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

TL;DR

A hybrid quantum operator network (Quantum AS-DeepOnet) suitable for solving 2D evolution equations is proposed by combining Parameterized Quantum Circuits and cross-subnet attention methods.

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.

Figures (5)

• Figure 1: Architecture of quantum layers.The pre- and post-processing layers of the quantum circuit consist of affine transformations and nonlinear activation functions. An angle encoder is used in the quantum circuit. The circuit employs three distinct structures—Nearest-neighbour, All-to-all, and Circuit-block—corresponding to circuits 2, 6, and 19 in sim2019expressibility, respectively. These structures are implemented within the geometrically irregular region following the Data Encoder, as illustrated in Figure \ref{['fig:hybrid system']}. Measurements in the quantum circuit are performed by calculating the expected value of each qubit under the Pauli-Z operator.
• Figure 2: Stacked DeepONet structure
• Figure 3: Architecture of Quantum AS-DeepOnet.
• Figure 4: Comparison results for 2D advection equation.
• Figure 5: Comparison results for 2D Burgers' equation.

Theorems & Definitions (2)

• Example 1
• Example 2