# Quantum Kernel Methods: Convergence Theory, Separation Bounds and Applications to Marketing Analytics

arXiv: https://arxiv.org/abs/2510.11744 · HTML: https://mlsanity.com/paper/2510.11744/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 11 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Quantum Kernel Methods under Scrutiny: A Benchmarking Study](https://mlsanity.com/paper/2409.04406/) (2024)
- [Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training](https://mlsanity.com/paper/2401.02879/) (2024)

## Abstract (arXiv)

This work studies the feasibility of applying quantum kernel methods to a real consumer classification task in the NISQ regime. We present a hybrid pipeline that combines a quantum-kernel Support Vector Machine (Q-SVM) with a quantum feature extraction module (QFE), and benchmark it against classical and quantum baselines in simulation and with limited shallow-depth hardware runs. With fixed hyperparameters, the proposed Q-SVM attains 0.7790 accuracy, 0.7647 precision, 0.8609 recall, 0.8100 F1, and 0.83 ROC AUC, exhibiting higher sensitivity while maintaining competitive precision relative to classical SVM. We interpret these results as an initial indicator and a concrete starting point for NISQ-era workflows and hardware integration, rather than a definitive benchmark. Methodologically, our design aligns with recent work that formalizes quantum-classical separations and verifies resources via XEB-style approaches, motivating shallow yet expressive quantum embeddings to achieve robust separability despite hardware noise constraints.