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

2026-02-28

AI Summary

This work proposes a hybrid quantum operator network that integrates parameterized quantum circuits with a cross-subnet attention mechanism to address the high parameter count and computational cost of classical DeepONets in solving two-dimensional evolution equations. By introducing quantum computing and attention mechanisms into the DeepONet architecture for the first time, the method constructs a quantum-classical hybrid neural network that maintains solution accuracy and convergence speed while requiring only 60% of the trainable parameters of the original model, thereby significantly improving parameter efficiency. This study achieves synergistic optimization between quantum enhancement and attention mechanisms in operator learning, offering a novel paradigm for efficiently solving partial differential equations.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• 2D evolution equations
• DeepONet
• computational cost
• operator learning
• quantum machine learning

Innovation

• Quantum DeepONet
• Parameterized Quantum Circuits
• Attention Mechanism
• 2D Evolution Equations
• Hybrid Quantum-Classical Network