# Quantum support vector machine for big data classification

arXiv: https://arxiv.org/abs/1307.0471 · HTML: https://mlsanity.com/paper/1307.0471/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2013.

## Built on by (most cited first, 30 of 35)

- [Quantum federated learning through blind quantum computing](https://mlsanity.com/paper/2103.08403/) (2021)
- [Machine Learning for Anomaly Detection in Particle Physics](https://mlsanity.com/paper/2312.14190/) (2023)
- [Automatic design of quantum feature maps](https://mlsanity.com/paper/2105.12626/) (2021)
- [Hybrid quantum neural network for drug response prediction](https://mlsanity.com/paper/2211.05777/) (2022)
- [Style-based quantum generative adversarial networks for Monte Carlo events](https://mlsanity.com/paper/2110.06933/) (2021)
- [Hybrid quantum ResNet for car classification and its hyperparameter optimization](https://mlsanity.com/paper/2205.04878/) (2022)
- [Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning](https://mlsanity.com/paper/2203.15368/) (2022)
- [Hybrid quantum image classification and federated learning for hepatic steatosis diagnosis](https://mlsanity.com/paper/2311.02402/) (2023)
- [Variational Quanvolutional Neural Networks with enhanced image encoding](https://mlsanity.com/paper/2106.07327/) (2021)
- [The role of entanglement for enhancing the efficiency of quantum kernels towards classification](https://mlsanity.com/paper/2209.05142/) (2022)
- [Unravelling physics beyond the standard model with classical and quantum anomaly detection](https://mlsanity.com/paper/2301.10787/) (2023)
- [Quantum Gaussian Process Regression for Bayesian Optimization](https://mlsanity.com/paper/2304.12923/) (2023)
- [A kernel-based quantum random forest for improved classification](https://mlsanity.com/paper/2210.02355/) (2022)
- [Quantum Vision Transformers for Quark-Gluon Classification](https://mlsanity.com/paper/2405.10284/) (2024)
- [quantum Case-Based Reasoning (qCBR)](https://mlsanity.com/paper/2104.00409/) (2021)
- [AutoQML: Automatic Generation and Training of Robust Quantum-Inspired Classifiers by Using Genetic Algorithms on Grayscale Images](https://mlsanity.com/paper/2208.13246/) (2022)
- [Facial Expression Recognition on a Quantum Computer](https://mlsanity.com/paper/2102.04823/) (2021)
- [Efficient Quantum Feature Extraction for CNN-based Learning](https://mlsanity.com/paper/2201.01246/) (2022)
- [Review of Ansatz Designing Techniques for Variational Quantum Algorithms](https://mlsanity.com/paper/2212.04913/) (2022)
- [Multi-Armed Bandits and Quantum Channel Oracles](https://mlsanity.com/paper/2301.08544/) (2023)
- [KACQ-DCNN: Uncertainty-Aware Interpretable Kolmogorov-Arnold Classical-Quantum Dual-Channel Neural Network for Heart Disease Detection](https://mlsanity.com/paper/2410.07446/) (2024)
- [Evaluating the Potential of Quantum Machine Learning in Cybersecurity: A Case-Study on PCA-based Intrusion Detection Systems](https://mlsanity.com/paper/2502.11173/) (2025)
- [Quantum continual learning of quantum data realizing knowledge backward transfer](https://mlsanity.com/paper/2203.14032/) (2022)
- [Early-stage detection of cognitive impairment by hybrid quantum-classical algorithm using resting-state functional MRI time-series](https://mlsanity.com/paper/2405.01554/) (2024)
- [Verifiable cloud-based variational quantum algorithms](https://mlsanity.com/paper/2408.13713/) (2024)
- [Q2SAR: A Quantum Multiple Kernel Learning Approach for Drug Discovery](https://mlsanity.com/paper/2506.14920/) (2025)
- [Quantum Semi-Supervised Kernel Learning](https://mlsanity.com/paper/2204.10700/) (2022)
- [High-rate discretely-modulated continuous-variable quantum key distribution using quantum machine learning](https://mlsanity.com/paper/2308.03283/) (2023)
- [Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan engines](https://mlsanity.com/paper/2504.20823/) (2025)
- [Stochastic Entanglement Configuration for Constructive Entanglement Topologies in Quantum Machine Learning with Application to Cardiac MRI](https://mlsanity.com/paper/2507.11401/) (2025)

## Abstract (arXiv)

Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases when classical sampling algorithms require polynomial time, an exponential speed-up is obtained. At the core of this quantum big data algorithm is a non-sparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.