Learning quantum many-body data locally: A provably scalable framework
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_ | 1866912590202929152 |
|---|---|
| author | Chinzei, Koki Tran, Quoc Hoan Matsumoto, Norifumi Endo, Yasuhiro Oshima, Hirotaka |
| author_facet | Chinzei, Koki Tran, Quoc Hoan Matsumoto, Norifumi Endo, Yasuhiro Oshima, Hirotaka |
| contents | Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments. This approach can efficiently solve certain quantum problems that are classically intractable, suggesting potential advantages of harnessing quantum data. However, addressing large-scale problems still requires significant amounts of data beyond the limited computational resources of near-term quantum devices. We propose a scalable ML framework called Geometrically Local Quantum Kernel (GLQK), designed to efficiently learn quantum many-body experimental data by leveraging the exponential decay of correlations, a phenomenon prevalent in noncritical systems. In the task of learning an unknown polynomial of quantum expectation values, we rigorously prove that GLQK substantially improves polynomial sample complexity in the number of qubits $n$, compared to the existing shadow kernel, by constructing a feature space from local quantum information at the correlation length scale. This improvement is particularly notable when each term of the target polynomial involves few local subsystems. Remarkably, for translationally symmetric data, GLQK achieves constant sample complexity, independent of $n$. We numerically demonstrate its high scalability in two learning tasks on quantum many-body phenomena. These results establish new avenues for utilizing experimental data to advance the understanding of quantum many-body physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13705 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning quantum many-body data locally: A provably scalable framework Chinzei, Koki Tran, Quoc Hoan Matsumoto, Norifumi Endo, Yasuhiro Oshima, Hirotaka Quantum Physics Statistical Mechanics Machine Learning Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments. This approach can efficiently solve certain quantum problems that are classically intractable, suggesting potential advantages of harnessing quantum data. However, addressing large-scale problems still requires significant amounts of data beyond the limited computational resources of near-term quantum devices. We propose a scalable ML framework called Geometrically Local Quantum Kernel (GLQK), designed to efficiently learn quantum many-body experimental data by leveraging the exponential decay of correlations, a phenomenon prevalent in noncritical systems. In the task of learning an unknown polynomial of quantum expectation values, we rigorously prove that GLQK substantially improves polynomial sample complexity in the number of qubits $n$, compared to the existing shadow kernel, by constructing a feature space from local quantum information at the correlation length scale. This improvement is particularly notable when each term of the target polynomial involves few local subsystems. Remarkably, for translationally symmetric data, GLQK achieves constant sample complexity, independent of $n$. We numerically demonstrate its high scalability in two learning tasks on quantum many-body phenomena. These results establish new avenues for utilizing experimental data to advance the understanding of quantum many-body physics. |
| title | Learning quantum many-body data locally: A provably scalable framework |
| topic | Quantum Physics Statistical Mechanics Machine Learning |
| url | https://arxiv.org/abs/2509.13705 |