Quantum advantage without exponential concentration: Trainable kernels for symmetry-structured data
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912591354265600 |
|---|---|
| author | Henderson, Laura J. Beer, Kerstin Karuvade, Salini Gupta, Riddhi White, Angela Shrapnel, Sally |
| author_facet | Henderson, Laura J. Beer, Kerstin Karuvade, Salini Gupta, Riddhi White, Angela Shrapnel, Sally |
| contents | Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We analytically prove that covariant quantum kernels tailored to datasets with group symmetries avoid exponential concentration, ensuring stable variance and guaranteed trainability independent of system size. Our results extend beyond prior two-coset constructions to arbitrary coset families, broadening the scope of problems where quantum kernels can achieve advantage. We further derive explicit bounds under coherent noise models - including unitary errors in fiducial state preparation, imperfect unitary representations, and perturbations in group element selection - and show through numerical simulations that the kernel variance remains finite and robust, even under substantial noise. These findings establish a family of quantum learning models that are simultaneously trainable, resilient to coherent noise, and linked to classically hard problems, positioning group-symmetric quantum kernels as a promising foundation for near-term and scalable quantum machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum advantage without exponential concentration: Trainable kernels for symmetry-structured data Henderson, Laura J. Beer, Kerstin Karuvade, Salini Gupta, Riddhi White, Angela Shrapnel, Sally Quantum Physics Data Analysis, Statistics and Probability Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We analytically prove that covariant quantum kernels tailored to datasets with group symmetries avoid exponential concentration, ensuring stable variance and guaranteed trainability independent of system size. Our results extend beyond prior two-coset constructions to arbitrary coset families, broadening the scope of problems where quantum kernels can achieve advantage. We further derive explicit bounds under coherent noise models - including unitary errors in fiducial state preparation, imperfect unitary representations, and perturbations in group element selection - and show through numerical simulations that the kernel variance remains finite and robust, even under substantial noise. These findings establish a family of quantum learning models that are simultaneously trainable, resilient to coherent noise, and linked to classically hard problems, positioning group-symmetric quantum kernels as a promising foundation for near-term and scalable quantum machine learning. |
| title | Quantum advantage without exponential concentration: Trainable kernels for symmetry-structured data |
| topic | Quantum Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2509.14337 |