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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.
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Master thesis
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https://hal.inria.fr/hal-01205747
Contributor : Julien Roussel <>
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

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  • HAL Id : hal-01205747, version 1

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

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