# Practical application improvement to Quantum SVM: theory to practice

arXiv: https://arxiv.org/abs/2012.07725 · HTML: https://mlsanity.com/paper/2012.07725/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Dec 2020.

## Built on by (most cited first, 11 of 11)

- [Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines](https://mlsanity.com/paper/2207.05865/) (2022)
- [Structural risk minimization for quantum linear classifiers](https://mlsanity.com/paper/2105.05566/) (2021)
- [Enhancing Quantum Support Vector Machines through Variational Kernel Training](https://mlsanity.com/paper/2305.06063/) (2023)
- [Neural auto-designer for enhanced quantum kernels](https://mlsanity.com/paper/2401.11098/) (2024)
- [Compositional optimization of quantum circuits for quantum kernels of support vector machines](https://mlsanity.com/paper/2203.13848/) (2022)
- [Several fitness functions and entanglement gates in quantum kernel generation](https://mlsanity.com/paper/2309.03307/) (2023)
- [Hybrid Quantum-Classical Machine Learning for Sentiment Analysis](https://mlsanity.com/paper/2310.10672/) (2023)
- [A novel feature selection method based on quantum support vector machine](https://mlsanity.com/paper/2311.17646/) (2023)
- [Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data](https://mlsanity.com/paper/2409.14089/) (2024)
- [Quantum feature encoding optimization](https://mlsanity.com/paper/2512.02422/) (2025)
- [Beyond the Gegenbauer Paradigm: q-Orthogonal Kernels for Machine Learning](https://mlsanity.com/paper/2608.03482/) (2026)

## Abstract (arXiv)

Quantum machine learning (QML) has emerged as an important area for Quantum applications, although useful QML applications would require many qubits. Therefore our paper is aimed at exploring the successful application of the Quantum Support Vector Machine (QSVM) algorithm while balancing several practical and technical considerations under the Noisy Intermediate-Scale Quantum (NISQ) assumption. For the quantum SVM under NISQ, we use quantum feature maps to translate data into quantum states and build the SVM kernel out of these quantum states, and further compare with classical SVM with radial basis function (RBF) kernels. As data sets are more complex or abstracted in some sense, classical SVM with classical kernels leads to less accuracy compared to QSVM, as classical SVM with typical classical kernels cannot easily separate different class data. Similarly, QSVM should be able to provide competitive performance over a broader range of data sets including ``simpler'' data cases in which smoother decision boundaries are required to avoid any model variance issues (i.e., overfitting). To bridge the gap between ``classical-looking'' decision boundaries and complex quantum decision boundaries, we propose to utilize general shallow unitary transformations to create feature maps with rotation factors to define a tunable quantum kernel, and added regularization to smooth the separating hyperplane model. We show in experiments that this allows QSVM to perform equally to SVM regardless of the complexity of the data sets and outperform in some commonly used reference data sets.