Quantum computing holds significant potential to accelerate machine learning algorithms, especially in solving optimization problems like those encountered in Support Vector Machine (SVM) training. However, current QUBO-based Quantum SVM (QSVM) methods rely solely on binary optimal solutions, limiting their ability to identify fuzzy boundaries in data. Additionally, the limited qubit count in contemporary quantum devices constrains training on larger datasets. In this paper, we propose a probabilistic quantum SVM training framework suitable for Coherent Ising Machines (CIMs). By formulating the SVM training problem as a QUBO model, we leverage CIMs' energy minimization capabilities and introduce a Boltzmann distribution-based probabilistic approach to better approximate optimal SVM solutions, enhancing robustness. To address qubit limitations, we employ batch processing and multi-batch ensemble strategies, enabling small-scale quantum devices to train SVMs on larger datasets and support multi-class classification tasks via a one-vs-one approach. Our method is validated through simulations and real-machine experiments on binary and multi-class datasets. On the banknote binary classification dataset, our CIM-based QSVM, utilizing an energy-based probabilistic approach, achieved up to 20% higher accuracy compared to the original QSVM, while training up to $10^4$ times faster than simulated annealing methods. Compared with classical SVM, our approach either matched or reduced training time. On the IRIS three-class dataset, our improved QSVM outperformed existing QSVM models in all key metrics. As quantum technology advances, increased qubit counts are expected to further enhance QSVM performance relative to classical SVM.

翻译：量子计算在加速机器学习算法方面具有巨大潜力，尤其在解决支持向量机（SVM）训练等优化问题上。然而，当前基于二次无约束二进制优化（QUBO）的量子支持向量机（QSVM）方法仅依赖于二元最优解，限制了其识别数据模糊边界的能力。此外，当代量子设备有限的量子比特数制约了在更大数据集上的训练。本文提出了一种适用于相干伊辛机（CIM）的概率量子支持向量机训练框架。通过将SVM训练问题构建为QUBO模型，我们利用CIM的能量最小化能力，并引入一种基于玻尔兹曼分布的概率方法，以更好地逼近最优SVM解，从而增强鲁棒性。为应对量子比特限制，我们采用批处理与多批次集成策略，使小规模量子设备能够在更大数据集上训练SVM，并通过一对一方法支持多类分类任务。我们的方法在二分类与多类数据集上通过仿真和真实机器实验得到验证。在钞票二分类数据集上，我们基于CIM的QSVM采用基于能量的概率方法，相比原始QSVM实现了高达20%的准确率提升，同时训练速度比模拟退火方法快达$10^4$倍。与经典SVM相比，我们的方法在训练时间上持平或更短。在IRIS三分类数据集上，我们改进的QSVM在所有关键指标上均优于现有QSVM模型。随着量子技术的进步，量子比特数量的增加有望进一步提升QSVM相对于经典SVM的性能。