Quantum computers have demonstrable ability to solve problems at a scale beyond brute-
force classical simulation. Interest in quantum algorithms has developed in many areas …

Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

Recent advances in quantum computers are demonstrating the ability to solve problems at a
scale beyond brute force classical simulation. As such, a widespread interest in quantum …

About sixty years ago, the anomalous magnetic response of certain magnetic alloys drew
the attention of theoretical physicists. It soon became clear that understanding these …

The problem of optimizing over random structures emerges in many areas of science and
engineering, ranging from statistical physics to machine learning and artificial intelligence …

Recent years witnessed the development of powerful generative models based on flows,
diffusion, or autoregressive neural networks, achieving remarkable success in generating …

Passive error correction protects logical information forever (in the thermodynamic limit) by
updating the system based only on local information and few-body interactions. A …

A theoretical perspective is provided on the glass transition in molecular liquids at thermal
equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials …

The combination of the compactness of networks, featuring small diameters, and their
complex architectures results in a variety of critical effects dramatically different from those in …

These notes survey and explore an emerging method, which we call the low-degree
method, for understanding statistical-versus-computational tradeoffs in high-dimensional …