%0 Journal Article
%T Adaptive low-rank approximation and denoised Monte-Carlo approach for high-dimensional Lindblad equations
%A Claude Le Bris
%A Pierre Rouchon
%A Julien Roussel
%J Mathematics
%D 2015
%I arXiv
%X We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics is described: a deterministic low-rank approximation of the density operator is computed, and its rank is adjusted dynamically, using an on-the-fly estimator of the error committed when reducing the dimension. On the other hand, when the intrinsic dimension of the Lindblad equation is too high to allow for such a deterministic approximation, we combine classical ensemble averages of quantum Monte Carlo trajectories and a denoising technique. Specifically, a variance reduction method based upon the consideration of a low-rank dynamics as a control variate is developed. Numerical tests for quantum collapse and revivals show the efficiency of each approach, along with the complementarity of the two approaches.
%U http://arxiv.org/abs/1509.07960v2