AI 中文总结
研究可训练量子特征映射的损失函数，通过对数似然损失函数与距离损失、测量损失对比，经大量数值实验，比较优化动态、计算成本和分类性能，为量子核优化平衡多方面性能提供实用指导。
AI 中文摘要
许多量子机器学习模型使用量子特征映射将经典数据编码到量子态中。虽然固定特征映射对于复杂非线性分类任务往往缺乏足够的表现力，但可训练量子特征映射（TQFMs）能实现具有增强学习能力的自适应量子核。不同损失函数会引发不同的优化动态，但人们对其效果了解甚少。本文将对数似然损失函数应用于TQFMs，并与距离损失和测量损失进行系统比较。通过大量数值实验，比较了它们的优化动态、计算成本和分类性能。结果表明，对数似然损失在保持线性计算复杂度的同时，始终比测量损失实现更稳定的优化。所得基准为量子核优化中平衡可训练性、计算效率和预测性能提供了实用指导。
英文摘要
Many quantum machine learning models employ quantum feature maps to encode classical data into quantum states. While fixed feature maps often lack sufficient expressivity for complex nonlinear classification tasks, trainable quantum feature maps (TQFMs) enable adaptive quantum kernels with enhanced learning capability. Different loss functions can induce distinct optimization dynamics, yet their effects remain poorly understood. In this work, we apply the Log-Likelihood Loss function for TQFMs and provide a systematic comparison with Distance Loss and Measurement Loss. Through extensive numerical experiments, we compare their optimization dynamics, computational costs, and classification performance. Our results show that Log-Likelihood Loss consistently achieves more stable optimization than Measurement Loss while retaining linear computational complexity. The resulting benchmark offers practical guidance for balancing trainability, computational efficiency, and predictive performance in quantum kernel optimization.
Comments10 pages, 9 figures
