Conformalized Quantum DeepONet Ensembles for Scalable Operator Learning with Distribution-Free Uncertainty

2026-04-30

AI Summary

Existing operator learning methods struggle to meet the demands of trustworthy modeling for high-dimensional dynamical systems in safety-critical scenarios due to their O(n²) inference complexity and unreliable uncertainty quantification. This work proposes a novel framework that integrates quantum orthogonal neural networks (QOrthoNNs) with adaptive conformal prediction, introducing for the first time superpositional parameterized quantum circuits (SPQCs) to enable concurrent ensemble modeling under constant hardware resources. The approach reduces inference complexity to O(n) while preserving distribution-free coverage guarantees. Empirical evaluations on synthetic partial differential equations and real-world power grid dynamics demonstrate that the method achieves high predictive accuracy and well-calibrated uncertainty intervals, even under realistic quantum noise conditions.

Abstract

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical settings. We propose Conformalized Quantum DeepONet Ensembles, a framework that addresses both challenges simultaneously. By leveraging Quantum Orthogonal Neural Networks (QOrthoNNs), we reduce operator inference complexity from O(n^2) to O(n), enabling scalable evaluation over fine discretizations. To provide rigorous uncertainty quantification, we combine ensemble-based epistemic modeling with adaptive conformal prediction, yielding distribution-free coverage guarantees. A key challenge in ensembling is that naive parallelism scales hardware resources linearly with the number of models. We resolve this by using Superposed Parameterized Quantum Circuits (SPQCs), which compress multiple ensemble members into a single circuit and enable simultaneous multi-model execution. Experiments on synthetic partial differential equations and real-world power system dynamics demonstrate that our approach achieves accurate predictions while maintaining calibrated uncertainty under realistic quantum noise. These results establish a practical pathway toward scalable, uncertainty-aware operator learning in quantum machine learning.

Problem

• operator learning
• inference complexity
• uncertainty quantification
• quantum machine learning
• scalability

Innovation

• Quantum DeepONet
• Conformal Prediction
• Operator Learning
• SPQC
• Scalable Inference