# Compositional optimization of quantum circuits for quantum kernels of support vector machines

arXiv: https://arxiv.org/abs/2203.13848 · HTML: https://mlsanity.com/paper/2203.13848/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 64 references that are in the map.
- First posted on arXiv 25 Mar 2022.

## Builds on (most cited first, 16 of 16)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (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)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Structure Discovery in Nonparametric Regression through Compositional Kernel Search](https://mlsanity.com/paper/1302.4922/) (2013)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Quantum machine learning of large datasets using randomized measurements](https://mlsanity.com/paper/2108.01039/) (2021)
- [Automatic design of quantum feature maps](https://mlsanity.com/paper/2105.12626/) (2021)
- [QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks](https://mlsanity.com/paper/2110.03861/) (2021)
- [Hybrid quantum-classical classifier based on tensor network and variational quantum circuit](https://mlsanity.com/paper/2011.14651/) (2020)
- [Introduction to Quantum Reinforcement Learning: Theory and PennyLane-based Implementation](https://mlsanity.com/paper/2108.06849/) (2021)
- [Experimental kernel-based quantum machine learning in finite feature space](https://mlsanity.com/paper/1906.04137/) (2019)
- [Practical application improvement to Quantum SVM: theory to practice](https://mlsanity.com/paper/2012.07725/) (2020)

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

- [A Survey on Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead](https://mlsanity.com/paper/2310.10315/) (2023)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Neural auto-designer for enhanced quantum kernels](https://mlsanity.com/paper/2401.11098/) (2024)
- [The Impact of Feature Embedding Placement in the Ansatz of a Quantum Kernel in QSVMs](https://mlsanity.com/paper/2409.13147/) (2024)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)
- [Quantum Enhanced Anomaly Detection for ADS-B Data using Hybrid Deep Learning](https://mlsanity.com/paper/2509.15991/) (2025)

## Abstract (arXiv)

While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a Bayesian algorithm for constructing quantum kernels for support vector machines that adapts quantum gate sequences to data. The algorithm increases the complexity of quantum circuits incrementally by appending quantum gates selected with Bayesian information criterion as circuit selection metric and Bayesian optimization of the parameters of the locally optimal quantum circuits identified. The goal is to build quantum kernels for SVM that can solve classification problems with as little training data as possible. The performance of the resulting quantum models for the classification problems considered here significantly exceeds that of optimized classical models with conventional kernels.