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.

翻译：算子学习能够实现高维动力系统的快速替代建模，但现有方法面临两个基本限制：二次推理复杂度和安全关键场景下不可靠的不确定性量化。我们提出基于共形化的量子深度算子网络集成框架，同时解决这两个挑战。通过利用量子正交神经网络，我们将算子推理复杂度从O(n²)降至O(n)，从而实现在精细离散化上的可扩展评估。为提供严格的不确定性量化，我们将基于集成的认知建模与自适应共形预测相结合，产生无分布覆盖保证。集成的关键挑战在于朴素并行化会使硬件资源随模型数量线性增长。我们通过使用叠加参数化量子电路解决这一问题，该电路将多个集成成员压缩至单个电路，实现同步多模型执行。在合成偏微分方程和真实电力系统动力学上的实验表明，本文方法能在现实量子噪声下保持校准不确定性的同时实现准确预测。这些结果为量子机器学习中可扩展、感知不确定性的算子学习奠定了基础。