ETIENNEY, Mr Paul-Louis (2024) A posteriori error estimates for Lindblad’s equation PFE - Project Graduation, ENSTA.
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Abstract
We focus on simulating open quantum systems within bosonic modes, where one challenge lies in solving the Lindblad master equation in an infinite-dimensional Hilbert space. A standard method involves truncating the Hilbert space to compute a finite-dimensional approximation. Our main goal is to establish a computable error bound for this truncation. To achieve this, we present a novel a posteriori estimate for the Lindblad master equation. Through numerical examples, we illustrate the efficiency of the method, highlighting empirically the tightness of the upper bound, and show how it enables adaptive simulations by dynamically adjusting the truncated Hilbert space of the density matrix. For large-scale simulations, this approach significantly reduces computational time while also relieving users of the challenge of selecting a good truncation, thereby achieving a balance between precision and computational efficiency.
Item Type: | Thesis (PFE - Project Graduation) |
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Uncontrolled Keywords: | Estimate, a posteriori, quantum information, numerical simulation, density matrix, bosonic codes. |
Subjects: | Mathematics and Applications Physics, Optics |
ID Code: | 10385 |
Deposited By: | Paul-louis ETIENNEY |
Deposited On: | 04 oct. 2024 17:43 |
Dernière modification: | 04 oct. 2024 17:43 |
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