Unitary Quantum Algorithm for the Lattice-Boltzmann Method
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910474230038528 |
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| author | Wawrzyniak, David Winter, Josef Schmidt, Steffen Indinger, Thomas Schramm, Uwe Janßen, Christian Adams, Nikolaus A. |
| author_facet | Wawrzyniak, David Winter, Josef Schmidt, Steffen Indinger, Thomas Schramm, Uwe Janßen, Christian Adams, Nikolaus A. |
| contents | We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium within a single time step. Our quantum algorithm enables the computation of multiple time steps in the linearized case, specifically for solving the advection-diffusion equation, before necessitating a full state measurement. Moreover, our formulation can be extended to compute the non-linear equilibrium distribution function for a single time step prior to measurement, utilizing the measurement as an essential algorithmic step. However, in the non-linear case, a classical postprocessing step is necessary for computing the moments of the distribution function. We validate our algorithm by solving the one dimensional advection-diffusion of a Gaussian hill. Our results demonstrate that our quantum algorithm captures non-linearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13391 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitary Quantum Algorithm for the Lattice-Boltzmann Method Wawrzyniak, David Winter, Josef Schmidt, Steffen Indinger, Thomas Schramm, Uwe Janßen, Christian Adams, Nikolaus A. Quantum Physics We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium within a single time step. Our quantum algorithm enables the computation of multiple time steps in the linearized case, specifically for solving the advection-diffusion equation, before necessitating a full state measurement. Moreover, our formulation can be extended to compute the non-linear equilibrium distribution function for a single time step prior to measurement, utilizing the measurement as an essential algorithmic step. However, in the non-linear case, a classical postprocessing step is necessary for computing the moments of the distribution function. We validate our algorithm by solving the one dimensional advection-diffusion of a Gaussian hill. Our results demonstrate that our quantum algorithm captures non-linearity. |
| title | Unitary Quantum Algorithm for the Lattice-Boltzmann Method |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.13391 |