arXiv:2607.22516quant-phcs.AI2026-07

量子模型通过输入依赖的谱特征提升分类性能,实现更精准的结构感知。

Quantum Spectral Model: Data Reuploading with Input-Conditioned Frequency Support

论文配图:Quantum Spectral Model: Data Reuploading with Input-Conditioned Frequency Support
图 1 · 摘自论文原文
  • 基于输入矩阵的谱特性构造数据编码哈密顿量,显式建模矩阵级关系。
  • 在四个基准测试中,最大深度下平均准确率领先现有量子模型,最高达98.3%。
  • 适用于需结构感知的机器学习任务,尤其适合矩阵数据与谱分析场景。

现代机器学习的核心设计原则是使模型的归纳偏置与输入数据结构对齐。对于矩阵输入,相关矩阵级关系可通过谱值和谱子空间表征;然而,多数量子机器学习模型采用坐标旋转门进行数据编码,未能显式构建此类矩阵级表示。本文提出量子谱模型(QSM),直接从每个输入矩阵构造数据编码酉算子的生成元。研究了三种基于对称、全局块及非重叠局部块哈密顿量的QSM变体。其输出在截断傅里叶表示中,输入依赖的谱间隙提供相位载体,谱子空间决定系数。在两种手写数字Pendigits的矩阵表示及两类由谱统计定义的可控合成任务上评估了QSM与对比模型。在最大电路深度下,所有四个基准测试中QSM变体的平均测试准确率均领先于其他量子模型。局部块型QSM在Pendigits上表现最优,全局块型在合成谱任务上领先。消融实验显示任务依赖性:保留子空间控制在Pendigits上更优,仅保留谱值控制在合成任务上更佳。结果表明,输入条件化的谱表示可提供可分析的归纳偏置,为量子机器学习模型设计提供了新视角,并拓展了结构感知模型设计的通用思路。

原文摘要 · Abstract (English)

A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data. For matrix-valued inputs, relevant matrix-level relationships can be characterised through spectral values and spectral subspaces; however, common coordinate-wise rotation-gate data-encoding unitaries used in most quantum machine learning models do not explicitly construct such a matrix-level representation. We introduce Quantum Spectral Models (QSMs), in which we construct the generator of the data-encoding unitary directly from each input matrix. We study three QSM variants based on symmetric, global block, and non-overlapping patch-local block Hamiltonians. Their outputs admit truncated Fourier representations in which input-dependent spectral gaps supply candidate phase carriers, while spectral subspaces help determine their coefficients. We evaluate the QSMs and comparison quantum models on two matrix representations of Pendigits and two controlled synthetic tasks defined by spectral statistics. At the largest evaluated circuit depth, QSM variants lead the tested quantum models in mean test accuracy across all four benchmarks. The patch-local QSM leads on Pendigits, whereas the global block-Hamiltonian QSM leads on the controlled spectral tasks. Ablations show a task-dependent reversal: subspace-preserving controls perform better on Pendigits, whereas spectral-value-only controls lead among the tested ablations on the synthetic tasks. Together, these results shed new light on quantum machine-learning model design by showing how input-conditioned spectral representations can provide an analysable inductive bias, while offering a broader perspective on structure-aware model design in machine learning and artificial intelligence.

量子机器学习谱分析结构感知矩阵数据

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