The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

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

Classical machine learning (ML) provides a potentially powerful approach to solving
challenging quantum many-body problems in physics and chemistry. However, the …

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

Originally developed in the context of condensed-matter physics and based on
renormalization group ideas, tensor networks have been revived thanks to quantum …

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 …

The concept of topological phases is a powerful framework for characterizing ground states
of quantum many-body systems that goes beyond the paradigm of symmetry breaking …

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 explore the effect of decoherence on many-body mixed states from a purification
perspective. Here, quantum channels map to unitary transformations acting on a purified …

What are topological phases of matter? First, they are phases of matter at zero temperature.
Second, they have a nonzero energy gap for the excitations above the ground state. Third …