[2603.24196] Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks

Quantum Physics arXiv:2603.24196 (quant-ph) [Submitted on 25 Mar 2026] Title:Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks Authors:Jucai Zhai, Muhammad Abdullah, Boyang Chen, Fazal Chaudry, Paul N. Smith, Claire E. Heaney, Yanghua Wang, Jiansheng Xiang, Christopher C. Pain View a PDF of the paper titled Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks, by Jucai Zhai and Muhammad Abdullah and Boyang Chen and Fazal Chaudry and Paul N. Smith and Claire E. Heaney and Yanghua Wang and Jiansheng Xiang and Christopher C. Pain View PDF HTML (experimental) Abstract:In scientific computing, the formulation of numerical discretisations of partial differential equations (PDEs) as untrained convolutional layers within Convolutional Neural Networks (CNNs), referred to by some as Neural Physics, has demonstrated good efficiency for executing physics-based solvers on GPUs. However, classical grid-based methods still face computational bottlenecks when solving problems involving billions of degrees of freedom. To address this challenge, this paper proposes a novel framework called 'Quantum Neural Physics' and develops a Hybrid Quantum-Classical CNN Multigrid Solver (HQC-CNNMG). This approach maps analytically-determined stencils of discretised differential operators into parameter-free or untrained quantum convolutional kernels. ...