# Provably scalable learning from quantum many-body data via locality

arXiv: https://arxiv.org/abs/2509.13705 · HTML: https://mlsanity.com/paper/2509.13705/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 65 references that are in the map.
- First posted on arXiv 17 Sep 2025.

## Builds on (most cited first, 17 of 17)

- [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)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data](https://mlsanity.com/paper/2306.07331/) (2023)
- [Predicting Properties of Quantum Systems with Conditional Generative Models](https://mlsanity.com/paper/2211.16943/) (2022)
- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)
- [Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networks](https://mlsanity.com/paper/2406.18316/) (2024)
- [Exponentially improved efficient machine learning for quantum many-body states with provable guarantees](https://mlsanity.com/paper/2304.04353/) (2023)
- [Learning quantum properties from short-range correlations using multi-task networks](https://mlsanity.com/paper/2310.11807/) (2023)
- [Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithms](https://mlsanity.com/paper/2405.18489/) (2024)

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

- [Learning Quantum Data Distribution via Chaotic Quantum Diffusion Model](https://mlsanity.com/paper/2602.22061/) (2026)

## Abstract (arXiv)

Machine learning (ML) holds great promise for extracting insights from complex quantum many-body data obtained in quantum experiments, potentially solving certain classically intractable problems. However, addressing large-scale problems still requires significant amounts of data that exceed the capabilities of near-term quantum devices. We propose a scalable ML framework, the Geometrically Local Quantum Kernel (GLQK), that efficiently learns from quantum many-body data by leveraging the exponential decay of correlations prevalent in noncritical systems. For learning an unknown polynomial of quantum expectation values, we rigorously prove that the GLQK substantially improves the sample complexity in the system size n over 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, the GLQK achieves constant sample complexity, independent of n. Numerical experiments on two quantum many-body tasks corroborate these theoretical results, demonstrating the high scalability of the GLQK. Beyond the polynomial setting, we further show that it can efficiently learn certain non-polynomial functions. Our framework establishes new avenues for utilizing experimental data to advance the understanding of quantum many-body physics.