多类量子分类中可观测集的实证研究
Empirical Study of Observable Sets in Multiclass Quantum Classification
AI总结：
本文通过实证研究探讨多类量子分类中两种分类标准的性能差异，分析不同可观测集对模型效果的影响。
摘要：
变分量子算法作为量子计算机早期应用于学习任务的尝试已引起关注。在监督学习的背景下，大多数处理分类问题的参数化量子电路工作都局限于二分类场景或通过二分类器的集成（如一对一策略）进行多类分类。然而，提出原生多类模型的工作却未说明所选可观测量进行分类的原因。本文研究了多类量子机器学习中的两种主要分类标准：最大化一个代表类的可观测量的预期值或最大化编码量子态与代表类的参考态之间的保真度。为了比较这两种方法，选择Pauli字符串集和计算基态的投影集作为量子机器学习模型中的可观测量。观察每种模型类型的实证行为，在巴伦平顶（Barren Plateaus）和神经塌缩（Neural Collapse）的背景下分析不同可观测集选择对量子机器学习模型性能的影响。结果提供了可能指导未来多类量子机器学习模型设计的见解。
英文摘要：
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.
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