A Classical-Quantum Hybrid Architecture for Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2511.07216v1
• Date: Mon, 10 Nov 2025 15:39:18 GMT
• Title: A Classical-Quantum Hybrid Architecture for Physics-Informed Neural Networks
• Authors: Said Lantigua, Gilson Giraldi, Renato Portugal,
• Abstract summary: We introduce the Quantum-Classical Hybrid Physics-Informed Neural Network with Multiplicative and Additive Couplings (QPINN-MAC)<n>Through strategic couplings between classical and quantum components, the QPINN-MAC retains the universal approximation property.<n>We prove that these couplings prevent gradient collapse, ensuring trainability even in high-dimensional regimes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we introduce the Quantum-Classical Hybrid Physics-Informed Neural Network with Multiplicative and Additive Couplings (QPINN-MAC): a novel hybrid architecture that integrates the framework of Physics-Informed Neural Networks (PINNs) with that of Quantum Neural Networks (QNNs). Specifically, we prove that through strategic couplings between classical and quantum components, the QPINN-MAC retains the universal approximation property, ensuring its theoretical capacity to represent complex solutions of ordinary differential equations (ODEs). Simultaneously, we demonstrate that the hybrid QPINN-MAC architecture actively mitigates the barren plateau problem, regions in parameter space where cost-function gradients decay exponentially with circuit depth, a fundamental obstacle in QNNs that hinders optimization during training. Furthermore, we prove that these couplings prevent gradient collapse, ensuring trainability even in high-dimensional regimes. Thus, our results establish a new pathway for constructing quantum-classical hybrid models with theoretical convergence guarantees, which are essential for the practical application of QPINNs.

Related papers

• A Trainable-Embedding Quantum Physics-Informed Framework for Multi-Species Reaction-Diffusion Systems [1.7887197093662073]
  We study embedding strategies for trainable embedding quantum physics-informed neural networks (TE-QPINNs) in the context of nonlinear reaction-diffusion systems.<n>We introduce an extended TE-QPINN (x-TE-QPINN) architecture that supports both classical and fully quantum embeddings.
  arXiv  Detail & Related papers  (2026-02-10T00:19:12Z)
• Explaining the advantage of quantum-enhanced physics-informed neural networks [0.05997422707234518]
  Partial differential equations (PDEs) form the backbone of simulations of many natural phenom- ena.<n>We show how quantum computing can improve the ability of physics-informed neural networks to solve PDEs.
  arXiv  Detail & Related papers  (2026-01-21T14:50:17Z)
• Quantum Recurrent Embedding Neural Network [11.54075064463256]
  We propose a quantum recurrent embedding neural network (QRENN) inspired by fast-track information pathways in ResNet.<n>We provide a rigorous proof of the trainability of QRENN circuits, demonstrating that this deep quantum neural network can avoid barren plateaus.<n>Our results highlight the power of recurrent data embedding in quantum neural networks and the potential for scalable quantum supervised learning.
  arXiv  Detail & Related papers  (2025-06-16T07:50:31Z)
• VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learning [50.95799256262098]
  Variational quantum circuits (VQCs) hold promise for quantum machine learning but face challenges in expressivity, trainability, and noise resilience.<n>We propose VQC-MLPNet, a hybrid architecture where a VQC generates the first-layer weights of a classical multilayer perceptron during training, while inference is performed entirely classically.
  arXiv  Detail & Related papers  (2025-06-12T01:38:15Z)
• RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations [44.13836547616739]
  Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers.<n> choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task.<n>Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem.
  arXiv  Detail & Related papers  (2025-06-04T08:30:35Z)
• TunnElQNN: A Hybrid Quantum-classical Neural Network for Efficient Learning [0.0]
  We develop TunnElQNN, a non-sequential architecture composed of alternating classical and quantum layers.<n>We evaluate the performance of this hybrid model on a synthetic dataset of interleaving half-circle for multi-class classification tasks.<n>Our results show that the TunnElQNN model consistently outperforms the ReLUQNN counterpart.
  arXiv  Detail & Related papers  (2025-05-02T00:30:50Z)
• QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs [0.45880283710344066]
  Physics-informed neural networks (PINNs) have emerged as promising methods for solving partial differential equations (PDEs) by embedding physical laws within neural architectures.<n>We present a quantum-classical physics-informed neural network (QCPINN) that combines quantum and classical components, allowing us to solve PDEs with significantly fewer parameters while maintaining comparable accuracy and convergence to classical PINNs.
  arXiv  Detail & Related papers  (2025-03-20T19:52:26Z)
• Seismic inversion using hybrid quantum neural networks [2.897792418778358]
  Quantum computers operate using qubits, which exploit superposition and entanglement, offering the potential to solve classically intractable problems.<n>We develop a hybrid quantum physics-informed neural network (HQ-PINN) for post-stack and pre-stack seismic inversion.
  arXiv  Detail & Related papers  (2025-03-06T22:21:45Z)
• A Hybrid Quantum-Classical Physics-Informed Neural Network Architecture for Solving Quantum Optimal Control Problems [1.4811951486536687]
  The study showcases an innovative approach to optimizing quantum state manipulations. The proposed hybrid model effectively applies machine learning techniques to solve optimal control problems. This is illustrated through the design and implementation of a hybrid PINN network to solve a quantum state transition problem.
  arXiv  Detail & Related papers  (2024-04-23T13:22:22Z)
• Towards Efficient Quantum Hybrid Diffusion Models [68.43405413443175]
  We propose a new methodology to design quantum hybrid diffusion models. We propose two possible hybridization schemes combining quantum computing's superior generalization with classical networks' modularity.
  arXiv  Detail & Related papers  (2024-02-25T16:57:51Z)
• A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity [50.387179833629254]
  We introduce a collaborative classical-quantum architecture called co-TenQu. Co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. It outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.
  arXiv  Detail & Related papers  (2024-02-23T14:09:41Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Entanglement Classification via Neural Network Quantum States [58.720142291102135]
  In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS)
  arXiv  Detail & Related papers  (2019-12-31T07:40:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.