Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and therefore aligned with a specific dataset. While quantum kernel alignment is a promising technique, it has been hampered by considerable training costs because the full kernel matrix must be constructed at every training iteration. Addressing this challenge, we introduce a novel method that seeks to balance efficiency and performance. We present a sub-sampling training approach that uses a subset of the kernel matrix at each training step, thereby reducing the overall computational cost of the training. In this work, we apply the sub-sampling method to synthetic datasets and a real-world breast cancer dataset and demonstrate considerable reductions in the number of circuits required to train the quantum kernel while maintaining classification accuracy.

中文翻译：

---

量子核对齐的高效参数优化：变分训练中的子采样方法


使用量子内核进行分类问题的量子机器学习是一个不断增长的研究领域。最近，已经开发了参数化内核的量子核对齐技术，允许对内核进行训练，从而与特定数据集对齐。虽然量子核对齐是一项很有前途的技术，但它一直受到相当大的训练成本的阻碍，因为必须在每次训练迭代中构建完整的核矩阵。为了应对这一挑战，我们引入了一种寻求平衡效率和性能的新方法。我们提出了一种子采样训练方法，该方法在每个训练步骤中使用核矩阵的子集，从而降低了训练的总体计算成本。在这项工作中，我们将子采样方法应用于合成数据集和真实世界的乳腺癌数据集，并证明在保持分类准确性的同时，训练量子核所需的电路数量大大减少。