# Probabilistic Quantum SVM Training on Ising Machine

arXiv: https://arxiv.org/abs/2503.16363 · HTML: https://mlsanity.com/paper/2503.16363/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 36 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 11 of 11)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [SE(3) Equivariant Augmented Coupling Flows](https://mlsanity.com/paper/2308.10364/) (2023)
- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [QUBO Formulations for Training Machine Learning Models](https://mlsanity.com/paper/2008.02369/) (2020)
- [The Boltzmann Policy Distribution: Accounting for Systematic Suboptimality in Human Models](https://mlsanity.com/paper/2204.10759/) (2022)
- [Training an Ising Machine with Equilibrium Propagation](https://mlsanity.com/paper/2305.18321/) (2023)
- [Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines](https://mlsanity.com/paper/2207.05865/) (2022)
- [Training Deep Boltzmann Networks with Sparse Ising Machines](https://mlsanity.com/paper/2303.10728/) (2023)
- [The complexity of quantum support vector machines](https://mlsanity.com/paper/2203.00031/) (2022)
- [Cluster and Aggregate: Face Recognition with Large Probe Set](https://mlsanity.com/paper/2210.10864/) (2022)
- [Von Mises Mixture Distributions for Molecular Conformation Generation](https://mlsanity.com/paper/2306.07472/) (2023)

## Built on by (most cited first, 1 of 1)

- [Q-Detection: A Quantum-Classical Hybrid Poisoning Attack Detection Method](https://mlsanity.com/paper/2507.06262/) (2025)

## Abstract (arXiv)

Quantum computing holds significant potential to accelerate machine learning algorithms, especially in solving optimization problems like those encountered in Support Vector Machine (SVM) training. However, current QUBO-based Quantum SVM (QSVM) methods rely solely on binary optimal solutions, limiting their ability to identify fuzzy boundaries in data. Additionally, the limited qubit count in contemporary quantum devices constrains training on larger datasets. In this paper, we propose a probabilistic quantum SVM training framework suitable for Coherent Ising Machines (CIMs). By formulating the SVM training problem as a QUBO model, we leverage CIMs' energy minimization capabilities and introduce a Boltzmann distribution-based probabilistic approach to better approximate optimal SVM solutions, enhancing robustness. To address qubit limitations, we employ batch processing and multi-batch ensemble strategies, enabling small-scale quantum devices to train SVMs on larger datasets and support multi-class classification tasks via a one-vs-one approach. Our method is validated through simulations and real-machine experiments on binary and multi-class datasets. On the banknote binary classification dataset, our CIM-based QSVM, utilizing an energy-based probabilistic approach, achieved up to 20% higher accuracy compared to the original QSVM, while training up to 104 times faster than simulated annealing methods. Compared with classical SVM, our approach either matched or reduced training time. On the IRIS three-class dataset, our improved QSVM outperformed existing QSVM models in all key metrics. As quantum technology advances, increased qubit counts are expected to further enhance QSVM performance relative to classical SVM.