Classical simulation of thermal equilibrium and quantum dynamics

Quantum systems of many interacting particles appear in numerous branches of physics, from condensed matter to statistical or high energy physics. Their study, however, is often very complicated due to the high dimensions of the Hilbert spaces involved.

The field of quantum information brings a new perspective to the study of those systems. Through it, we can rigorously analyze whether specific physical problems are fundamentally complex, and will require a quantum computer, or whether they can be solved efficiently with (classical) numerical means.

In this talk, we show how many interesting properties about many-body systems both in equilibrium and out of it can be computed in polynomial time, with provable efficiency guarantees. In particular, we focus on the classical simulation of Gibbs or thermal states, and on the simulation of arbitrary dynamics for short times. We do this through the frameworks of tensor network methods, as well as cluster expansions, which highlight how fundamental physical features, such as locality, constrain the complexity of quantum systems.