Title: Detecting emergent 1-form symmetries with quantum error correction Speaker: Michael Knap (Technical University of Munich) Date & Time: May 6, 2025, 1:00pm Where to Attend: ATL 3100A and Virtual Via Zoom: https://umd.zoom.us/j/2821742741?pwd=SWJSRm1DTGFoYUtVMllVSEo5bzdmdz09
Quantum many-body systems can host exotic phases of matter characterized by their quantum entanglement. Among them are phases with topological order. In this talk we discuss how to explore the toric code model in a field (or equivalently the Fradkin-Shenker lattice gauge theory) — a paradigmatic model hosting a Z2 topologically ordered phase and a trivial phase — on a quantum processor [1]. We then focus on the higher-form symmetries of the model. In contrast to global on-site (0-form) symmetries, higher-from symmetries act on subdimensional manifolds. For example, the 1-form symmetries in the toric code fixed point are Wilson and ’t Hooft loop operators. However, higher-form symmetries can be emergent, making them hard to detect in practice. To address this challenge, we propose a criterion for the existence of emergent 1-form symmetries motivated by quantum error correction (QEC) [2]. We show that the loss of an emergent 1-form symmetry is an information theoretic transition revealed from the ensemble of post-measurement states, that is in general unrelated to any quantum phase transitions. This approach allows us to define the Higgs and confinement regimes in the trivial phase of the toric code model. By connecting quantum error correction and generalized symmetries, our work offers a better understanding and provides new tools for characterizing phases of matter.