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arXiv · 1509.07960

Adaptive low-rank approximation and denoised Monte-Carlo approach for high-dimensional Lindblad equations

Claude Le Bris·Pierre Rouchon·Julien Roussel
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Abstract

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.

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Claude Le Bris, Pierre Rouchon, Julien Roussel. 2015-09-26. Adaptive low-rank approximation and denoised Monte-Carlo approach for high-dimensional Lindblad equations. https://doi.org/10.1103/physreva.92.062126

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