# Local Binary and Multiclass SVMs Trained on a Quantum Annealer

arXiv: https://arxiv.org/abs/2403.08584 · HTML: https://mlsanity.com/paper/2403.08584/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 13 Mar 2024.

## Builds on (most cited first, 4 of 4)

- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [Optimal Learning Rates for Localized SVMs](https://mlsanity.com/paper/1507.06615/) (2015)
- [Penalty Weights in QUBO Formulations: Permutation Problems](https://mlsanity.com/paper/2206.11040/) (2022)
- [A Single-Step Multiclass SVM based on Quantum Annealing for Remote Sensing Data Classification](https://mlsanity.com/paper/2303.11705/) (2023)

## Built on by (most cited first, 2 of 2)

- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Multitask Learning for Earth Observation Data Classification with Hybrid Quantum Network](https://mlsanity.com/paper/2601.22195/) (2026)

## Abstract (arXiv)

Support vector machines (SVMs) are widely used machine learning models (e.g., in remote sensing), with formulations for both classification and regression tasks. In the last years, with the advent of working quantum annealers, hybrid SVM models characterised by quantum training and classical execution have been introduced. These models have demonstrated comparable performance to their classical counterparts. However, they are limited in the training set size due to the restricted connectivity of the current quantum annealers. Hence, to take advantage of large datasets (like those related to Earth observation), a strategy is required. In the classical domain, local SVMs, namely, SVMs trained on the data samples selected by a k-nearest neighbors model, have already proven successful. Here, the local application of quantum-trained SVM models is proposed and empirically assessed. In particular, this approach allows overcoming the constraints on the training set size of the quantum-trained models while enhancing their performance. In practice, the FaLK-SVM method, designed for efficient local SVMs, has been combined with quantum-trained SVM models for binary and multiclass classification. In addition, for comparison, FaLK-SVM has been interfaced for the first time with a classical single-step multiclass SVM model (CS SVM). Concerning the empirical evaluation, D-Wave's quantum annealers and real-world datasets taken from the remote sensing domain have been employed. The results have shown the effectiveness and scalability of the proposed approach, but also its practical applicability in a real-world large-scale scenario.