Skip to Main content Skip to Navigation
Master thesis

Simulation numérique de systèmes quantiques ouverts en grande dimension

Abstract : Solving exactely the Lindblad equations, that model the evolution of open quantum systems, is only possible for small sizes. This is why we wish to have a range of methods enabling us to compute approximate solutions. We presente a deterministic low-rank method that is based upon a reduced approximate form of the density matrix, then a stochastic method of Monte-Carlo that gives the solution up to a statistical noise. We will first introduce an extension of the low-rank method, allowing us to use an adaptive rank while enforcing an upper bound on the error, and then a new variance reduction method. This new method speeds a lot the Monte-Carlo simulations by using the approximate solution given by the low-rank method as a control variate.
Document type :
Master thesis
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download
Contributor : Julien Roussel Connect in order to contact the contributor
Submitted on : Sunday, September 27, 2015 - 1:45:36 PM
Last modification on : Monday, March 21, 2016 - 5:40:00 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 6:38:06 PM


  • HAL Id : hal-01205747, version 1



Julien Roussel. Simulation numérique de systèmes quantiques ouverts en grande dimension. Analyse numérique [math.NA]. 2015. ⟨hal-01205747⟩



Record views


Files downloads