Can one generate Long-ranged entangled (LRE) states using an ideal (universal) quantum computer?

Question

Long-range entanglement (LRE) came out of studying ground states of Hamiltonians with topological order. It is different from short-range entanglement (SRE), in that LRE =/= LU|product states> = SRE, where LU is local unitary operations. My question: is it possible to generate LRE states on a finite size but ideal quantum computer, where one can apply unlimited depths of LU? Suppose one is able to generate a LRE state on a quantum computer, how do we test whether it is indeed LRE, as opposed to SRE? Is topological entanglement entropy (TEE) a metric to distinguish the two? Finally, how are LRE, SRE, and TEE defined for mixed states? A recent preprint showed how to generate SPT states (which is SRE) on a nonideal quantum computer with ~7 qubits https://arxiv.org/abs/1910.05351 , this interesting paper motivated me to ask this question.

Answer 1

Long-ranged entangled state can indeed be created in quantum processors. Two milestone experiments using superconducting qubits and Rydberg atoms:

• ​https://arxiv.org/abs/2104.04119
• https://arxiv.org/abs/2104.01180