**Time/Venue**Tuesday, October 4 at 11 am in Pacific time in Physics North 402

and via Zoom:

https://berkeley.zoom.us/j/99523499113pwd=REovb3pyam03WXQwbEhrU3dqNHZvdz09

Meeting ID: 995 2349 9113 Passcode: 600704**Host **Ehud Altman**Title** Topological order from finite-depth circuits and measurements: from theory to quantum devices**Abstract** A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter, such as cat states, topological order, or critical states cannot be created by finite-depth circuits. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE states such as preparing the toric code from measuring a sublattice of a 2D cluster state. I will present a general framework of how and why these known protocols give rise to long range entanglement based on interpreting the cluster state measurement as implementing the non-local Kramers-Wannier transformation. This provides a scalable and practical way to “gauge” a symmetry in finite time, and moreover allows us to go beyond the preparation of stabilizer states. In addition, we find a complexity hierarchy on long-range entangled states based on the minimal number of measurement layers required to create the state. I will argue that certain phases of matter cannot be prepared using any finite number of layers, while remarkably certain non-Abelian topological orders can be prepared in a single round of measurement. As an application, I will outline how current NISQ devices, ranging from Rydberg atom arrays to Google’s quantum processors, can scalably prepare a large class of exotic phases such as non-Abelian topological order and even fracton phases.

This talk is based on 2112.01519, 2112.03061, 2209.03964, and 2209.06202

# Special 290S/290K Quantum Materials Seminar speaker Nathanan Tantivasadakarn (Harvard) Tuesday, October 4 at 11 am in Physics North 402

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