mlsanityData to 14 Oct 2026

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

arXiv 2608.27626 ↗First posted 27 Aug 2026quant-ph cs.LGcited by 0

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Abstract (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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 39 of its 82 references that are in the map. First posted on arXiv 27 Aug 2026.

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References · 39

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
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  3. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
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  11. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  12. 2019Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networkscited by 368
27 more
  1. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  2. 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 333
  3. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
  4. 2015Unitary Evolution Recurrent Neural Networkscited by 294
  5. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 284
  6. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 214
  7. 2022MIONet: Learning multiple-input operators via tensor productcited by 181
  8. 2024Barren Plateaus in Variational Quantum Computingcited by 133
  9. 2022Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transportcited by 92
  10. 2021Improved architectures and training algorithms for deep operator networkscited by 86
  11. 2019Digital Twin: Values, Challenges and Enablerscited by 81
  12. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  13. 2022Quantum Vision Transformerscited by 48
  14. 2023LNO: Laplace Neural Operator for Solving Differential Equationscited by 47
  15. 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
  16. 2023Let Quantum Neural Networks Choose Their Own Frequenciescited by 22
  17. 2023PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systemscited by 19
  18. 2023On fundamental aspects of quantum extreme learning machinescited by 18
  19. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  20. 2023Hybrid Genetic Optimisation for Quantum Feature Map Designcited by 8
  21. 2025FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learningcited by 8
  22. 2021A Quantum Generative Adversarial Network for distributionscited by 7
  23. 2025Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximationcited by 6
  24. 2024Unleashing the Expressive Power of Pulse-Based Quantum Neural Networkscited by 4
  25. 2026SIMR-NO: A Spectrally-Informed Multi-Resolution Neural Operator for Turbulent Flow Super-Resolutioncited by 4
  26. 2025Method of Manufactured Learning for Solver-free Training of Neural Operatorscited by 3
  27. 2026WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equationscited by 2

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