, or technical qualifications behind the reported results. The paper is listed as an arXiv preprint; the supplied metadata does not establish its review status.

The abstract also states that all proofs and selected examples were constructed by ChatGPT. That disclosure is a reason to seek close scrutiny of the arguments, but does not determine whether they are correct. The results should be read as claims reported by the preprint, not as independently verified conclusions.