# Hybrid Genetic Optimisation for Quantum Feature Map Design

arXiv: https://arxiv.org/abs/2302.02980 · HTML: https://mlsanity.com/paper/2302.02980/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2023.

## Built on by (most cited first, 8 of 8)

- [Neural auto-designer for enhanced quantum kernels](https://mlsanity.com/paper/2401.11098/) (2024)
- [Quantum autoencoders for image classification](https://mlsanity.com/paper/2502.15254/) (2025)
- [QuProFS: An Evolutionary Training-free Approach to Efficient Quantum Feature Map Search](https://mlsanity.com/paper/2508.07104/) (2025)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)
- [Generative Quantum Data Embeddings for Supervised Learning](https://mlsanity.com/paper/2605.30866/) (2026)
- [A Multiclass Quantum Aligned Centroid Kernel](https://mlsanity.com/paper/2607.19782/) (2026)
- [When Similarity Is Interaction-Driven: Quantum Kernels for Regime-Sensitive Learning](https://mlsanity.com/paper/2608.24631/) (2026)
- [Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations](https://mlsanity.com/paper/2608.27626/) (2026)

## Abstract (arXiv)

Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and doesn't require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20% larger) that improve further with circuit parameter training.