MINES ParisTech CAS - Centre automatique et systèmes

The many-body problem in quantum mechanics and some of its recent solutions

Thursday 18th November 2021, 4pm – 5pm (Paris time).

Antoine Tilloy, CAS, MINES ParisTech, France

We now know the fundamental laws of nature to a precision that is a priori good enough to understand all phenomena that can occur on earth, from materials, to nucleus, to particle colliders. In practice, however, the dimension of the state space of quantum mechanical systems increases exponentially with the number of constituents, making bottom-up simulations impossible. For example, the direct simulation of a quantum magnet made of a cube of 4 x 4 x 4 spins is out of reach of even exascale supercomputers. Perturbation theory and the Monte Carlo method have allowed us to deal with some problems, but many situations remain intractable. Two promising new approaches are quantum computing, which allows to work directly with exponentially growing state spaces, and tensor network methods, which allow to classically compress this state space. I'll explain the philosophy of the latter classical compression option, which boils down to carrying a non-trivial optimization over a carefully chosen "extensive" submanifold of a huge Hilbert space. I'll mention the successes and challenges involved. The seminar will be very basic, aimed at people knowing next to no quantum mechanics, and my aim will mostly be to give a tour of the field.

Antoine started a month ago as assistant professor in the CAS Mines ParisTech. He obtained a theoretical physics PhD at ENS in 2016 on the theory of continuous measurement in quantum mechanics. He then moved to the Max Planck Institute of Quantum Optics near Munich, where he worked on tensor networks as a solution to the many-body problem in quantum mechanics. Currently he works on the development of new compression methods for quantum field theory, and contributes to theoretical efforts towards quantum computing made in the Quantic group (Mines, Inria, ENS).