Conformalized Quantum DeepONet Ensembles for Scalable Operator Learning with Distribution-Free Uncertainty
conformalized 量子 deeponet 集团用于具有分布自由不确定性的可扩展操作学习
Purav Matlia, Christian Moya, Guang Lin
AI总结 本文提出一种结合量子正交神经网络和适应性置信预测的框架,解决高维动态系统运算学习中的二次推断复杂度和不确定性量化问题,通过压缩多个模型到单个电路实现高效并行计算。
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操作学习能够快速构建高维动态系统的替代模型,但现有方法面临两个根本性限制:二次推断复杂性和安全关键设置中不可靠的不确定性量化。我们提出了 conformalized 量子 deeponet 集团,一个同时解决这两个挑战的框架。通过利用量子正交神经网络(qorthonn),我们将操作推断复杂性从 O(n²) 降低到 O(n),使在细粒度离散化上可扩展的评估成为可能。为了提供严谨的不确定性量化,我们结合基于集合的epistemic建模与自适应 conformal 预测,从而获得分布自由的覆盖保证。在集合中的一个关键挑战是,朴素的并行性使硬件资源与模型数量线性增长。我们通过使用叠加参数化量子电路(spqcs)来解决这个问题,将多个集合成员压缩到一个电路中,并启用同时多模型执行。在合成偏微分方程和现实世界电力系统动态上的实验表明,我们的方法在保持现实量子噪声下的校准不确定性的同时实现了准确的预测。这些结果为量子机器学习中的可扩展、具有不确定性的操作学习建立了实用路径。
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.