arXiv:2503.16363cs.LGquant-ph2025-03被引 1

用量子伊辛机实现概率化支持向量机,提升分类准确率与训练速度。

Probabilistic Quantum SVM Training on Ising Machine

  • 将SVM训练转为带玻尔兹曼分布的概率化求解,更好捕捉数据边界。
  • 在银行券数据集上比传统QSVM高20%准确率,训练快10⁴倍于模拟退火。
  • 小量子设备通过分批和集成策略完成多分类,适合资源受限场景。

量子计算有望加速机器学习算法,尤其在解决支持向量机(SVM)训练中的优化问题方面。然而,现有基于QUBO的量子支持向量机(QSVM)方法仅依赖二值最优解,难以识别数据中的模糊边界。同时,当前量子设备的比特数有限,制约了在大规模数据上的训练。本文提出一种适用于相干伊辛机(CIM)的概率化量子SVM训练框架。通过将SVM训练问题建模为QUBO,利用CIM的能量最小化能力,并引入基于玻尔兹曼分布的概率性方法,更精准逼近最优解,提升鲁棒性。为克服比特数限制,采用分批处理与多批次集成策略,使小型量子设备可在更大数据集上训练SVM,并通过一对一分类实现多类任务。实验验证包括仿真与真实机器测试,在银行券二分类数据集上,基于能量的概率方法相比原版QSVM最高提升20%准确率,训练速度比模拟退火快达10⁴倍;与经典SVM相比,训练时间相当或更优。在鸢尾花三分类数据集上,改进后的QSVM在所有关键指标上均优于现有模型。随着量子技术发展,更多比特数有望进一步提升量子SVM性能。

原文摘要 · Abstract (English)

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.

量子机器学习支持向量机伊辛机概率推理

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