[论文] Task-aligned spectral inductive biases in parameterized quantum circui...

论文概要

研究领域: ML 作者: Felix Frohnert, Adrián Pérez-Salinas, Sebastian Lange, Marcus Schwaebisch, Evert van Nieuwenburg, Vedran Dunjko 发布时间: 2026-10-16 arXiv: 2610.23834

中文摘要

参数化量子电路在量子机器学习中受到广泛研究，但其架构如何提供与任务对齐的归纳偏差仍不甚明了。我们研究具有两个不同输入的数据重上传量子电路：一个在样本间变化的信号，和一个固定的、由任务定义的光谱查询，用于指定如何探测信号。我们表明，对查询进行编码可以通过调制电路现有信号频率的组合方式来改变电路在信号上的假设类，而不引入新的样本依赖信息。这一机制与基于非均匀傅里叶变换的任务相匹配：其求值频率定义查询，采样位置指导其编码。我们在一个受合成孔径雷达启发的分类任务中考察了这种联系，其中采集几何决定了在成像前对未聚焦光谱片段进行分类的查询。在小规模光谱和类雷达任务中，对齐的查询相比参数匹配但查询不匹配或缺失的电路，在有限数据下的学习效果更好。这些结果为从已知的光谱任务结构到参数化量子电路中归纳偏差的设计和验证提供了一条路径。

原文摘要

Parameterized quantum circuits are widely investigated in quantum machine learning, yet how their architecture can provide task-aligned inductive biases remains poorly understood. We study data reuploading quantum circuits with two distinct inputs: a signal that varies between samples and a fixed, task-defined spectral query that specifies how the signal should be probed. We show that encoding the query can change the circuit's hypothesis class over the signal by modulating how its existing signal frequencies are combined, without introducing new sample-dependent information. This mechanism matches tasks built on nonuniform Fourier transforms, whose evaluation frequencies specify the query and whose sampling positions guide its encoding. We examine this connection in a classification task ...

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