Ilya Vilkoviskiy : Efficient pseudomode representation and the complexity of quantum impurity models

Simulation of non-equilibrium properties of quantum systems is one of the central challenges in quantum physics.

I will concentrate on the quantum impurity models describing the small interacting degree of freedom coupled to a free and large bath. These models exhibit rich phenomena such as phase transitions and non-Markovian behavior but pose significant computational challenges.

I will review the influence matrix (IM) approach, which allows to approximate an infinite bath by a finite set of effective modes with rigorous complexity guarantees. In particular, I will explain why the computational cost can scale only polynomially with evolution time and desired accuracy. I will also describe a practical numerical procedure for extracting optimized pseudomodes, making the approach more effective for real simulations. Additionally, I will introduce a numerical routine for extracting optimal pseudomodes, enhancing practical applicability.

contact : andrej.meszaros@universite-paris-saclay.fr