Enhancing Quantum Support Vector Machines through Variational Kernel Training

TL;DR

This work tackles improving QSVM performance by integrating kernel-based quantum methods with variational training. It introduces QVK-SVM, a quantum variational kernel SVM that uses the kernel overlap $k(x_1,x_2)=|<phi(x_1)|phi(x_2)>|^2$ combined with a trainable variational circuit guided by hinge loss. Empirical evaluation on the Iris dataset shows QVK-SVM achieving up to 98.48% test accuracy, outperforming both QK-SVM and QV-SVM and demonstrating favorable loss and metric convergence. The results suggest a practical, hardware-friendly path for quantum machine learning with potential applicability to broader datasets and model families.

Abstract

Quantum machine learning (QML) has witnessed immense progress recently, with quantum support vector machines (QSVMs) emerging as a promising model. This paper focuses on the two existing QSVM methods: quantum kernel SVM (QK-SVM) and quantum variational SVM (QV-SVM). While both have yielded impressive results, we present a novel approach that synergizes the strengths of QK-SVM and QV-SVM to enhance accuracy. Our proposed model, quantum variational kernel SVM (QVK-SVM), leverages the quantum kernel and quantum variational algorithm. We conducted extensive experiments on the Iris dataset and observed that QVK-SVM outperforms both existing models in terms of accuracy, loss, and confusion matrix indicators. Our results demonstrate that QVK-SVM holds tremendous potential as a reliable and transformative tool for QML applications. Hence, we recommend its adoption in future QML research endeavors.

Figures (13)

• Figure 1: Graphical representation of linear and non-linear SVMs problems.
• Figure 2: Geometric components of support vector machines.
• Figure 3: Quantum circuit architecture for QSVMS: Generalized model description.
• Figure 4: QK-SVM circuit.
• Figure 5: QK-SVM circuit using Pennlyne.