Geometric Quantum Physics Informed Neural Network

• URL: http://arxiv.org/abs/2605.02352v1
• Date: Mon, 04 May 2026 08:55:29 GMT
• Title: Geometric Quantum Physics Informed Neural Network
• Abstract summary: We introduce geometric quantum physics-informed neural networks (GQPINNs) in which the geometric structure of the underlying PDE is incorporated directly into the quantum-circuit ansatz.<n>GQPINNs achieve improved solution accuracy, as quantified by lower mean absolute error, while requiring substantially fewer trainable parameters.<n>These results identify symmetry-aware quantum-circuit design as an effective route toward improved efficiency and generalization in quantum PDE solvers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum physics-informed neural networks (QPINNs) have recently emerged as a promising framework for the solution of partial differential equations (PDEs), with several studies reporting improved convergence and accuracy relative to classical physics-informed neural networks (PINNs) at reduced training cost. Motivated by these advances, we introduce geometric quantum physics-informed neural networks (GQPINNs), a symmetry-aware extension of QPINNs in which the geometric structure of the underlying PDE is incorporated directly into the quantum-circuit ansatz. Building on the framework of geometric quantum machine learning, we construct parametrized circuits that encode finite-group and compact Lie-group symmetries as inductive biases through problem-specific equivariant generator sets . Using a twirling-based construction, we derive symmetry-preserving gates that ensure that the model predictions respect the symmetries of the governing equation whenever the boundary and initial data are symmetry compatible. We benchmark GQPINNs against standard QPINNs and symmetry-adapted classical PINN baselines under matched training protocols across a representative set of linear and nonlinear PDEs. Across these benchmarks, GQPINNs achieve improved solution accuracy, as quantified by lower mean absolute error, while requiring substantially fewer trainable parameters. These results identify symmetry-aware quantum-circuit design as an effective route toward improved efficiency and generalization in quantum PDE solvers and provide a systematic framework for incorporating geometric inductive biases into quantum-enhanced scientific machine learning.

Related papers

• Symmetry-Reduced Physics-Informed Learning of Tensegrity Dynamics [33.52984112921709]
  Most existing physics-informed neural network (PINN) approaches for tensegrity dynamics do not explicitly exploit intrinsic geometric symmetries.<n>We propose a symmetry-reduced physics-informed neural network (SymPINN) framework that embeds group-theory-based symmetry directly into both the solution expression and the neural network architecture.
  arXiv  Detail & Related papers  (2026-03-18T15:23:23Z)
• 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)
• Performance Guarantees for Quantum Neural Estimation of Entropies [31.955071410400947]
  Quantum neural estimators (QNEs) combine classical neural networks with parametrized quantum circuits.<n>We study formal guarantees for QNEs of measured relative entropies in the form of non-asymptotic error risk bounds.<n>Our theory aims to facilitate principled implementation of QNEs for measured relative entropies.
  arXiv  Detail & Related papers  (2025-11-24T16:36:06Z)
• The GINN framework: a stochastic QED correspondence for stability and chaos in deep neural networks [0.0]
  We develop a Euclidean field-theoretic approach that maps deep neural networks (DNNs) to quantum electrodynamics (QED)<n> Neural activations and weights are represented by fermionic matter and gauge fields.<n>We validate the theoretical predictions through numerical simulations of standard multilayer perceptrons.
  arXiv  Detail & Related papers  (2025-08-26T11:41:11Z)
• Quantum neural ordinary and partial differential equations [38.77776626953413]
  We present a unified framework that brings the continuous-time formalism of classical neural ODEs/PDEs into quantum machine learning and quantum control.<n>We define QNODEs as the evolution of finite-dimensional quantum systems, and QNPDEs as infinite-dimensional (continuous-variable) counterparts.
  arXiv  Detail & Related papers  (2025-08-24T18:43:44Z)
• SPD Learning for Covariance-Based Neuroimaging Analysis: Perspectives, Methods, and Challenges [41.955864444491965]
  Neuroimaging provides a critical framework for characterizing brain activity by quantifying connectivity patterns and functional architecture across modalities.<n>Modern machine learning has significantly advanced our understanding of neural processing mechanisms through these datasets.<n>This review focuses on machine learning approaches for covariance-based neuroimaging data, where often symmetric positive definite (SPD) matrices under full-rank conditions encode inter-channel relationships.
  arXiv  Detail & Related papers  (2025-04-26T10:05:04Z)
• 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)
• Lie Point Symmetry and Physics Informed Networks [59.56218517113066]
  We propose a loss function that informs the network about Lie point symmetries in the same way that PINN models try to enforce the underlying PDE through a loss function. Our symmetry loss ensures that the infinitesimal generators of the Lie group conserve the PDE solutions. Empirical evaluations indicate that the inductive bias introduced by the Lie point symmetries of the PDEs greatly boosts the sample efficiency of PINNs.
  arXiv  Detail & Related papers  (2023-11-07T19:07:16Z)
• Adaptive Log-Euclidean Metrics for SPD Matrix Learning [73.12655932115881]
  We propose Adaptive Log-Euclidean Metrics (ALEMs), which extend the widely used Log-Euclidean Metric (LEM) The experimental and theoretical results demonstrate the merit of the proposed metrics in improving the performance of SPD neural networks.
  arXiv  Detail & Related papers  (2023-03-26T18:31:52Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)

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.