标题： 基于分割的量子神经网络回归方法 显示英文标题

标题： Segmentation-Based Regression for Quantum Neural Networks

摘要： 最近量子硬件的进展促使了将量子采样与经典推理相结合的算法框架的发展。 本工作引入了一种基于分割的回归方法，专门用于量子神经网络（QNNs），其中实数值输出被编码为基数b的数字序列，并通过贪心逐位优化进行推断。 通过将回归任务转化为结构化数字格上的约束组合问题，该方法用可解释且易于处理的更新代替了连续推理。 采用了一种混合量子-经典架构：量子电路通过投影测量生成候选数字，而经典前向模型则根据特定任务的误差泛函评估这些候选数字。 我们从基本原理出发形式化了该算法，推导了收敛性和复杂度边界，并在涉及PDE约束模型的反问题中展示了其有效性。 该框架提供了一种稳健、高精度的接口，用于量子输出与连续科学推理之间的交互。 显示英文摘要

摘要： Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference. This work introduces a segmentation-based regression method tailored to quantum neural networks (QNNs), where real-valued outputs are encoded as base-b digit sequences and inferred through greedy digitwise optimization. By casting the regression task as a constrained combinatorial problem over a structured digit lattice, the method replaces continuous inference with interpretable and tractable updates. A hybrid quantum-classical architecture is employed: quantum circuits generate candidate digits through projective measurement, while classical forward models evaluate these candidates based on task-specific error functionals. We formalize the algorithm from first principles, derive convergence and complexity bounds, and demonstrate its effectiveness on inverse problems involving PDE-constrained models. The resulting framework provides a robust, high-precision interface between quantum outputs and continuous scientific inference.