Computational Methods for Quantum Many-Body Problems, Spring 2024
SynopsisMany-body problems in quantum physics and chemistry are among the most important scientific challenges, and remain difficult despite decades of research efforts. Many methods have been developed to address the high dimensionality of the many-body problem, including various model reduction techniques using mean field and embedding ideas, quantum Monte Carlo algorithms, tensor networks, and more recent approaches related to machine learning. Recent efforts aim at using quantum computers as solvers. The ideas and sophisticated tools developed in this context often find applications beyond physics, chemistry, and materials science in other areas where high dimensionality has to be dealt with, a recent example being the development of mean-field games.The course gives an introduction to the frontier of computational quantum many-body physics and discusses general mathematical challenges of high-dimensional sampling and optimization, as well as the connections to other fields, such as mathematical physics and quantum information theory.
AudienceThe course is intended for students from physics, math, chemistry, materials science, and quantum engineering. We expect basic knowledge of quantum mechanics (Schrödinger equation, bra-ket notation, spin), will start with a short reminder, and then discuss density operators, tensor products, and second quantization as needed for the rest of the course. Every student will pick a computational project for which you can work with your favorite programming language.have a nice day! |