# Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data

arXiv: https://arxiv.org/abs/2412.07915 · HTML: https://mlsanity.com/paper/2412.07915/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 10 of 10)

- [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)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Robust Subspace Clustering via Thresholding](https://mlsanity.com/paper/1307.4891/) (2013)
- [Quantum kernels for real-world predictions based on electronic health records](https://mlsanity.com/paper/2112.06211/) (2021)
- [Numerical evidence against advantage with quantum fidelity kernels on classical data](https://mlsanity.com/paper/2211.16551/) (2022)
- [Subspace Clustering via Thresholding and Spectral Clustering](https://mlsanity.com/paper/1303.3716/) (2013)
- [Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap](https://mlsanity.com/paper/2205.13527/) (2022)
- [A Machine Learning Approach to Boost the Vehicle-2-Grid Scheduling](https://mlsanity.com/paper/2407.20802/) (2024)

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

- [Enhancing the Scalability of Classical Surrogates for Real-World Quantum Machine Learning Applications](https://mlsanity.com/paper/2508.06131/) (2025)
- [Shallow-circuit Supervised Learning on a Quantum Processor](https://mlsanity.com/paper/2601.03235/) (2026)
- [Spectral Phase Encoding for Quantum Kernel Methods](https://mlsanity.com/paper/2602.19644/) (2026)
- [Enhancing Quantum Machine Learning with Anyons](https://mlsanity.com/paper/2606.16090/) (2026)
- [A Multiclass Quantum Aligned Centroid Kernel](https://mlsanity.com/paper/2607.19782/) (2026)
- [Fractal dimension predicts quantum kernel collapse in angle-encoded data](https://mlsanity.com/paper/2609.00475/) (2026)
- [A Hybrid Quantum Neural Network to Analyse Big Experimental Powder X-ray Diffraction Data](https://mlsanity.com/paper/2609.22376/) (2026)
- [Quantum Machine Learning Protection of Military Quantum Key Distribution Against Cryptographically Camouflaged Attacks](https://mlsanity.com/paper/2610.04543/) (2026)

## Abstract (arXiv)

Fidelity quantum kernels have shown promise in classification tasks, particularly when a group structure in the data can be identified and exploited through a covariant feature map. In fact, there exist classification problems on which covariant kernels provide a provable advantage, thus establishing a separation between quantum and classical learners. However, their practical application poses two challenges: on one side, the group structure may be unknown and approximate in real-world data, and on the other side, scaling to the `utility' regime (above 100 qubits) is affected by exponential concentration. In this work, we address said challenges by applying fidelity kernels to real-world data with unknown structure, related to the scheduling of a fleet of electric vehicles, and to synthetic data generated from the union of subspaces, which is then close to many relevant real-world datasets. Furthermore, we propose a novel error mitigation strategy specifically tailored for fidelity kernels, called Bit Flip Tolerance (BFT), to alleviate the exponential concentration in our utility-scale experiments. Our multiclass classification reaches accuracies comparable to classical SVCs up to 156 qubits, thus constituting the largest experimental demonstration of quantum machine learning on IBM devices to date. For the real-world data experiments, the effect of the proposed BFT becomes manifest on 40+ qubits, where mitigated accuracies reach 80%, in line with classical, compared to 33% without BFT. Through the union-of-subspace synthetic dataset with 156 qubits, we demonstrate a mitigated accuracy of 80%, compared to 83% of classical models, and 37% of unmitigated quantum, using a test set of limited size.