# Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data

arXiv: https://arxiv.org/abs/2409.14089 · HTML: https://mlsanity.com/paper/2409.14089/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 58 references that are in the map.
- First posted on arXiv 21 Sep 2024.

## Builds on (most cited first, 18 of 18)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [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)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [On the expressivity of embedding quantum kernels](https://mlsanity.com/paper/2309.14419/) (2023)
- [Quantum kernels for real-world predictions based on electronic health records](https://mlsanity.com/paper/2112.06211/) (2021)
- [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)
- [Numerical evidence against advantage with quantum fidelity kernels on classical data](https://mlsanity.com/paper/2211.16551/) (2022)
- [Automatic and effective discovery of quantum kernels](https://mlsanity.com/paper/2209.11144/) (2022)

## Built on by (most cited first, 1 of 1)

- [Quantum Machine Unlearning: Foundations, Mechanisms, and Taxonomy](https://mlsanity.com/paper/2511.00406/) (2025)

## Abstract (arXiv)

Quantum Machine Learning (QML) is considered one of the most promising applications of Quantum Computing in the Noisy Intermediate Scale Quantum (NISQ) era for the impact it is thought to have in the near future. Although promising theoretical assumptions, the exploration of how QML could foster new discoveries in Medicine and Biology fields is still in its infancy with few examples. In this study, we aimed to assess whether Quantum Kernels (QK) could effectively classify subtypes of Breast Cancer (BC) patients on the basis of molecular characteristics. We performed an heuristic exploration of encoding configurations with different entanglement levels to determine a trade-off between kernel expressivity and performances. Our results show that QKs yield comparable clustering results with classical methods while using fewer data points, and are able to fit the data with a higher number of clusters. Additionally, we conducted the experiments on the Quantum Processing Unit (QPU) to evaluate the effect of noise on the outcome. We found that less expressive encodings showed a higher resilience to noise, indicating that the computational pipeline can be reliably implemented on the NISQ devices. Our findings suggest that QK methods show promises for application in Precision Oncology, especially in scenarios where the dataset is limited in size and a granular non-trivial stratification of complex molecular data cannot be achieved classically.