# Quantum-Inspired Support Vector Machine

arXiv: https://arxiv.org/abs/1906.08902 · HTML: https://mlsanity.com/paper/1906.08902/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 10 of 10)

- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Scalable Quantum Neural Networks for Classification](https://mlsanity.com/paper/2208.07719/) (2022)
- [Quantum Normalizing Flows for Anomaly Detection](https://mlsanity.com/paper/2402.02866/) (2024)
- [Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning](https://mlsanity.com/paper/2106.09028/) (2021)
- [Review of Ansatz Designing Techniques for Variational Quantum Algorithms](https://mlsanity.com/paper/2212.04913/) (2022)
- [Robust Dequantization of the Quantum Singular value Transformation and Quantum Machine Learning Algorithms](https://mlsanity.com/paper/2304.04932/) (2023)
- [Quantum Imitation Learning](https://mlsanity.com/paper/2304.02480/) (2023)
- [A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity](https://mlsanity.com/paper/2402.15333/) (2024)
- [Quantum Semi-Supervised Kernel Learning](https://mlsanity.com/paper/2204.10700/) (2022)
- [Quantum QSAR for drug discovery](https://mlsanity.com/paper/2505.04648/) (2025)

## Abstract (arXiv)

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM algorithm was proposed, which is claimed to achieve exponential speedup for least squares SVM (LS-SVM). Here, inspired by the quantum SVM algorithm, we present a quantum-inspired classical algorithm for LS-SVM. In our approach, a improved fast sampling technique, namely indirect sampling, is proposed for sampling the kernel matrix and classifying. We first consider the LS-SVM with a linear kernel, and then discuss the generalization of our method to non-linear kernels. Theoretical analysis shows our algorithm can make classification with arbitrary success probability in logarithmic runtime of both the dimension of data space and the number of data points for low rank, low condition number and high dimensional data matrix, matching the runtime of the quantum SVM.