Conformalized Quantum DeepONet Ensembles for Scalable Operator Learning with Distribution-Free Uncertainty
For researchers in quantum machine learning and scientific computing, this work provides a scalable and uncertainty-aware operator learning framework, though it is incremental as it combines existing techniques (quantum neural networks, conformal prediction) in a novel hybrid.
The paper tackles the dual challenges of quadratic inference complexity and unreliable uncertainty quantification in operator learning for high-dimensional dynamical systems. By introducing Conformalized Quantum DeepONet Ensembles, they achieve O(n) inference complexity and distribution-free coverage guarantees, with experiments showing accurate predictions and calibrated uncertainty under quantum noise.
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.