Solving nonlinear PDEs with Quantum Neural Networks: A variational approach to the Bratu Equation
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910009473892352 |
|---|---|
| author | Cheimarios, Nikolaos |
| author_facet | Cheimarios, Nikolaos |
| contents | We present a variational quantum algorithm (VQA) to solve the nonlinear one-dimensional Bratu equation. By formulating the boundary value problem within a variational framework and encoding the solution in a parameterized quantum neural network (QNN), the problem reduces to an optimization task over quantum circuit parameters. The trial solution incorporates a predictor from the previous continuation step and boundary-enforcing terms, allowing the circuit to focus on minimizing the residual of the differential operator. Using a noiseless quantum simulator, we demonstrate that the method accurately captures both solution branches of the Bratu equation and shows excellent agreement with classical pseudo arc-length continuation results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04372 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving nonlinear PDEs with Quantum Neural Networks: A variational approach to the Bratu Equation Cheimarios, Nikolaos Quantum Physics We present a variational quantum algorithm (VQA) to solve the nonlinear one-dimensional Bratu equation. By formulating the boundary value problem within a variational framework and encoding the solution in a parameterized quantum neural network (QNN), the problem reduces to an optimization task over quantum circuit parameters. The trial solution incorporates a predictor from the previous continuation step and boundary-enforcing terms, allowing the circuit to focus on minimizing the residual of the differential operator. Using a noiseless quantum simulator, we demonstrate that the method accurately captures both solution branches of the Bratu equation and shows excellent agreement with classical pseudo arc-length continuation results. |
| title | Solving nonlinear PDEs with Quantum Neural Networks: A variational approach to the Bratu Equation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.04372 |