Description
Local operator entanglement (LOE) dictates the complexity of simulating Heisenberg evolution using tensor network methods, and serves as a strong dynamical signature of quantum chaos.
I will discuss how LOE is also sensitive to how non-Clifford a unitary is: its magic resources. In particular, we prove that LOE is always upper-bound by three distinct magic monotones: T-count, unitary nullity, and the recently introduced operator stabilizer Rényi entropy. Moreover, in the average case for large, random circuits, we prove that LOE and magic monotones approximately coincide.
Our results imply that an operator evolution that is expensive to simulate using tensor network methods must also be inefficient using both stabilizer and Pauli truncation methods. A direct corollary of our bounds is that any quantum chaotic dynamics cannot be simulated classically. Entanglement in operator space therefore measures a unified picture of non-classical resources, in stark contrast to the Schrödinger picture.
arXiv: 2501.18679
