# Semisupervised Anomaly Detection using Support Vector Regression with Quantum Kernel

arXiv: https://arxiv.org/abs/2308.00583 · HTML: https://mlsanity.com/paper/2308.00583/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 1 Aug 2023.

## Builds on (most cited first, 14 of 14)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Quantum anomaly detection in the latent space of proton collision events at the LHC](https://mlsanity.com/paper/2301.10780/) (2023)
- [Enhancing Unsupervised Anomaly Detection with Score-Guided Network](https://mlsanity.com/paper/2109.04684/) (2021)
- [Double-Adversarial Activation Anomaly Detection: Adversarial Autoencoders are Anomaly Generators](https://mlsanity.com/paper/2101.04645/) (2021)
- [Quantum Machine Learning with HQC Architectures using non-Classically Simulable Feature Maps](https://mlsanity.com/paper/2103.11381/) (2021)
- [R2-AD2: Detecting Anomalies by Analysing the Raw Gradient](https://mlsanity.com/paper/2206.10259/) (2022)

## Built on by (most cited first, 6 of 6)

- [Anomaly Detection for Real-World Cyber-Physical Security using Quantum Hybrid Support Vector Machines](https://mlsanity.com/paper/2409.04935/) (2024)
- [The role of data embedding in quantum autoencoders for improved anomaly detection](https://mlsanity.com/paper/2409.04519/) (2024)
- [Quantum Autoencoder for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2504.17548/) (2025)
- [Quantum Autoencoders for Anomaly Detection in Cybersecurity](https://mlsanity.com/paper/2510.21837/) (2025)
- [Quantum Support Vector Regression for Robust Anomaly Detection](https://mlsanity.com/paper/2505.01012/) (2025)
- [Quantum-Hybrid Support Vector Machines for Anomaly Detection in Industrial Control Systems](https://mlsanity.com/paper/2506.17824/) (2025)

## Abstract (arXiv)

Anomaly detection (AD) involves identifying observations or events that deviate in some way from the rest of the data. Machine learning techniques have shown success in automating this process by detecting hidden patterns and deviations in large-scale data. The potential of quantum computing for machine learning has been widely recognized, leading to extensive research efforts to develop suitable quantum machine learning (QML) algorithms. In particular, the search for QML algorithms for near-term NISQ devices is in full swing. However, NISQ devices pose additional challenges due to their limited qubit coherence times, low number of qubits, and high error rates. Kernel methods based on quantum kernel estimation have emerged as a promising approach to QML on NISQ devices, offering theoretical guarantees, versatility, and compatibility with NISQ constraints. Especially support vector machines (SVM) utilizing quantum kernel estimation have shown success in various supervised learning tasks. However, in the context of AD, semisupervised learning is of great relevance, and yet there is limited research published in this area. This paper introduces an approach to semisupervised AD based on the reconstruction loss of a support vector regression (SVR) with quantum kernel. This novel model is an alternative to the variational quantum and quantum kernel one-class classifiers, and is compared to a quantum autoencoder as quantum baseline and a SVR with radial-basis-function (RBF) kernel as well as a classical autoencoder as classical baselines. The models are benchmarked extensively on 10 real-world AD data sets and one toy data set, and it is shown that our SVR model with quantum kernel performs better than the SVR with RBF kernel as well as all other models, achieving highest mean AUC over all data sets. In addition, our QSVR outperforms the quantum autoencoder on 9 out of 11 data sets.