Classification of gliders for non-involutive Yang–Baxter gates

Determine which members of the representation-theoretic glider construction for involutive Yang–Baxter gates remain gliders for non-involutive Yang–Baxter gates.

Background

The braid relation produces elementary ballistically propagating gliders for general unitary Yang–Baxter gates, and products of these gliders generate conserved quantities. A substantially larger family of gliders is known in the involutive case through representation-theoretic constructions. The paper states that it is unresolved which elements of that larger construction survive when involutivity is removed.

References

For noninvolutive gates, it is not known which members of that construction remain gliders; to the best of our knowledge, this question has not yet been investigated.

— On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates  (2609.05121 - Pozsgay, 4 Sep 2026) in Section 2, Subsection 2.4, paragraph following the discussion of conserved charges