Advanced Topics in Computational Physics: Computational Quantum Mechanics
Contents
Advanced Topics in Computational Physics: Computational Quantum Mechanics¶
Introduction¶
A theoretical understanding of the behavior of quantum-mechanical many-body systems - that is, systems containing many interacting particles - is a considerable challenge in that no exact solution can be found; instead, reliable methods are needed for approximate but accurate simulations of such systems on modern computers. New insights and a better understanding of complicated quantum mechanical systems can only be obtained via large-scale simulations. The capability to study such systems is of high relevance for both fundamental research and industrial and technological advances.
The aim of these lecture notes is to present applications of, through various computational projects, some of the most widely used many-body methods with pertinent algorithms and high-performance computing topics such as advanced parallelization techniques and object orientation. Furthermore, elements of Machine Learning and quantum computing may be presented if of interest. In particular we will here employ deep learning techniques based on neural networks and so-called Boltzmann machines. The methods and algorithms that will be studied may vary from year to year depending on the interests of the participants, but the main focus will be on systems from computational material science, solid-state physics, atomic and molecular physics, nuclear physics and quantum chemistry. The most relevant algorithms and methods are microscopic mean-field theories (Hartree-Fock and Kohn-Sham theories and density functional theories), large-scale diagonalization methods, coupled-cluster theory, similarity renormalization methods, and quantum Monte Carlo like Variational Monte Carlo and Diffusion Monte Carlo approaches. Quantum Computing, Machine Learning and Quantum Machine Learning applied to the solution of quantum mechanical problems are also relevant topics.