# Several fitness functions and entanglement gates in quantum kernel generation

arXiv: https://arxiv.org/abs/2309.03307 · HTML: https://mlsanity.com/paper/2309.03307/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 83 references that are in the map.
- First posted on arXiv 22 Aug 2023.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [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)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [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)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [How Complex is your classification problem? A survey on measuring classification complexity](https://mlsanity.com/paper/1808.03591/) (2018)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Automatic design of quantum feature maps](https://mlsanity.com/paper/2105.12626/) (2021)
- [Reproducibility in Machine Learning for Health](https://mlsanity.com/paper/1907.01463/) (2019)
- [Quantum autoencoders via quantum adders with genetic algorithms](https://mlsanity.com/paper/1709.07409/) (2017)
- [Mixed Quantum-Classical Method For Fraud Detection with Quantum Feature Selection](https://mlsanity.com/paper/2208.07963/) (2022)
- [Practical application improvement to Quantum SVM: theory to practice](https://mlsanity.com/paper/2012.07725/) (2020)
- [Quantum Advantage Seeker with Kernels (QuASK): a software framework to speed up the research in quantum machine learning](https://mlsanity.com/paper/2206.15284/) (2022)
- [A Novel Intrinsic Measure of Data Separability](https://mlsanity.com/paper/2109.05180/) (2021)
- [Quantum Embedding Search for Quantum Machine Learning](https://mlsanity.com/paper/2105.11853/) (2021)
- [Study of Feature Importance for Quantum Machine Learning Models](https://mlsanity.com/paper/2202.11204/) (2022)

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

- [A novel feature selection method based on quantum support vector machine](https://mlsanity.com/paper/2311.17646/) (2023)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)

## Abstract (arXiv)

Quantum machine learning (QML) represents a promising frontier in the quantum technologies. In this pursuit of quantum advantage, the quantum kernel method for support vector machine has emerged as a powerful approach. Entanglement, a fundamental concept in quantum mechanics, assumes a central role in quantum computing. In this paper, we investigate the optimal number of entanglement gates in the quantum kernel feature maps by a multi-objective genetic algorithm. We distinct the fitness functions of genetic algorithm for non-local gates for entanglement and local gates to gain insights into the benefits of employing entanglement gates. Our experiments reveal that the optimal configuration of quantum circuits for the quantum kernel method incorporates a proportional number of non-local gates for entanglement. The result complements the prior literature on quantum kernel generation where non-local gates were largely suppressed. Furthermore, we demonstrate that the separability indexes of data can be leveraged to estimate the number of non-local gates required for the quantum support vector machine's feature maps. This insight can be helpful in selecting appropriate parameters, such as the entanglement parameter, in various quantum programming packages like https://qiskit.org/ based on data analysis. Our findings offer valuable guidance for enhancing the efficiency and accuracy of quantum machine learning algorithms.