Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and doesn't require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20\% larger) that improve further with circuit parameter training.

翻译：核方法是机器学习中一类重要的技术。为使其有效，良好的特征映射至关重要，它能将非线性可分输入数据映射到更高维（特征）空间，从而在特征空间中实现数据线性可分。已有研究表明，针对给定数据集，使用遗传算法NSGA-II可自动设计量子特征映射，同时最小化电路规模并最大化分类准确率。然而，候选特征映射准确率的评估成本较高。本研究证明，在基于遗传算法的量子特征映射设计中，核-目标对齐可作为准确率的替代指标。核-目标对齐的评估速度优于准确率，且无需保留部分数据点用于评估。为进一步加速遗传适应度评估，我们提出一种核-目标对齐的近似计算方法。为提升核-目标对齐与均方根误差，对生成电路的最终可训练参数进一步采用COBYLA方法训练，以探究结合常规电路参数训练的混合方法能否轻松补充遗传结构优化方法。我们共提出了八种新方法，并与原始方法在UCI机器学习库的九个不同二分类问题上进行对比，结果表明：核-目标对齐及其近似方法生成的量子特征映射电路可实现与先前工作相当的分类准确率，但在训练数据上的分类间隔更大（超出20%），且通过电路参数训练可获得进一步改善。