We present a novel approach for efficiently generating quantum feature maps
for quantum-enhanced support vector machines, a kernel-based classifier,
enabling access to high-dimensional Hilbert space. Our method employs a
multi-objective genetic algorithm that simultaneously maximizes classification
accuracy while minimizing both the local and non-local gate costs of the
quantum feature map's circuit. To achieve this, we define distinct fitness
functions for local gates and entanglement gates. Comparisons with classical
classifiers are given in order to understand the advantages of using quantum
machine learning. Surprisingly, our experiments reveal that the optimal
configuration of quantum circuits for the quantum kernel method incorporates a
proportional number of non-local gates for entanglement, contrary to previous
literature where non-local gates were largely suppressed.
Furthermore, we demonstrate that the separability indexes of data can be
effectively leveraged to determine the number of non-local gates required for
the quantum support vector machine's feature maps. This insight can
significantly aid in selecting appropriate parameters, such as the entanglement
parameter, in various quantum programming packages like quiskit.org based on
data analysis. Our findings offer valuable guidance for enhancing the
efficiency and accuracy of quantum machine learning algorithms.

我们使用一种多目标遗传算法来高效生成支持向量机的量子特征映射，该方法能使得访问高维希尔伯特空间成为可能，并通过最小化量子特征映射电路的本地和非本地门成本来同时最大化分类准确度，对比了经典分类器以了解量子机器学习的优势，并显示出量子核方法的优化配置中需要包含比例数量的非本地门用于纠缠，以及证明数据的可分离性指标可以有效地用于确定量子支持向量机特征映射所需的非本地门数量，从而在基于数据分析的各种量子编程包（如 quiskit.org）中选择适当的参数（例如纠缠参数），我们的发现为增强量子机器学习算法的效率和准确性提供了有价值的指导。

使用多目标遗传算法生成量子特征映射

Generating quantum feature maps using multi-objective genetic algorithm

We propose a new hybrid system for automatically generating and training
quantum-inspired classifiers on grayscale images by using multiobjective
genetic algorithms. We define a dynamic fitness function to obtain the smallest
possible circuit and highest accuracy on unseen data, ensuring that the
proposed technique is generalizable and robust. We minimize the complexity of
the generated circuits in terms of the number of entanglement gates by
penalizing their appearance. We reduce the size of the images with two
dimensionality reduction approaches: principal component analysis (PCA), which
is encoded in the individual for optimization purpose, and a small
convolutional autoencoder (CAE). These two methods are compared with one
another and with a classical nonlinear approach to understand their behaviors
and to ensure that the classification ability is due to the quantum circuit and
not the preprocessing technique used for dimensionality reduction.

本研究提出了一个新的混合系统，通过使用多目标遗传算法，自动生成和训练基于量子启发式分类器来处理灰度图像。通过定义动态适应性函数来确保所提出的技术具有通用性和鲁棒性，我们能够在视觉数据集上获得最小电路和最高精度，同时在量子电路和图像降维方法之间进行比较。