Tensor Networks: From Numerical Methods to Understanding Quantum Systems

Tensor networks are a modern mathematical language that allows for a compact and efficient description of many-body quantum states, where direct computation becomes impossible. This talk discusses how this approach helps to understand the structure of entanglement and the dynamics of systems with a large number of particles, as well as how it is used for the numerical solution of quantum mechanical problems. The main ideas underlying tensor networks, intuitive examples of how they work, and key directions of practical application — from modeling many-body quantum systems to describing states of light — will be presented. Special attention is given to how tensor methods unify theory, computation, and experiment, opening new possibilities for the study of quantum systems.