A defining property of topological order is that it is difficult to create by any unitary process, requiring a time scaling with system size. Here, we will discuss a loophole which obtains these states from single-site measurements on symmetry-protected topological (SPT) phases—the latter being prepared by finite-depth unitary circuits. This generalizes previously known examples, such as measuring the cluster state to obtain the toric code, by observing that one can physically enact the Kramers-Wannier or Jordan-Wigner transformation on an arbitrary initial state. Remarkably, some of these schemes can be implemented in existing Rydberg atom array platforms to efficiently create non-abelian topological order and potentially the first experimental realization of fracton order.
Based on work with Nat Tantivasadakarn, Ryan Thorngren and Ashvin Vishwanath: arXiv:2112.01519 and arXiv:2112.03061