Classification of 2D Gapped Ground States With Strict Area Law

Explore a 50-minute lecture on the classification of 2D gapped ground states with strict area law, presented by Isaac Kim from UC Davis at the Simons Institute. Delve into the assumption of a strict form of the area law and its implications for classifying gapped ground states in two dimensions. Learn how these ground states can be transformed into the ground states of a local commuting Hamiltonian, specifically the generalized string-net Hamiltonian, using constant-depth quantum circuits. Gain insights into the intersection of quantum complexity, quantum PCP, area laws, and quantum gravity. Discover the findings of this research, which is based on a joint work with Daniel Ranard from MIT.