Quantum Support Vector Machines (QSVM) play a vital role in using quantum
resources for supervised machine learning tasks, such as classification.
However, current methods are strongly limited in terms of scalability on Noisy
Intermediate Scale Quantum (NISQ) devices. In this work, we propose a novel
approach called the Variational Quantum Linear Solver (VQLS) enhanced QSVM.
This is built upon our idea of utilizing the variational quantum linear solver
to solve system of linear equations of a least squares-SVM on a NISQ device.
The implementation of our approach is evaluated by an extensive series of
numerical experiments with the Iris dataset, which consists of three distinct
iris plant species. Based on this, we explore the practicality and
effectiveness of our algorithm by constructing a classifier capable of
classification in a feature space ranging from one to seven dimensions.
Furthermore, by strategically exploiting both classical and quantum computing
for various subroutines of our algorithm, we effectively mitigate practical
challenges associated with the implementation. These include significant
improvement in the trainability of the variational ansatz and notable
reductions in run-time for cost calculations. Based on the numerical
experiments, our approach exhibits the capability of identifying a separating
hyperplane in an 8-dimensional feature space. Moreover, it consistently
demonstrated strong performance across various instances with the same dataset.

利用量子支持向量机和变分量子线性求解器，我们提出了一种用于处理分类问题的新颖方法，并在 Noisy Intermediate Scale Quantum (NISQ) 设备上进行了全面的数值实验，通过构建一个分类器，实现从一个到七个维度的特征空间的分类。