# Automatic and effective discovery of quantum kernels

arXiv: https://arxiv.org/abs/2209.11144 · HTML: https://mlsanity.com/paper/2209.11144/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 22 Sep 2022.

## Builds on (most cited first, 19 of 19)

- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [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)
- [Hierarchical Representations for Efficient Architecture Search](https://mlsanity.com/paper/1711.00436/) (2017)
- [BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search](https://mlsanity.com/paper/1910.11858/) (2019)
- [Spectral Bias and Task-Model Alignment Explain Generalization in Kernel Regression and Infinitely Wide Neural Networks](https://mlsanity.com/paper/2006.13198/) (2020)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [On scientific understanding with artificial intelligence](https://mlsanity.com/paper/2204.01467/) (2022)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Automatic design of quantum feature maps](https://mlsanity.com/paper/2105.12626/) (2021)
- [Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines](https://mlsanity.com/paper/2207.05865/) (2022)
- [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)

## Built on by (most cited first, 10 of 10)

- [Reinforcement learning-based architecture search for quantum machine learning](https://mlsanity.com/paper/2406.02717/) (2024)
- [Quantum Kernel Learning for Small Dataset Modeling in Semiconductor Fabrication: Application to Ohmic Contact](https://mlsanity.com/paper/2409.10803/) (2024)
- [Learning Reduced Representations for Quantum Classifiers](https://mlsanity.com/paper/2512.01509/) (2025)
- [Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data](https://mlsanity.com/paper/2409.14089/) (2024)
- [Position: Quantum Kernel Machines Should Move Beyond Scalar-Valued Kernels to Realize Their Potential](https://mlsanity.com/paper/2506.03779/) (2025)
- [Embedding-Aware Quantum-Classical SVMs for Scalable Quantum Machine Learning](https://mlsanity.com/paper/2508.00024/) (2025)
- [Integrated Encoding and Quantization to Enhance Quanvolutional Neural Networks](https://mlsanity.com/paper/2410.05777/) (2024)
- [AutoQML: A Framework for Automated Quantum Machine Learning](https://mlsanity.com/paper/2502.21025/) (2025)
- [Generative Quantum Data Embeddings for Supervised Learning](https://mlsanity.com/paper/2605.30866/) (2026)
- [Statevector-to-Hardware Reconstruction of a Four-Qubit ZZ Quantum Kernel: A Single-Backend Case Study of Three Execution Jobs](https://mlsanity.com/paper/2607.20377/) (2026)

## Abstract (arXiv)

Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not efficiently computable on classical devices. However, there is no straightforward method to engineer the optimal quantum kernel for each specific use case. We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML, to automatically find an optimal kernel in a heuristic manner. To this purpose we define an algorithm for constructing a quantum circuit implementing the similarity measure as a combinatorial object, which is evaluated based on a cost function and then iteratively modified using a meta-heuristic optimization technique. The cost function can encode many criteria ensuring favorable statistical properties of the candidate solution, such as the rank of the Dynamical Lie Algebra. Importantly, our approach is independent of the optimization technique employed. The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach, showing the potential of our technique to deliver superior results with reduced effort.