Conformalized Quantum DeepONet Ensembles: Towards Scalable Operator Learning with Distribution-Free Guarantees
cs.LG
Submitted: 2026-05-01
Updated: 2026-09-07
Code: https://github.com/purav-0000/conformalized-quantum-deeponet
License: http://creativecommons.org/licenses/by/4.0/
The gist: Operator learning enables fast surrogate modelling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: the quadratic cost of dense neural layers and
Terminology
Abstract
Operator learning enables fast surrogate modelling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: the quadratic cost of dense neural layers and unreliable uncertainty quantification in safety-critical settings. We propose Conformalized Quantum DeepONet Ensembles, a framework that addresses both challenges simultaneously. Using Quantum Orthogonal Neural Networks (QOrthoNNs), we characterize the resource regime in which their established (n) hidden-layer running-time scaling improves on the O(n 2) cost of a classical dense layer. To quantify uncertainty, we combine ensemble predictions with split conformal calibration. For a new input-output function pair jointly exchangeable with the calibration pairs, we prove a finite-sample, distribution-free lower bound on the expected fraction of covered query locations. As a secondary proof-of-concept, we explore hybrid classical-quantum architectures and superposed execution to manage ensemble runtime and hardware requirements. Experiments on synthetic operator benchmarks and real-world power-system dynamics show accurate predictions under ideal simulation and empirical coverage near the target under both ideal conditions and selected compact-circuit simulations with depolarizing or device-calibrated composite noise. Together, these results connect resource-aware scalability analysis with finite-sample uncertainty guarantees for quantum operator learning.
Sources
- Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics
- Orthogonal Deep Neural Networks
- Quantum variational PDE solver with machine learning
- Classical and Quantum Algorithms for Orthogonal Neural Networks
- Why M Heads are Better than One: Training a Diverse Ensemble of Deep Networks
- Superposed parameterised quantum circuits
- Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
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