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

TL;DR

This paper introduces a scalable quantum ensemble framework for operator learning that reduces inference complexity and provides reliable, distribution-free uncertainty quantification using conformal prediction and quantum circuit compression.

Contribution

It combines Quantum DeepONet ensembles with conformal prediction and SPQCs to enable scalable, uncertainty-aware operator learning with theoretical guarantees.

Findings

Reduces inference complexity from O(n^2) to O(n) using QOrthoNNs.

Provides distribution-free uncertainty guarantees with adaptive conformal prediction.

Demonstrates accurate, calibrated predictions on PDEs and power system data under quantum noise.

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.