用量子深度网络集成实现快速且可靠不确定度估计的算子学习
Conformalized Quantum DeepONet Ensembles for Scalable Operator Learning with Distribution-Free Uncertainty
- 通过量子正交神经网络将算子推理复杂度从O(n²)降至O(n)
- 在真实量子噪声下仍保持校准的不确定性估计，覆盖率达95%以上
- 适合需要高可靠性预测的物理系统建模与量子机器学习场景
算子学习可快速构建高维动态系统的代理模型，但现有方法存在两个根本局限：推理复杂度为二次方，且在安全关键场景中不确定性量化不可靠。本文提出共形化量子DeepONet集成框架，同时解决上述问题。利用量子正交神经网络（QOrthoNNs），将算子推理复杂度从O(n²)降至O(n)，实现对精细离散化的可扩展评估。通过集成式认知建模与自适应共形预测结合，获得无需分布假设的覆盖保证。集成中的并行化会线性消耗硬件资源，为此采用叠加参数化量子电路（SPQCs），将多个集成成员压缩至单一电路，支持多模型并行执行。在合成偏微分方程与真实电力系统动力学实验中，该方法在真实量子噪声下仍实现精准预测与校准不确定性，验证了其在量子机器学习中可扩展、带不确定度感知算子学习的实际可行性。
原文摘要 · Abstract (English)
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.
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