Quantum Enhanced Numerical Homogenization
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914431749849088 |
|---|---|
| author | Balazi, Loïc Deiml, Matthias Peterseim, Daniel |
| author_facet | Balazi, Loïc Deiml, Matthias Peterseim, Daniel |
| contents | We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the Localized Orthogonal Decomposition, we employ quantum local problem solvers to capture fine-scale features efficiently. Crucially, the approach does not rely on the periodicity of the problem, and the integration of the quantum computation within a coarse model requires only selected measurements of the quantum representative volume elements, overcoming the information bottleneck of quantum interfaces that could eliminate the speed-up. We demonstrate that the local quantum solver can achieve solutions with sufficient accuracy, with a number of operations that scales only logarithmically with the fine-scale resolution, determined by the smallest length scale encoded in the diffusion coefficient. The potential of the approach is illustrated through two-dimensional test cases, using a classical simulation of the local quantum solver. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28521 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Enhanced Numerical Homogenization Balazi, Loïc Deiml, Matthias Peterseim, Daniel Numerical Analysis 65N30, 68Q12, 35J15 We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the Localized Orthogonal Decomposition, we employ quantum local problem solvers to capture fine-scale features efficiently. Crucially, the approach does not rely on the periodicity of the problem, and the integration of the quantum computation within a coarse model requires only selected measurements of the quantum representative volume elements, overcoming the information bottleneck of quantum interfaces that could eliminate the speed-up. We demonstrate that the local quantum solver can achieve solutions with sufficient accuracy, with a number of operations that scales only logarithmically with the fine-scale resolution, determined by the smallest length scale encoded in the diffusion coefficient. The potential of the approach is illustrated through two-dimensional test cases, using a classical simulation of the local quantum solver. |
| title | Quantum Enhanced Numerical Homogenization |
| topic | Numerical Analysis 65N30, 68Q12, 35J15 |
| url | https://arxiv.org/abs/2603.28521 |