In this lecture note, we give a basic introduction to the rapidly developing concepts of
generalized symmetries, from the perspectives of both high energy physics and condensed …

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–
Anderson–Higgs mechanism, ie, after a spontaneous symmetry breaking, a bosonic field …

Non-Abelian topological order is a coveted state of matter with remarkable properties,
including quasiparticles that can remember the sequence in which they are exchanged …

The preparation of long-range entangled states using unitary circuits is limited by Lieb-
Robinson bounds, but circuits with projective measurements and feedback (“adaptive …

Long-range entanglement—the backbone of topologically ordered states—cannot be
created in finite time using local unitary circuits, or, equivalently, adiabatic state preparation …

A fundamental distinction between many-body quantum states are those with short-and long-
range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits …

Symmetry-protected topological (SPT) phases are many-body quantum states that are
topologically nontrivial as long as the relevant symmetries are unbroken. In this work we …

We propose a general framework for using local measurements, local unitaries, and
nonlocal classical communication to construct quantum channels, which can efficiently …

Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of
measurements, stemming from the competition between scrambling unitary dynamics and …

A bstract It has been proposed recently that interacting Symmetry Protected Topological
Phases can be classified using cobordism theory. We test this proposal in the case of …