# Quantum-classical physics-informed Kolmogorov-Arnold networks for PDEs

arXiv: https://arxiv.org/abs/2606.20326 · HTML: https://mlsanity.com/paper/2606.20326/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification](https://mlsanity.com/paper/2310.01433/) (2023)
- [Physics-Informed Kolmogorov-Arnold Networks for Power System Dynamics](https://mlsanity.com/paper/2408.06650/) (2024)
- [Non-asymptotic Approximation Error Bounds of Parameterized Quantum Circuits](https://mlsanity.com/paper/2310.07528/) (2023)
- [QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2503.16678/) (2025)
- [Understanding the Spectral Bias of Coordinate Based MLPs Via Training Dynamics](https://mlsanity.com/paper/2301.05816/) (2023)
- [Quantum-Classical Physics-Informed Neural Networks for Solving Reservoir Seepage Equations](https://mlsanity.com/paper/2512.03923/) (2025)

## Built on by (most cited first, 1 of 1)

- [Quantum-Classical Physics-Informed Kolmogorov-Arnold Networks for Solving Fuzzy Differential Equations](https://mlsanity.com/paper/2608.08782/) (2026)

## Abstract (arXiv)

We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs). Built upon Chebyshev-polynomial KAN layers and parameterized quantum circuits, this hybrid framework embeds physical constraints into the training loss to enforce physical consistency. Our theoretical investigations grounded in approximation theory prove that this design accelerates high-frequency error convergence to an exponential rate and effectively mitigates numerical dispersion. We validate the framework across three typical seepage scenarios in porous media, including single-phase flow, component transport and two-phase flow. Compared with existing quantum-classical physics-informed neural networks, QCPIKAN achieves superior performance in global prediction accuracy, local error control, dynamic evolution tracking and displacement front localization. This work provides a robust and efficient alternative for solving complex PDEs.