Lazy training of quantum physics informed neural networks
Abstract
We study the gradient-flow training dynamics of quantum physics-informed neural networks (QPINNs) for the solution of second-order elliptic partial differential equations with Dirichlet boundary conditions. We consider parameterized quantum circuits as function approximators and analyze their overparameterized regime through the lens of the neural tangent kernel (NTK). Our contribution is a nonasymptotic lazy-training theory for QPINNs and their variational formulation: we prove that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE.
Related
- Preconditioned Physics-Informed Neural Operator Training
- AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for approximating solutions to quasilinear partial differential equations
- Solving Fredholm Integral Equations with Physics-Informed Neural Networks: Single-and double-network approaches
- Error Estimates in Physics-Informed Neural Networks to Heat-Wave Fluid-Structure Interactive System
- Lie Symmetry-Guided Adaptive Sampling for Physics-Informed Neural Networks
BibTeX
@misc{hernandez2026lazy,
title = {{Lazy training of quantum physics informed neural networks}},
author = {Anderson Melchor Hernandez and Giacomo De Palma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19239},
eprint = {2609.19239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19239},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lazy training of quantum physics informed neural networks
AU - Anderson Melchor Hernandez
AU - Giacomo De Palma
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19239
UR - https://arxiv.org/abs/2609.19239
AB - We study the gradient-flow training dynamics of quantum physics-informed neural networks (QPINNs) for the solution of second-order elliptic partial differential equations with Dirichlet boundary conditions. We consider parameterized quantum circuits as function approximators and analyze their overparameterized regime through the lens of the neural tangent kernel (NTK). Our contribution is a nonasymptotic lazy-training theory for QPINNs and their variational formulation: we prove that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE.
ER -