Variational quantum algorithm for solving Helmholtz problems with high order finite elements
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908734714806272 |
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| author | Rémi, Arnaud Damanet, François Geuzaine, Christophe |
| author_facet | Rémi, Arnaud Damanet, François Geuzaine, Christophe |
| contents | Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this challenge. We first show that, for regular meshes, a block encoding of the operators $A$ and $A^\dagger A$ arising from the high-order finite element discretisation of Helmholtz problems can be designed, resulting in a quantum circuit of depth $\mathcal{O}(p^3\mathrm{poly}\log(Np))$ with $N$ the number of elements and $p$ the order of the finite elements. Then we apply our algorithm to a one-dimensional Helmholtz problem with Dirichlet and Neumann boundary conditions for various wavenumbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational quantum algorithm for solving Helmholtz problems with high order finite elements Rémi, Arnaud Damanet, François Geuzaine, Christophe Quantum Physics Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this challenge. We first show that, for regular meshes, a block encoding of the operators $A$ and $A^\dagger A$ arising from the high-order finite element discretisation of Helmholtz problems can be designed, resulting in a quantum circuit of depth $\mathcal{O}(p^3\mathrm{poly}\log(Np))$ with $N$ the number of elements and $p$ the order of the finite elements. Then we apply our algorithm to a one-dimensional Helmholtz problem with Dirichlet and Neumann boundary conditions for various wavenumbers. |
| title | Variational quantum algorithm for solving Helmholtz problems with high order finite elements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.22665 |