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

Hongquan Wang; Hanshu Chen; Ilia Marchevsky; Zhuojia Fu

quant-phFeb 28, 2026

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

Authors: Hongquan Wang, Hanshu Chen, Ilia Marchevsky, Zhuojia Fu

Organizations: School of Mathematics, Hohai University, Nanjing, Jiangsu 211100, China · College of Mechanics and Engineering Science, Hohai University, Nanjing, Jiangsu 211100, China · Department of Applied Mathematics, Bauman Moscow State Technical University, Moscow 105005, Russia

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.

PDE Operator Learning

Partial differential equation (PDE) operator learning builds models that map inputs such as coefficients and initial conditions to solution fields.

See all 228 papers

Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations
Aug 27, 2026Muhammad Abid, Arth Sojitra, Bipin Tiwari +1PDE Operator Learning Deep Operator Networks
Department of Mechanical and Aerospace Engineering University of Tennessee, Knoxville Knoxville, TN 37996, USA
Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures
Sep 3, 2026Amar Alem Koric, Qibang Liu, Seid KoricPDE Operator Learning Deep Operator Networks
Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA · National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 1205 W. Clark St., Urbana, IL, 61801, USA · The Grainger College of Engineering, Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL, 61801, USA
Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks
Mar 25, 2026Jucai Zhai, Muhammad Abdullah, Boyang Chen +6Neural PDE Solvers PDE Solving
Resource Geophysics Academy, Imperial College London, London, SW7 2AZ UK · Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ UK · Quantum AI Leadership (QUAIL) Ltd, London, WC2H 9JQ UK +2

Aug 27, 2026J/K move · Enter open · S save

Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations

Muhammad Abid, Arth Sojitra, Bipin Tiwari, Omer San

Department of Mechanical and Aerospace Engineering University of Tennessee, Knoxville Knoxville, TN 37996, USA

PDE Operator Learning Deep Operator Networks Quantum Machine Learning Quantum Neural Networks

Open paper AskPDF arXiv

Quantum DeepONet accelerates neural-operator inference by evaluating an orthogonally parameterized network on a quantum computer, reproducing in ideal simulation the accuracy of its classical counterpart at asymptotically lower inference cost. Its trunk network, however, receives query coordinates with limited spectral structure, requiring the network to learn oscillatory features through its nonlinearities. We propose Quantum SEDONet (Spectral-Embedded Deep Operator Network), which assigns each trunk coordinate a spectral basis according to its boundary condition: Fourier features for periodic coordinates and Chebyshev features for bounded, non-periodic coordinates. The basis is selected per coordinate rather than per problem, allowing both representations within a single problem. Under unary amplitude encoding, the embedding incurs no additional qubits or circuit depth when its dimension remains within the network width, while increasing the parameter count by only a few percent. Across four benchmarks, Quantum SEDONet reduces the mean relative L2 error by 54.1% for the antiderivative, 49.6% for advection, 36.0% for Burgers, and 36.2% for a mixed-boundary channel Poisson problem. Quantum and classical evaluation paths agree to within 10^-8 throughout. The channel Poisson problem simultaneously uses Fourier features in the periodic direction and Chebyshev features in the bounded direction, demonstrating coordinate-wise boundary-matched spectral embedding without additional quantum-resource cost.

Abstract

PDE Operator Learning

Explore similar work

Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations

Disentangling Attention in Deep Operator Learning: A Controlled Study of Data-Driven and Physics-Informed Architectures

Quantum Neural Physics: Solving Partial Differential Equations on Quantum Simulators using Quantum Convolutional Neural Networks