# Quantum AS-DeepOnet: Quantum Attentive Stacked DeepONet for Solving 2D Evolution Equations

arXiv: https://arxiv.org/abs/2603.02261 · HTML: https://mlsanity.com/paper/2603.02261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 28 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [ECA-Net: Efficient Channel Attention for Deep Convolutional Neural Networks](https://mlsanity.com/paper/1910.03151/) (2019)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications](https://mlsanity.com/paper/2004.04276/) (2020)
- [Introduction to Quantum Reinforcement Learning: Theory and PennyLane-based Implementation](https://mlsanity.com/paper/2108.06849/) (2021)
- [QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2503.16678/) (2025)

## Abstract (arXiv)

DeepONet enables retraining-free inference across varying initial conditions or source terms at the cost of high computational requirements. This paper proposes a hybrid quantum operator network (Quantum AS-DeepOnet) suitable for solving 2D evolution equations. By combining Parameterized Quantum Circuits and cross-subnet attention methods, we can solve 2D evolution equations using only 60% of the trainable parameters while maintaining accuracy and convergence comparable to the classical DeepONet method.