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

TL;DR

This paper introduces Quantum AS-DeepOnet, a hybrid quantum neural network that efficiently solves 2D evolution equations with fewer parameters while maintaining accuracy, leveraging quantum circuits and attention mechanisms.

Contribution

It presents a novel hybrid quantum neural network architecture combining quantum circuits and attention for solving PDEs more efficiently.

Findings

Uses only 60% of trainable parameters compared to classical DeepONet.

Maintains accuracy and convergence comparable to classical methods.

Demonstrates effectiveness on 2D evolution equations.

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.