Séminaire d'Automatique du plateau de Saclay : Some Mathematical and Numerical questions on the Lindblad equation. Application to Quantum Control.

Séminaire le 20 Juin 2017, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S
Claude Le Bris (Ecole des Ponts & Inria)

We overview a series of joint works with P. Rouchon (Mines de Paris) and other collaborators devoted to the mathematical analysis and the numerical simulation of high-dimensional Lindblad equations. These equations rule the time evolution of density matrices of open quantum systems. The numerical techniques we present aim
at adaptively constructing a low-rank approximation of the density matrices, deriving an evolution equation for this reduced model, and using it as a surrogate model for the original evolution. Alternately, using that reduced model, we also consider and improve advanced Monte-Carlo type techniques that simulate the stochastic system of equations equivalent to the Lindblad equation. The practically relevant setting where we test our approaches arises in stabilization/control problems for quantum optics and circuits. We believe that, interestingly, our approaches may be readily adapted to problems involving the simulation and control of the evolution of density matrices in other contexts.

Bio. Claude Le Bris is a civil engineer in chief, HdR from University Paris Dauphine. His applied mathematics works have primarily been devoted to the design and analysis of numerical approaches for Physics and Mechanics. He holds a research position at Ecole des Ponts et Chaussées. He is the scientific leader of the project-team  MATHERIALS at INRIA, the activity of which is focused on multiscale numerical simulation.