arXiv:2602.08485quant-phcs.LG2026-02

对比量子分类中两种可观测量选择,揭示其对模型性能的影响。

Empirical Study of Observable Sets in Multiclass Quantum Classification

  • 用泡利字符串和计算基投影作为可观测量,比较多类分类效果。
  • 发现可观测量选择显著影响模型是否陷入梯度消失(空谷现象)。
  • 为未来量子机器学习模型设计提供实证指导,适合量子算法研究者。

变分量子算法作为量子计算机早期学习任务的应用备受关注。在监督学习中,多数工作聚焦于二分类或通过二分类器集成(如一对多策略)实现多类分类。少数提出原生多类模型的研究未充分说明可观测量的选择依据。本文研究多类量子机器学习中的两种主要分类准则:最大化表示类别的可观测量期望值,或最大化编码量子态与参考态的保真度。选取保罗字符串集合和计算基投影作为可观测量,在不同设置下评估模型表现,分析其在空谷现象(Barren Plateaus)和神经坍缩(Neural Collapse)背景下的行为。结果揭示了可观测量选择对模型性能的关键影响,为未来多类量子机器学习模型的设计提供实证依据。

原文摘要 · Abstract (English)

Variational quantum algorithms have gained attention as early applications of quantum computers for learning tasks. In the context of supervised learning, most of the works that tackle classification problems with parameterized quantum circuits constrain their scope to the setting of binary classification or perform multiclass classification via ensembles of binary classifiers (strategies such as one versus rest). Those few works that propose native multiclass models, however, do not justify the choice of observables that perform the classification. This work studies two main classification criteria in multiclass quantum machine learning: maximizing the expected value of an observable representing a class or maximizing the fidelity of the encoded quantum state with a reference state representing a class. To compare both approaches, sets of Pauli strings and sets of projectors into the computational basis are chosen as observables in the quantum machine learning models. Observing the empirical behavior of each model type, the effect of different observable set choices on the performance of quantum machine learning models is analyzed in the context of Barren Plateaus and Neural Collapse. The results provide insights that may guide the design of future multiclass quantum machine learning models.

量子机器学习多类分类可观测量

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