On the growth of operator entanglement in brickwork circuits with Yang--Baxter gates
This research investigates how operator entanglement grows in one-dimensional brickwork circuits using Yang–Baxter gates, which satisfy a specific braid relation. The study establishes rigorous upper bounds on measures like operator Schmidt rank ($ ext{OSR}_c$) and associated entropies. Findings show that for many gate types, entanglement remains bounded or grows logarithmically, but counterexamples exist where entanglement can grow exponentially.